L. V. Abad, Principles of classical statistical mechanics: A perspective from the notion of complementarity, Annals of Physics, vol.327, p.1682, 2012.

E. Abbena, S. Salamon, and A. Gray, Modern Di erential Geometry of Curves and Surfaces with Mathematica, 2006.

B. P. Abbott, GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02059393

R. Abraham, J. E. Marsden, T. Ratiu, and M. , Tensor Analysis, and Applications, 2001.

Y. Achdou, F. J. Buera, J. Lasry, P. Lions, and B. Moll, Partial di erential equation models in macroeconomics, Philosophical Transactions of the Royal Society A, vol.372, p.20130397, 2014.

A. D. Aczel, God's Equation: Einstein, Relativity, and the Expanding Universe (Delta, 2000.

K. Aki, P. G. Richards, and Q. Seismology, , 2009.

M. Alcubierre, Introduction to 3+1 Numerical Relativity, 2012.

M. Alcubierre, G. Allen, B. Brügmann, E. Seidel, and W. Suen, Towards an understanding of the stability properties of the 3+1 evolution equations in general relativity, Physical Review D, vol.62, p.124011, 2000.

P. Amaro-seoane, Laser Interferometer Space Antenna, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02417094

P. Amaro-seoane, The Gravitational Universe, 2013.

P. Amaro-seoane, Relativistic dynamics and extreme mass ratio inspirals, Living Reviews in Relativity, vol.21, p.4, 2018.

P. Amaro-seoane, X-MRIs: Extremely Large Mass-Ratio Inspirals, 2019.

J. L. Anderson and P. G. Bergmann, Constraints in Covariant Field Theories, vol.83, p.1018, 1951.

L. Andersson, T. Bäckdahl, and P. Blue, Geometry of black hole spacetimes, 2016.

S. Aoudia and A. D. Spallicci, Source-free integration method for black hole perturbations and self-force computation: Radial fall, Physical Review D, vol.83, p.64029, 2011.
URL : https://hal.archives-ouvertes.fr/insu-01254554

M. Armano, Beyond the Required LISA Free-Fall Performance: New LISA Path nder Results down to 20 muHz, Physical Review Letters, vol.120, p.61101, 2018.

M. Armano, Sub-Femto-g Free Fall for Space-Based Gravitational Wave Observatories: LISA Path nder Results, Physical Review Letters, vol.116, p.231101, 2016.

V. I. Arnold, Mathematical Methods of Classical Mechanics, trans, 1997.

R. Arnowitt, S. Deser, and C. W. Misner, Dynamical Structure and De nition of Energy in General Relativity, Physical Review, vol.116, p.1322, 1959.

R. Arnowitt, S. Deser, and C. W. Misner, The dynamics of general relativity, Gravitation: An Introduction to Current Research, p.227, 1962.

R. Arnowitt, S. Deser, and C. W. Misner, Republication of: The dynamics of general relativity, General Relativity and Gravitation, vol.40, 1997.

A. Ashtekar, New Hamiltonian formulation of general relativity, Physical Review D, vol.36, p.1587, 1987.

A. Ashtekar, M. Reuter, and C. Rovelli, From General Relativity to Quantum Gravity, General Relativity and Gravitation: A Centennial Perspective, p.553, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01476565

S. Babak, J. Gair, A. Sesana, E. Barausse, C. F. Sopuerta et al., Science with the space-based interferometer LISA. V. Extreme mass-ratio inspirals, Physical Review D, vol.95, p.103012, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01554417

J. G. Baker, J. Centrella, D. Choi, M. Koppitz, and J. Van-meter, Gravitational-Wave Extraction from an Inspiraling Con guration of Merging Black Holes, Physical Review Letters, vol.96, p.111102, 2006.

L. Barack and D. A. Golbourn, Scalar-eld perturbations from a particle orbiting a black hole using numerical evolution in 2+1 dimensions, Physical Review D, vol.76, p.44020, 2007.

L. Barack, D. A. Golbourn, and N. Sago, M-mode regularization scheme for the selfforce in Kerr spacetime, Physical Review D, vol.76, p.124036, 2007.

L. Barack and C. O. Lousto, Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation, Physical Review D, vol.72, p.104026, 2005.

L. Barack, Y. Mino, H. Nakano, A. Ori, and M. Sasaki, Calculating the gravitational self force in Schwarzschild spacetime, Physical Review Letters, vol.88, p.91101, 2002.

L. Barack and A. Ori, Mode sum regularization approach for the self force in black hole spacetime, Physical Review D, vol.61, p.61502, 2000.

L. Barack and A. Ori, Regularization parameters for the self force in Schwarzschild spacetime. I: Scalar case, Physical Review D, vol.66, p.84022, 2002.

L. Barack, A. Ori, and N. Sago, Frequency-domain calculation of the self force: The High-frequency problem and its resolution, Physical Review D, vol.78, p.84021, 2008.

L. Barack and A. Pound, Self-force and radiation reaction in general relativity, Reports on Progress in Physics, vol.82, p.16904, 2018.

J. F. Barbero and G. , Real Ashtekar variables for Lorentzian signature space-times, Physical Review D, vol.51, p.5507, 1995.

J. Barbour, Shape Dynamics. An Introduction, Quantum Field Theory and Gravity: Conceptual and Mathematical Advances in the Search for a Uni ed Framework, p.257, 2012.

J. Barbour, T. Koslowski, and F. Mercati, A Gravitational Origin of the Arrows of Time, 2013.

J. Barbour, T. Koslowski, and F. Mercati, Identi cation of a Gravitational Arrow of Time, Physical Review Letters, vol.113, p.181101, 2014.

J. M. Bardeen, Gauge-invariant cosmological perturbations, Physical Review D, vol.22, p.1882, 1980.

A. O. Barut, Electrodynamics and Classical Theory of Fields and Particles, 1980.

T. W. Baumgarte and S. L. Shapiro, Numerical integration of Einstein's eld equations, Physical Review D, vol.59, p.24007, 1998.

T. W. Baumgarte and S. L. Shapiro, Numerical Relativity: Solving Einstein's Equations on the Computer, 2010.

J. D. Bekenstein, Black Holes and Entropy, Physical Review D, vol.7, p.2333, 1973.

J. S. Bell, How to Teach Special Relativity, Progress in Scienti c Culture, vol.1, p.1, 1976.

V. Benci, Ultrafunctions and Generalized Solutions, Advanced Nonlinear Studies, vol.13, p.461, 2013.

A. Bernstein, A. Chertock, and A. Kurganov, Central-upwind scheme for shallow water equations with discontinuous bottom topography, Bulletin of the Brazilian Mathematical Society, vol.47, p.91, 2016.

C. P. Berry, S. A. Hughes, C. F. Sopuerta, A. J. Chua, A. He-ernan et al., The unique potential of extreme mass-ratio inspirals for gravitational-wave astronomy, 2019.

L. Blanchet, A. Spallicci, and B. Whiting, Mass and Motion in General Relativity, Fundamental Theories of Physics, vol.162, 2011.

M. Bojowald, Canonical Gravity and Applications: Cosmology, Black Holes, and Quantum Gravity, 2011.

L. Boltzmann, Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen, Sitzungsberichte der Akademie der Wissenschaften, vol.66, p.275, 1872.

E. Bottazzi, Grid functions of nonstandard analysis in the theory of distributions and in partial di erential equations, Advances in Mathematics, vol.345, p.429, 2019.

J. P. Boyd, Chebyshev and Fourier Spectral Methods, 2001.

R. H. Brandenberger, Lectures on the Theory of Cosmological Perturbations, The Early Universe and Observational Cosmology, p.127, 2004.

H. R. Brown, W. Myrvold, and J. Nk, Boltzmann's H-theorem, its discontents, and the birth of statistical mechanics, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, vol.40, p.174, 2009.

J. D. Brown, S. R. Lau, and J. W. York, Action and Energy of the Gravitational Field, Annals of Physics, vol.297, p.175, 2002.

J. D. Brown and J. W. York, Quasilocal energy and conserved charges derived from the gravitational action, Physical Review D, vol.47, p.1407, 1993.

M. Bruni, S. Matarrese, S. Mollerach, and S. Sonego, Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond, Classical and Quantum Gravity, vol.14, p.2585, 1997.

M. Burger, L. Ca-arelli, P. A. Markowich, and M. Wolfram, On a Boltzmann-type price formation model, Proceedings of the Royal Society A, vol.469, p.20130126, 2013.

M. J. Cáceres, J. A. Carrillo, and B. Perthame, Analysis of nonlinear noisy integrate & re neuron models: blow-up and steady states, The Journal of Mathematical Neuroscience, vol.1, p.7, 2011.

M. J. Cáceres and R. Schneider, Blow-up, steady states and long time behaviour of excitatory-inhibitory nonlinear neuron models, Kinetic and Related Models, vol.10, p.587, 2016.

L. A. Ca-arelli, P. A. Markowich, and J. Pietschmann, On a price formation free boundary model by Lasry and Lions, Comptes Rendus Mathematique, vol.349, p.621, 2011.

M. Campanelli, C. O. Lousto, P. Marronetti, and Y. Zlochower, Accurate Evolutions of Orbiting Black-Hole Binaries without Excision, Physical Review Letters, vol.96, p.111101, 2006.

P. Canizares, Extreme-Mass-Ratio Inspirals, 2011.

P. Canizares and C. F. Sopuerta, E cient pseudospectral method for the computation of the self-force on a charged particle: Circular geodesics around a Schwarzschild black hole, Physical Review D, vol.79, p.84020, 2009.

P. Canizares and C. F. Sopuerta, Overcoming the Gauge Problem for the Gravitational Self-Force, 2014.

P. Canizares and C. F. Sopuerta, Simulations of Extreme-Mass-Ratio Inspirals Using Pseudospectral Methods, Journal of Physics: Conference Series, vol.154, p.12053, 2009.

P. Canizares and C. F. Sopuerta, Time-domain modelling of Extreme-Mass-Ratio Inspirals for the Laser Interferometer Space Antenna, Journal of Physics: Conference Series, vol.314, p.12075, 2011.

P. Canizares and C. F. Sopuerta, Tuning time-domain pseudospectral computations of the self-force on a charged scalar particle, Classical and Quantum Gravity, vol.28, p.134011, 2011.

P. Canizares, C. F. Sopuerta, and J. L. Jaramillo, Pseudospectral collocation methods for the computation of the self-force on a charged particle: Generic orbits around a Schwarzschild black hole, Physical Review D, vol.82, p.44023, 2010.

V. Cardoso, L. Gualtieri, C. Herdeiro, U. Sperhake, P. M. Chesler et al., NR/HEP: roadmap for the future, Classical and Quantum Gravity, vol.29, p.244001, 2012.

S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity, 2003.

S. M. Carroll and G. N. Remmen, What is the Entropy in Entropic Gravity?, Physical Review D, vol.93, p.124052, 2016.

É. Cartan, Les systèmes di érentiels extérieurs et leurs applications géométriques (Hermann et Cie, 1945.

É. Cartan, Sur certaines expressions di érentielles et le problème de Pfa, Annales scienti ques de l'École Normale Supérieure, vol.16, p.239, 1899.

A. R. Casti, A. Omurtag, A. Sornborger, E. Kaplan, B. Knight et al., A population study of integrate-and-re-or-burst neurons, Neural Computation, vol.14, p.957, 2002.

M. Celoria, R. Oliveri, A. Sesana, and M. Mapelli, Lecture notes on black hole binary astrophysics, 2018.

S. Chandrasekhar, Newton's Principia for the Common Reader, 2003.

S. Chandrasekhar, The Mathematical Theory of Black Holes, 1998.

S. Chandrasekhar and S. Detweiler, The quasi-normal modes of the Schwarzschild black hole, Royal Society of London Proceedings Series A, vol.344, p.441, 1975.

Y. Choquet-bruhat, General Relativity and the Einstein Equations, 2009.

Y. Choquet-bruhat and R. Geroch, Global aspects of the Cauchy problem in general relativity, Communications in Mathematical Physics, vol.14, pp.329-335, 1969.

D. Christodoulou and S. Klainerman, The Global Nonlinear Stability of the Minkowski Space, 1993.

D. Codazzi, Sulle coordinate curvilinee d'una super cie dello spazio, Annali di Matematica Pura ed Applicata, vol.2, p.101, 1868.

A. A. Coley, Mathematical General Relativity, 2018.

A. A. Coley, Open problems in mathematical physics, Physica Scripta, vol.92, p.93003, 2017.

J. F. Colombeau, Nonlinear Generalized Functions: their origin, some developments and recent advances, The São Paulo Journal of Mathematical Sciences, vol.7, p.201, 2013.

M. Colpi and A. Sesana, Gravitational Wave Sources in the Era of Multi-Band Gravitational Wave Astronomy, An Overview of Gravitational Waves: Theory, Sources and Detection, p.43, 2016.

G. Constantine and T. Savits, A Multivariate Faa di Bruno Formula with Applications, Transactions of the American Mathematical Society, vol.348, p.503, 1996.

S. F. Cortizo, On Dirac's Delta Calculus, 1995.

J. Corvino and R. M. Schoen, On the Asymptotics for the Vacuum Einstein Constraint Equations, Journal of Di erential Geometry, vol.73, p.185, 2006.

?. Crnkovi?, Symplectic geometry and (super-)Poincaré algebra in geometrical theories, Nuclear Physics B, vol.288, p.419, 1987.

?. Crnkovi? and E. Witten, Covariant description of canonical formalism in geometrical theories, Three Hundred Years of Gravitation, p.676, 1989.

C. T. Cunningham, R. H. Price, and V. Moncrief, Radiation from collapsing relativistic stars. I -Linearized odd-parity radiation, The Astrophysical Journal, vol.224, p.643, 1978.

P. C. Davies, The Physics of Time Asymmetry, 1977.

S. Detweiler and B. F. Whiting, Self-force via a Green's function decomposition, Physical Review D, vol.67, p.24025, 2003.

E. Dewan and M. Beran, Note on Stress E ects due to Relativistic Contraction, American Journal of Physics, vol.27, p.517, 1959.

B. S. Dewitt and R. W. Brehme, Radiation damping in a gravitational eld, Annals of Physics, vol.9, p.220, 1960.

L. M. Diaz-rivera, E. Messaritaki, B. F. Whiting, and S. Detweiler, Scalar eld self-force e ects on orbits about a Schwarzschild black hole, Physical Review D, vol.70, p.124018, 2004.

P. A. Dirac, Classical Theory of Radiating Electrons, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.167, p.148, 1938.

P. A. Dirac, Generalized Hamiltonian dynamics, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol.246, p.326, 1958.

P. A. Dirac, The theory of gravitation in Hamiltonian form, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol.246, p.333, 1958.

R. M. Dreizler and E. Engel, Density Functional Theory, 2011.

J. Droste, Het veld van een enkel centrum in Einstein's theorie der zwaartekracht, en de beweging van een sto elijk punt in dat veld, Koninklijke Akademie van Wetenschappen Amsterdam, vol.25, p.163, 1916.

J. Droste, Het zwaartekrachtsveld van een of meer lichamen volgens de theorie van Einstein, 1916.

M. D. Duez and Y. Zlochower, Numerical relativity of compact binaries in the 21st century, Reports on Progress in Physics, vol.82, p.16902, 2018.

J. Ehlers and R. Geroch, Equation of motion of small bodies in relativity, Annals of Physics, vol.309, p.232, 2004.

A. Einstein, Die Grundlage der allgemeinen Relativitätstheorie, Annalen der Physik, vol.354, p.769, 1916.

A. Einstein, Zur Theorie des statischen Gravitationsfeldes, Annalen der Physik, vol.343, p.443, 1912.

A. Einstein and N. Rosen, The Particle Problem in the General Theory of Relativity, Physical Review, vol.48, p.73, 1935.

A. Einstein, Autobiographical Notes, The Library of Living Philosophers, vol.VII, 1949.

A. Einstein, Die Feldgleichungen der Gravitation, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften, p.844, 1915.

A. Einstein, Four Lectures on the Theory of Relativity, 1921.

A. Einstein, Four Lectures on the Theory of Relativity, The Collected Papers of Albert Einstein, vol.7, 1918.

D. K. Lehner and . Buchwald, , p.261, 2002.

A. Einstein, Geometrie Und Erfahrung (Erweiterte Fassung des Festvortrages Gehalten an der Preussischen Akademie der Wissenschaften, 1921.

A. Einstein, The Field Equations of Gravitation, The Collected Papers of Albert Einstein, vol.6, p.117, 1996.

A. Einstein, The Foundation of the General Theory of Relativity, The Collected Papers of Albert Einstein, vol.6, p.146, 1996.

A. Einstein, The Meaning of Relativity (Routledge, 2003.

A. Einstein, What Is the Theory of Relativity?, in Ideas and Opinions, 1954.

A. Einstein, Zum gegenwärtigen Stande des Gravitationsproblems, Physikalische Zeitschrift, vol.14, p.1249, 1913.

A. Einstein and L. Infeld, The Evolution of Physics, 1938.

A. Einstein, L. Infeld, and B. Ho-mann, The Gravitational Equations and the Problem of Motion, Annals of Mathematics, vol.39, p.65, 1938.

R. J. Epp, R. B. Mann, and P. L. Mcgrath, On the Existence and Utility of Rigid Quasilocal Frames, Classical and Quantum Gravity: Theory, Analysis and Applications, 2012.

R. J. Epp, R. B. Mann, and P. L. Mcgrath, Rigid motion revisited: rigid quasilocal frames, Classical and Quantum Gravity, vol.26, p.35015, 2009.

R. J. Epp, P. L. Mcgrath, and R. B. Mann, Momentum in general relativity: local versus quasilocal conservation laws, Classical and Quantum Gravity, vol.30, p.195019, 2013.

L. C. Evans, , 1998.

B. Felsager, Geometry, Particles, and Fields, 2012.

S. E. Field, J. S. Hesthaven, and S. R. Lau, Discontinuous Galerkin method for computing gravitational waveforms from extreme mass ratio binaries, Classical and Quantum Gravity, vol.26, p.165010, 2009.

Y. Fourès-bruhat, Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires, Acta Mathematica, vol.88, p.141, 1952.

L. Freidel, Gravitational energy, local holography and non-equilibrium thermodynamics, Classical and Quantum Gravity, vol.32, p.55005, 2015.

L. Freidel and Y. Yokokura, Non-equilibrium thermodynamics of gravitational screens, Classical and Quantum Gravity, vol.32, p.215002, 2015.

V. Frolov and I. Novikov, Black Hole Physics: Basic Concepts and New Developments, 1998.

P. Galison, M. Gordin, and D. Kaiser, The Roots of Special Relativity: Science and Society, 2001.

J. Gaset and N. Román-roy, Multisymplectic formulation of Lagrangian models in gravitation, 2019.

J. Gaset and N. Román-roy, Multisymplectic uni ed formalism for Einstein-Hilbert gravity, Journal of Mathematical Physics, vol.59, p.32502, 2018.

C. F. Gauss, Disquisitiones Generales circa Super cies Curvas, Comm. Soc. Reg. Sc. Gott. Rec, vol.6, p.99, 1827.

R. Geroch and P. S. Jang, Motion of a body in general relativity, Journal of Mathematical Physics, vol.16, p.65, 1975.

R. Geroch and J. Traschen, Strings and other distributional sources in general relativity, Physical Review D, vol.36, p.1017, 1987.

G. W. Gibbons and S. W. Hawking, Action integrals and partition functions in quantum gravity, Physical Review D, vol.15, p.2752, 1977.

J. W. Gibbs, Letter to the Editor, Nature, vol.59, p.606, 1899.

D. Giulini, Dynamical and Hamiltonian Formulation of General Relativity, Springer Handbook of Spacetime, p.323, 2014.

J. Gleick and I. Newton, , 2004.

H. Goenner, J. Renn, J. Ritter, and T. Sauer, The Expanding Worlds of General Relativity, Einstein Studies, 1999.

S. E. Gralla, Gauge and averaging in gravitational self-force, Physical Review D, vol.84, p.84050, 2011.

S. E. Gralla, Second-order gravitational self-force, Physical Review D, vol.85, p.124011, 2012.

S. E. Gralla, A. I. Harte, and R. M. Wald, Rigorous derivation of electromagnetic selfforce, Physical Review D, vol.80, p.24031, 2009.

S. E. Gralla and R. M. Wald, A note on the coordinate freedom in describing the motion of particles in general relativity, Classical and Quantum Gravity, vol.28, p.177001, 2011.

S. E. Gralla and R. M. Wald, A rigorous derivation of gravitational self-force, Classical and Quantum Gravity, vol.25, p.205009, 2008.

P. Grandclément and J. Novak, Spectral Methods for Numerical Relativity, Living Reviews in Relativity, vol.12, p.1, 2009.

A. Gsponer, The classical point electron in Colombeau's theory of nonlinear generalized functions, Journal of Mathematical Physics, vol.49, p.102901, 2008.

R. Haas and E. Poisson, Mode-sum regularization of the scalar self-force: Formulation in terms of a tetrad decomposition of the singular eld, Physical Review D, vol.74, p.44009, 2006.

H. Hankel, Zur allgemeinen Theorie der Bewegung der Flüssigkeiten. Eine von der philosophischen Facultät der Georgia Augusta am 4.Juni 1861 gekrönte Preisschrift, 1861.

A. I. Harte, Electromagnetic self-forces and generalized Killing elds, Classical and Quantum Gravity, vol.26, p.155015, 2009.

A. I. Harte, Self-forces from generalized Killing elds, Classical and Quantum Gravity, vol.25, p.235020, 2008.

E. Haskell, D. Q. Nykamp, and D. Tranchina, Population density methods for large-scale modelling of neuronal networks with realistic synaptic kinetics: cutting the dimension down to size, Network, vol.12, p.141, 2001.

S. W. Hawking, Particle creation by black holes, Communications in Mathematical Physics, vol.43, p.199, 1975.

S. W. Hawking and G. F. Ellis, The Large Scale Structure of Space-Time, 1975.

D. Hilbert, Die Grundlagen der Physik, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen -Mathematisch-Physikalische Klasse, vol.3, p.395, 1915.

D. Hilditch, An introduction to well-posedness and free-evolution, International Journal of Modern Physics A, vol.28, p.1340015, 2013.

H. Hofer and E. Zehnder, Symplectic Invariants and Hamiltonian Dynamics, 2011.

S. Holst, Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action, Physical Review D, vol.53, p.5966, 1996.

G. Horwitz, Steepest descent path for the microcanonical ensemble-resolution of an ambiguity, Communications in Mathematical Physics, vol.89, p.117, 1983.

G. Immirzi, Real and complex connections for canonical gravity, Classical and Quantum Gravity, vol.14, p.177, 1997.

J. D. Jackson, Classical Electrodynamics, 1999.

J. L. Jaramillo and E. Gourgoulhon, Mass and Angular Momentum in General Relativity, Mass and Motion in General Relativity, p.87, 2011.

J. L. Jaramillo, C. F. Sopuerta, and P. Canizares, Are time-domain self-force calculations contaminated by Jost solutions?, Physical Review D, vol.83, p.61503, 2011.

J. Jezierski, Energy and Angular Momentum ofthe Weak Gravitational Waves on the Schwarzschild Background -Quasilocal Gauge-invariant Formulation, General Relativity and Gravitation, vol.31, p.1855, 1999.

J. Jung, A Note on the Spectral Collocation Approximation of Some Di erential Equations with Singular Source Terms, Journal of Scienti c Computing, vol.39, p.49, 2009.

J. Jung and W. S. Don, Collocation Methods for Hyperbolic Partial Di erential Equations with Singular Sources, Advances in Applied Mathematics and Mechanics, p.769, 2009.

M. Kaltenbacher, Computational Acoustics, 2017.

V. J. Katz, The History of Stokes' Theorem, vol.52, p.146, 1979.

J. Kepler, Astronomia Nova aitiologetos [romanized] : seu physica coelestis, tradita commentariis de motibus stellae Martis ex observationibus G.V. Tychonis Brahe (Voegelin, 1609.

J. Kepler, Prodromus dissertationum cosmographicarum, continens mysterium cosmographicum, de admirabili proportione orbium coelestium, deque causis coelorum numeri, magnitudinis, motuumque periodicorum genuinis & propriis, demonstratum, per quinque regularia corpora geometrica

R. P. Kerr, Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics, Physical Review Letters, vol.11, p.237, 1963.

D. Kim, Radiation reaction in curved spacetime, 2005.

D. Kim, Regularization parameters for the self-force of a scalar particle in a general orbit about a Schwarzschild black hole, 2004.

W. Kinnersley, Type D Vacuum Metrics, Journal of Mathematical Physics, vol.10, p.1195, 1969.

A. Koestler, The Sleepwalkers, 1959.

C. Lanczos, The Variational Principles of Mechanics, 1949.

J. Laskar, Is the Solar System Stable?, Progress in Mathematical Physics, p.239, 2010.

J. Lasry and P. Lions, Mean eld games, Japanese Journal of Mathematics, vol.2, p.229, 2007.

J. M. Lee, Introduction to Smooth Manifolds, 2002.

D. , Why Einstein did not believe that general relativity geometrizes gravity, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, vol.46, p.316, 2014.

L. Lehner and F. Pretorius, Annual Review of Astronomy and Astrophysics, vol.52, p.661, 2014.

J. Leray, Hyperbolic Di erential Equations (Institute for Advanced Studies, 1952.

C. K. Li, A review on the products of distributions, Mathematical Methods in Engineering, p.71, 2007.

R. López-alemán, G. Khanna, and J. Pullin, Perturbative evolution of particle orbits around Kerr black holes: time-domain calculation, Classical and Quantum Gravity, vol.20, p.3259, 2003.

J. J. Loschmidt, Über den Zustand des Wärmegleichgewichtes eines Systems von Körpern mit Rücksicht auf die Schwerkraft, Sitz. Akad. Wiss. Wien, vol.73, p.128, 1876.

L. Barreira, Poincaré recurrence: old and new, XIVth International Congress on Mathematical Physics, pp.415-422, 2006.

R. Madariaga, Seismic Source Theory, Treatise on Geophysics, p.59, 2007.

M. Maggiore and G. Waves, Theory and Experiments, vol.1, 2007.

G. Mainardi, Sulle coordinate curvilinee d'una super cie dello spazio, Giornale del R. Istituto Lombardo, vol.9, p.385, 1856.

P. A. Markowich, N. Matevosyan, J. Pietschmann, and M. Wolfram, On a parabolic free boundary equation modeling price formation, Mathematical Models and Methods in Applied Sciences, vol.19, p.1929, 2009.

K. Martel and E. Poisson, Gravitational perturbations of the Schwarzschild spacetime: A practical covariant and gauge-invariant formalism, Physical Review D, vol.71, p.104003, 2005.

P. Mcgrath, Rigid Quasilocal Frames, 2014.

P. L. Mcgrath, M. Chanona, R. J. Epp, M. J. Koop, and R. B. Mann, Post-Newtonian conservation laws in rigid quasilocal frames, Classical and Quantum Gravity, vol.31, p.95006, 2014.

P. L. Mcgrath, R. J. Epp, and R. B. Mann, Quasilocal conservation laws: why we need them, Classical and Quantum Gravity, vol.29, p.215012, 2012.

Y. Mino, M. Sasaki, and T. Tanaka, Gravitational radiation reaction to a particle motion, Physical Review D, vol.55, p.3457, 1997.

C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation, 1973.

V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger, Theory of cosmological perturbations, Physics Reports, vol.215, p.203, 1992.

A. Nagar and L. Rezzolla, Gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes, Classical and Quantum Gravity, vol.22, p.167, 2005.

M. Nakahara, Geometry, Topology and Physics, 2003.

T. Nakamura, K. Oohara, and Y. Kojima, General Relativistic Collapse to Black Holes and Gravitational Waves from Black Holes, Progress of Theoretical Physics Supplement, vol.90, p.1, 1987.

E. Newman and R. Penrose, An Approach to Gravitational Radiation by a Method of Spin Coe cients, Journal of Mathematical Physics, vol.3, p.566, 1962.

R. P. Newman, Compact space-times and the no-return theorem, General Relativity and Gravitation, vol.18, p.1181, 1986.

I. Newton, Philosophiae naturalis principia mathematica, 1687.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 2010.

A. Nissenbaum, Multisymplectic Geometry in, General Relativity and other Classical Field Theories on Manifolds with Boundaries: A Deobfuscating Role, 2017.

E. T. Olsen, Classical mechanics and entropy, Foundations of Physics Letters, vol.6, p.327, 1993.

M. Oltean, L. Bonetti, A. D. Spallicci, and C. F. Sopuerta, Entropy theorems in classical mechanics, general relativity, and the gravitational two-body problem, Physical Review D, vol.94, p.64049, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01554300

M. Oltean, R. J. Epp, P. L. Mcgrath, and R. B. Mann, Geoids in general relativity: Geoid quasilocal frames, The Fourteenth Marcel Grossmann Meeting on General Relativity, p.3682, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01669682

M. Oltean, R. J. Epp, P. L. Mcgrath, and R. B. Mann, Geoids in general relativity: geoid quasilocal frames, Classical and Quantum Gravity, vol.33, p.105001, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01669682

M. Oltean, R. J. Epp, C. F. Sopuerta, A. D. Spallicci, and R. B. Mann, The motion of localized sources in general relativity: gravitational self-force from quasilocal conservation laws, physics:gr-qc, 2019.

M. Oltean, C. F. Sopuerta, and A. D. Spallicci, A frequency-domain implementation of the particle-without-particle approach to EMRIs, Journal of Physics: Conference Series, vol.840, p.12056, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01584609

M. Oltean, C. F. Sopuerta, and A. D. Spallicci, Particle-without-Particle: A Practical Pseudospectral Collocation Method for Linear Partial Di erential Equations with Distributional Sources, Journal of Scienti c Computing, vol.79, p.827, 2019.

T. Padmanabhan, Gravitation: Foundations and Frontiers, 2010.

K. M. Peterson, Über die Biegung der Flächen, 1853.

N. A. Petersson, O. O'reilly, B. Sjögreen, and S. Bydlon, Discretizing singular point sources in hyperbolic wave propagation problems, Journal of Computational Physics, vol.321, pp.532-555, 2016.

N. A. Petersson and B. Sjogreen, Stable Grid Re nement and Singular Source Discretization for Seismic Wave Simulations, Commun. Comput. Phys, vol.8, p.1074, 2010.

R. Peyret, Chebyshev method, Spectral Methods for Incompressible Viscous Flow, Applied Mathematical Sciences, p.39, 2002.

J. Pietschmann, On some partial di erential equation models in socio-economic contexts -analysis and numerical simulations, 2012.

F. A. Pirani, On the Quantization of the Gravitational Field of General Relativity, 1951.

F. A. Pirani and A. Schild, On the Quantization of Einstein's Gravitational Field Equations, Physical Review, vol.79, p.986, 1950.

H. Poincaré, Sur le problème des trois corps et les équations de la dynamique, Acta mathematica, vol.13, p.1, 1890.

H. Poincaré, Sur les tentatives d'explication mecanique des principes de la thermodynamique, C. R. Acad. Sci, vol.108, p.550, 1889.

E. Poisson and . Relativist's-toolkit, The Mathematics of Black-Hole Mechanics, 2007.

E. Poisson, An introduction to the Lorentz-Dirac equation, 1999.

E. Poisson, A. Pound, and I. Vega, The Motion of Point Particles in Curved Spacetime, Living Reviews in Relativity, vol.14, p.7, 2011.

A. Pound, Gauge and motion in perturbation theory, Physical Review D, vol.92, p.44021, 2015.

A. Pound, Motion of Small Objects in Curved Spacetimes: An Introduction to Gravitational Self-Force, Equations of Motion in Relativistic Gravity, vol.179, p.399, 2015.

A. Pound, Nonlinear gravitational self-force: Second-order equation of motion, Physical Review D, vol.95, p.104056, 2017.

A. Pound, Second-Order Gravitational Self-Force, Physical Review Letters, vol.109, p.51101, 2012.

A. Pound, Self-consistent gravitational self-force, Physical Review D, vol.81, p.24023, 2010.

A. Pound, C. Merlin, and L. Barack, Gravitational self-force from radiation-gauge metric perturbations, Physical Review D, vol.89, p.24009, 2014.

C. Prescod-weinstein and E. Bertschinger, An extension of the Faddeev-Jackiw technique to elds in curved spacetimes, Classical and Quantum Gravity, vol.32, p.75011, 2014.

F. Pretorius, Evolution of Binary Black-Hole Spacetimes, Physical Review Letters, vol.95, p.121101, 2005.

L. R. Price, Developments in the perturbation theory of algebraically special spacetimes, 2007.

D. Puetzfeld and Y. N. Obukhov, Generalized deviation equation and determination of the curvature in general relativity, Physical Review D, vol.93, p.44073, 2016.

M. H. Van-putten, Entropic force in black hole binaries and its Newtonian limits, Physical Review D, vol.85, p.64046, 2012.

T. C. Quinn and R. M. Wald, Axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime, Physical Review D, vol.56, p.3381, 1997.

T. Regge and C. Teitelboim, Role of surface integrals in the Hamiltonian formulation of general relativity, Annals of Physics, vol.88, p.286, 1974.

T. Regge and J. A. Wheeler, Stability of a Schwarzschild Singularity, Physical Review, vol.108, p.1063, 1957.

J. Renn, Boston Studies in the Philosophy and History of Science, vol.1, 2007.

P. Ritter, S. Aoudia, A. D. Spallicci, and S. Cordier, Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs, International Journal of Geometric Methods in Modern Physics, vol.13, p.1650021, 2015.
URL : https://hal.archives-ouvertes.fr/insu-01352535

P. Ritter, S. Aoudia, A. D. Spallicci, and S. Cordier, Indirect (source-free) integration method. II. Self-force consistent radial fall, International Journal of Geometric Methods in Modern Physics, vol.13, p.1650019, 2016.
URL : https://hal.archives-ouvertes.fr/insu-01352535

P. Ritter, A. D. Spallicci, S. Aoudia, and S. Cordier, A fourth-order indirect integration method for black hole perturbations: even modes, Classical and Quantum Gravity, vol.28, p.134012, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00715438

, Seismology and Structure of the Earth, 2007.

N. Román-roy, Some Properties of Multisymplectic Manifolds, Springer Proceedings in Physics, p.325, 2019.

T. Rothman, Editor's note: the eld of a single centre in Einstein's theory of gravitation, and the motion of a particle in that eld, General Relativity and Gravitation, vol.34, p.1541, 2002.

C. Rovelli, General relativistic statistical mechanics, Physical Review D, vol.87, p.84055, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00845526

C. Rovelli, Quantum Gravity, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00017397

L. Ryvkin and T. Wurzbacher, An invitation to multisymplectic geometry, Journal of Geometry and Physics, vol.142, p.9, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02471860

C. Sagan, Cosmos (Random House, 1980.

V. Sahni, Y. Shtanov, and A. Toporensky, Arrow of time in dissipationless cosmology, Classical and Quantum Gravity, vol.32, p.182001, 2015.

V. Sahni and A. Toporensky, Cosmological hysteresis and the cyclic universe, Physical Review D, vol.85, p.123542, 2012.

D. Santos-oliván and C. F. Sopuerta, Pseudo-Spectral Collocation Methods for Hyperbolic Equations with Arbitrary Precision: Applications to Relativistic Gravitation, 2018.

O. Sarbach and M. Tiglio, Continuum and Discrete Initial-Boundary Value Problems and Einstein's Field Equations, Living Reviews in Relativity, vol.15, p.9, 2012.

S. Sasa and Y. Yokokura, Thermodynamic Entropy as a Noether Invariant, Physical Review Letters, vol.116, p.140601, 2016.

M. Sasaki and H. Tagoshi, Analytic Black Hole Perturbation Approach to Gravitational Radiation, Living Reviews in Relativity, vol.6, p.6, 2003.

J. S. Schi-rin and R. M. Wald, Measure and Probability in Cosmology, Physical Review D, vol.86, p.23521, 2012.

L. Schwartz, Sur l'impossibilité de la multiplication des distributions, C. R. Acad. Sci. Paris, vol.29, pp.847-848, 1954.

L. Schwartz, Théorie des distributions, 1957.

K. Schwarzschild, Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften, p.189, 1916.

P. M. Shearer, Introduction to Seismology, 2009.

M. Shibata, Numerical Relativity (World Scienti c, 2015.

M. Shibata and T. Nakamura, Evolution of three-dimensional gravitational waves: Harmonic slicing case, Physical Review D, vol.52, p.5428, 1995.

B. Shin and J. Jung, Spectral collocation and radial basis function methods for one-dimensional interface problems, Applied Numerical Mathematics, vol.61, p.911, 2011.

A. C. Silva, Lectures on Symplectic Geometry, 2008.

A. C. Silva, Symplectic geometry, Handbook of Di erential Geometry, vol.2, p.79, 2006.

L. Sklar, Physics and Chance: Philosophical Issues in the Foundations of Statistical Mechanics, 1995.

A. D. Spallicci and P. Ritter, A fully relativistic radial fall, International Journal of Geometric Methods in Modern Physics, vol.11, p.1450090, 2014.
URL : https://hal.archives-ouvertes.fr/insu-01284889

A. D. Spallicci, P. Ritter, and S. Aoudia, Self-force driven motion in curved spacetime, International Journal of Geometric Methods in Modern Physics, vol.11, p.1450072, 2014.
URL : https://hal.archives-ouvertes.fr/insu-01257754

A. D. Spallicci, P. Ritter, S. Jubertie, S. Cordier, and S. Aoudia, Towards a Self-consistent Orbital Evolution for EMRIs, Astronomical Society of the Paci c Conference Series, vol.467, p.221, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00798833

I. Stakgold and M. J. Holst, Green's Functions and Boundary Value Problems, 2011.

R. Steinbauer and J. A. Vickers, The use of generalized functions and distributions in general relativity, Classical and Quantum Gravity, vol.23, p.91, 2006.

J. M. Stewart and M. Walker, Perturbations of space-times in general relativity, Royal Society of London. A. Mathematical and Physical Sciences, vol.341, p.49, 1974.

J. Stewart, Advanced General Relativity, 1993.

S. Suhr and K. Zehmisch, Linking and closed orbits, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol.86, p.133, 2016.

L. B. Szabados, Quasi-Local Energy-Momentum and Angular Momentum in GR: A Review Article, Living Reviews in Relativity, vol.7, p.4, 2004.

S. A. Teukolsky, Perturbations of a Rotating Black Hole. I. Fundamental Equations for Gravitational, Electromagnetic, and Neutrino-Field Perturbations, The Astrophysical Journal, vol.185, p.635, 1973.

S. A. Teukolsky, Rotating Black Holes: Separable Wave Equations for Gravitational and Electromagnetic Perturbations, Physical Review Letters, vol.29, p.1114, 1972.

S. A. Teukolsky, The Kerr metric, Classical and Quantum Gravity, vol.32, p.124006, 2015.

F. J. Tipler, General Relativity and the Eternal Return, Essays in General Relativity, p.21, 1980.

F. J. Tipler, General relativity, thermodynamics, and the Poincaré cycle, Nature, vol.280, p.203, 1979.

A. Tornberg and B. Engquist, Numerical approximations of singular source terms in di erential equations, Journal of Computational Physics, vol.200, p.462, 2004.

L. N. Trefethen, Spectral Methods in MATLAB, 2001.

I. Vega and S. Detweiler, Regularization of elds for self-force problems in curved spacetime: Foundations and a time-domain application, Physical Review D, vol.77, p.84008, 2008.

E. P. Verlinde, On the Origin of Gravity and the Laws of Newton, Journal of High Energy Physics, vol.1104, p.29, 2010.

V. Villani-cedric, H-Theorem and beyond: Boltzmann's entropy in today's mathematics, Boltzmann's Legacy, p.129, 2008.

C. V. Vishveshwara, Stability of the Schwarzschild Metric, Physical Review D, vol.1, p.2870, 1970.

R. M. Wald, General Relativity, 1984.
URL : https://hal.archives-ouvertes.fr/hal-02116509

R. M. Wald, The Thermodynamics of Black Holes, Living Reviews in Relativity, vol.4, p.6, 2001.

B. , Self-force: Computational Strategies, Equations of Motion in Relativistic Gravity, vol.179, p.487, 2015.

J. O. Weatherall, Geometry and Motion in General Relativity, 2018.

H. Wilbraham, On a certain periodic function, The Cambridge and Dublin Mathematical Journal, vol.3, p.198, 1848.

D. C. Wilkins, Bound Geodesics in the Kerr Metric, Physical Review D, vol.5, p.814, 1972.

H. Yau, The work of Cedric Villani, Proceedings of the International Congress of Mathematicians 2010 (ICM 2010), p.87, 2011.

J. W. York, Role of Conformal Three-Geometry in the Dynamics of Gravitation, Physical Review Letters, vol.28, p.1082, 1972.

A. Zenginoglu, Hyperboloidal layers for hyperbolic equations on unbounded domains, Journal of Computational Physics, vol.230, p.2286, 2011.

F. J. Zerilli, Gravitational Field of a Particle Falling in a Schwarzschild Geometry Analyzed in Tensor Harmonics, Physical Review D, vol.2, p.2141, 1970.

J. G. Zhou, D. M. Causon, D. M. Ingram, and C. G. Mingham, Numerical solutions of the shallow water equations with discontinuous bed topography, International Journal for Numerical Methods in Fluids, vol.38, p.769, 2002.