Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries

Bern Z, Cheung C, Roiban R, Shen CH, Solon MP, Zeng M (2019b) Scattering amplitudes and the conservative Hamiltonian for binary systems at third post-Minkowskian order. Phys Rev Lett 122:201603. https://doi.org/10.1103/PhysRevLett.122.201603 . arXiv:1901.04424

Original

1901

Earlier work this paper cites.

Blümlein J, Maier A, Marquard P (2020a) Five-loop static contribution to the gravitational interaction potential of two point masses. Phys Lett B 800:135100. https://doi.org/10.1016/j.physletb.2019.135100 . arXiv:1902.11180 [gr-qc]

Original

1902

Earlier work this paper cites.

Foffa S, Mastrolia P, Sturani R, Sturm C, Torres Bobadilla WJ (2019a) Static two-body potential at fifth post-Newtonian order. Phys Rev Lett 122:241605. https://doi.org/10.1103/PhysRevLett.122.241605 . arXiv:1902.10571

Original

1902

Earlier work this paper cites.

Foffa S, Sturani R (2019) Conservative dynamics of binary systems to fourth post-Newtonian order in the EFT approach. I. Regularized Lagrangian. Phys Rev D 100:024047. https://doi.org/10.1103/PhysRevD.100.024047 . arXiv:1903.05113

Original

1903

Earlier work this paper cites.

Foffa S, Porto RA, Rothstein I, Sturani S (2019b) Conservative dynamics of binary systems to fourth post-Newtonian order in the EFT approach. II. Renormalized Lagrangian. Phys Rev D 100:024048. https://doi.org/10.1103/PhysRevD.100.024048 . arXiv:1903.05118

Original

1903

Earlier work this paper cites.

Foffa S, Sturani R (2020) Hereditary terms at next-to-leading order in two-body gravitational dynamics. Phys Rev D 101:064033. https://doi.org/10.1103/PhysRevD.101.064033 . arXiv:1907.02869

Original

1907

Earlier work this paper cites.

Bern Z, Cheung C, Roiban R, Shen CH, Solon MP, Zeng M (2019a) Black hole binary dynamics from the double copy and effective theory. JHEP 10:206. https://doi.org/10.1007/JHEP10(2019)206 . arXiv:1908.01493

Original

1908

Earlier work this paper cites.

Bini D, Damour T, Geralico A (2019) Novel approach to binary dynamics: application to the fifth post-Newtonian level. Phys Rev Lett 123:231104. https://doi.org/10.1103/PhysRevLett.123.231104 . arXiv:1909.0237 [gr-qc]

Original

1909

Earlier work this paper cites.

Damour T (2020) Classical and quantum scattering in post-Minkowskian gravity. Phys Rev D 102:024060. https://doi.org/10.1103/PhysRevD.102.024060 . arXiv:1912.02139

Original

1912

Earlier work this paper cites.

Henry Q, Faye G, Blanchet L (2020b) Tidal effects in the equations of motion of compact binary systems to next-to-next-to-leading post-Newtonian order. Phys Rev D 101:064047. https://doi.org/10.1103/PhysRevD.101.064047 . arXiv:1912.01920

Original

1912

Earlier work this paper cites.

Levi M, Mougiakakos S, Vieira M (2021b) Gravitational cubic-in-spin interaction at the next-to-leading post-Newtonian order. JHEP 2021(01):036. https://doi.org/10.1007/JHEP01(2021)036 . arXiv:1912.06276 [hep-th]

Original

1912

Earlier work this paper cites.

Droste J (1916) The field of n n moving centres in Einstein’s theory of gravitation. Proc Acad Sci Amst 19:447–455

1916

Earlier work this paper cites.

Lorentz HA, Droste J (1937) The motion of a system of bodies under the influence of their mutual attraction, according to Einstein’s theory, Parts I and II. In: The Collected Papers of H. A. Lorentz, Vol. 5. Nijhoff, The Hague. Original paper in Versl. K. Akad. Wet. Amsterdam, 26 (1917) 392

1917

Earlier work this paper cites.

de Sitter W (1917) Errata in prof. de Sitter’s papers on “Einstein’s theory of gravitation”. Mon Not R Astron Soc 77:481. https://doi.org/10.1093/mnras/77.5.481

1917

Earlier work this paper cites.

Bateman H (1931) On dissipative systems and related variational principles. Phys Rev 38:815–819. https://doi.org/10.1103/PhysRev.38.815

1931

Earlier work this paper cites.

Mathisson M (1937) Neue Mechanik materieller Systeme. Acta Phys Polon 6:163–200

1937

Earlier work this paper cites.

Eddington A, Clark GL (1938) The problem of motion of n n bodies in general relativity. Proc R Soc London A 166:465–475. https://doi.org/10.1098/rspa.1938.0104

1938

Earlier work this paper cites.

Einstein A, Infeld L, Hoffmann B (1938) The gravitational equations and the problem of motion. Ann Math 39:65–100. https://doi.org/10.2307/1968714

1938

Earlier work this paper cites.

Robertson HP (1938) Note on the preceding paper: The two body problem in general relativity. Ann Math 39:101–104

1938

Earlier work this paper cites.

Fock VA (1939) Sur le mouvement des masses finies d’après la théorie de gravitation einsteinienne. J Phys (Moscow) 1:81–116

1939

Earlier work this paper cites.

Petrova NM (1949) On the equations of motion and the mass tensor for systems of finite masses in the general theory of relativity. Zh Eksp Teor Fiz 19:989–999. In Russian

1949

Earlier work this paper cites.

Riesz M (1949) L’intégrale de Riemann-Liouville et le problème de Cauchy. Acta Math 81:1–218. https://doi.org/10.1007/BF02395016

1949

Earlier work this paper cites.

Fichtenholz IG (1950) The lagrangian form of the equations of motion in second approximation. Zh Eksp Teor Fiz 20:233–242. In Russian

1950

Earlier work this paper cites.

Corinaldesi E, Papapetrou A (1951) Spinning test-particles in general relativity. II. Proc R Soc London, Ser A 209:259–268. https://doi.org/10.1098/rspa.1951.0201

1951

Earlier work this paper cites.

Papapetrou A (1951b) Spinning test-particles in general relativity. I. Proc R Soc London, Ser A 209:248–258. https://doi.org/10.1098/rspa.1951.0200

1951

Earlier work this paper cites.

Shah AG, Friedman JL, Whiting BF (2014) Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation. Phys Rev D 89:064042. https://doi.org/10.1103/PhysRevD.89.064042 . arXiv:1312.1952

Original

1952

Earlier work this paper cites.

Infeld L (1954) On the motion of bodies in general relativity theory. Acta Phys Polon 13:187–204

1954

Earlier work this paper cites.

Bertotti B (1956) On gravitational motion. Nuovo Cimento 4:898–906. https://doi.org/10.1007/BF02746175

1956

Earlier work this paper cites.

Fourès-Bruhat Y (1956) Sur l’intégration des équations de la relativité général. J Rational Mech Anal 5:951

1956

Earlier work this paper cites.

Infeld L (1957) Equations of motion in general relativity theory and the action principle. Rev Mod Phys 29:398–411. https://doi.org/10.1103/RevModPhys.29.398

1957

Earlier work this paper cites.

Tulczyjew W (1957) On the energy-momentum tensor density for simple pole particles. Bull Acad Polon Sci Cl III 5:279

1957

Earlier work this paper cites.

Dirac PAM (1958) The theory of gravitation in Hamiltonian form. Proc R Soc London A 246:333–343. https://doi.org/10.1098/rspa.1958.0142

1958

Earlier work this paper cites.

Arnowitt R, Deser S, Misner CM (1959) Dynamical structure and definition of energy in general relativity. Phys Rev 116:1322–1330. https://doi.org/10.1103/PhysRev.116.1322

1959

Earlier work this paper cites.

Dirac PAM (1959) Fixation of coordinates in the Hamiltonian theory of gravitation. Phys Rev 114:924–930. https://doi.org/10.1103/PhysRev.114.924

1959

Earlier work this paper cites.

Fock VA (1959) Theory of Space, Time and Gravitation. Pergamon, London

1959

Earlier work this paper cites.

Komar A (1959) Covariant conservation laws in general relativity. Phys Rev 113:934–936. https://doi.org/10.1103/PhysRev.113.934

1959

Earlier work this paper cites.

Tulczyjew W (1959) Equations of motion of rotating bodies in general relativity. Acta Phys Polon 18:37–55

1959

Earlier work this paper cites.

Bertotti B, Plebański JF (1960) Theory of gravitational perturbations in the fast motion approximation. Ann Phys (N Y) 11:169–200. https://doi.org/10.1016/0003-4916(60)90132-9

1960

Earlier work this paper cites.

Infeld L, Plebański J (1960) Motion and Relativity. Pergamon Press, Oxford

1960

Earlier work this paper cites.

Brouwer D, Clemence GM (1961) Methods of Celestial Mechanics. Academic Press, Orlando

1961

Earlier work this paper cites.

Kimura T (1961) Fixation of physical space-time coordinates and equation of motion of two-body problem. Prog Theor Phys 26:157–172. https://doi.org/10.1143/PTP.26.157

1961

Earlier work this paper cites.

Ryteń J (1961) Equations of motion in general relativity in post-post-Newtonian approximation (in Polish). Master’s thesis, University of Warsaw, Poland. (unpublished)

1961

Earlier work this paper cites.

Schwinger J (1961) Brownian motion of a quantum oscillator. J Math Phys 2:407–432. https://doi.org/10.1063/1.1703727

1961

Earlier work this paper cites.

Arnowitt R, Deser S, Misner CM (1962) The dynamics of general relativity. In: Witten L (ed) Gravitation: An Introduction to Current Research. Wiley, New York. arXiv:gr-qc/0405109v1

1962

Earlier work this paper cites.

Dirac PAM (1962) Interacting gravitational and spinor fields. In: Recent Developments in General Relativity. Pergamon Press, Oxford, pp 191–200

1962

Earlier work this paper cites.

Brill DR, Lindquist RW (1963) Interaction energy in geometrostatics. Phys Rev 131:471–476. https://doi.org/10.1103/PhysRev.131.471

1963

Earlier work this paper cites.

Kibble TW (1963) Canonical variables for the interacting gravitational and Dirac fields. J Math Phys 4:1433–1437. https://doi.org/10.1063/1.1703923

1963

Earlier work this paper cites.

Komar A (1963) Positive-definite energy density and global consequences for general relativity. Phys Rev 129:1873–1876. https://doi.org/10.1103/PhysRev.129.1873

1963

Earlier work this paper cites.

Lindquist RW (1963) Initial-value problem on Einstein-Rosen manifolds. J Math Phys 4:938–950. https://doi.org/10.1063/1.1704020

1963

Earlier work this paper cites.

Misner CW (1963) The method of images in geometrostatics. Ann Phys (N Y) 24:102–117. https://doi.org/10.1016/0003-4916(63)90067-8

1963

Earlier work this paper cites.

Wheeler JA (1964) Geometrodynamics and the issue of the final state. In: DeWitt C, DeWitt B (eds) Relativity, Groups and Topology: Lectures delivered at Les Houches during the 1963 Session of the Summer School of Theoretical Physics, University of Grenoble, Les Houches 1963. Gordon and Breach, New York, pp 315–520

1963

Earlier work this paper cites.

Gel’fand IM, Shilov GE (1964) Generalized Functions, Vol. 1. Academic Press, New York

1964

Earlier work this paper cites.

Feynman RP, Hibbs AR (1965) Quantum Mechanics and Path Integrals. MacGraw-Hill Book Company, New York

1965

Earlier work this paper cites.

Fleming GN (1965) Covariant position operators, spin, and locality. Phys Rev 137:B188–B197. https://doi.org/10.1103/PhysRev.137.B188

1965

Earlier work this paper cites.

Keldysh LV (1965) Diagram technique for nonequilibrium processes. Soviet Physics JETP 20:1018–1026

1965

Earlier work this paper cites.

Hori G (1966) Theory of general perturbation with unspecified canonical variable. Publ Astron Soc Japan 18:287–296

1966

Earlier work this paper cites.

DeWitt BS (1967) Quantum theory of gravity. I. The canonical theory. Phys Rev 160:1113–1148. https://doi.org/10.1103/PhysRev.160.1113

1967

Earlier work this paper cites.

Steinhoff J, Schäfer G (2009a) Canonical formulation of self-gravitating spinning-object systems. Europhys Lett 87:50004. https://doi.org/10.1209/0295-5075/87/50004 . arXiv:0907.1967

Original

1967

Earlier work this paper cites.

Hiida K, Okamura H (1972) Gauge transformation and gravitational potentials. Prog Theor Phys 47:1743–1757. https://doi.org/10.1143/PTP.47.1743

1972

Earlier work this paper cites.

‘t Hooft G, Veltman M (1972) Regularization and renormalization of gauge fields. Nucl Phys B 44:189–213. https://doi.org/10.1016/0550-3213(72)90279-9

1972

Earlier work this paper cites.

Kimura T, Toiya T (1972) Potential in the canonical formalism of gravity. Prog Theor Phys 48:316–328. https://doi.org/10.1143/PTP.48.316

1972

Earlier work this paper cites.

Weinberg S (1972) Gravitation and Cosmology. Wiley, New York

1972

Earlier work this paper cites.

Bekenstein JD (1973) Gravitational radiation recoil and runaway black holes. Astrophys J 183:657–664. https://doi.org/10.1086/152255

1973

Earlier work this paper cites.

Misner CW, Thorne KS, Wheeler JA (1973) Gravitation. W. H. Freeman, San Francisco

1973

Earlier work this paper cites.

Ohta T, Okamura H, Hiida K, Kimura T (1973) Physically acceptable solution of Einstein’s equation for many-body system. Prog Theor Phys 50:492–514. https://doi.org/10.1143/PTP.50.492

1973

Earlier work this paper cites.

Hanson AJ, Regge T (1974) The relativistic spherical top. Ann Phys (N Y) 87:498–566. https://doi.org/10.1016/0003-4916(74)90046-3

1974

Earlier work this paper cites.

Regge T, Teitelboim C (1974) Role of surface integrals in the Hamiltonian formulation of general relativity. Ann Phys (N Y) 88:286–318. https://doi.org/10.1016/0003-4916(74)90404-7

1974

Earlier work this paper cites.

Bailey I, Israel W (1975) Lagrangian dynamics of spinning particles and polarized media in general relativity. Commun Math Phys 42:65–82. https://doi.org/10.1007/BF01609434

1975

Earlier work this paper cites.

Barker BM, O’Connell RF (1975) Gravitational two-body problem with arbitray masses, spins, and quadrupole moments. Phys Rev D 12:329–335. https://doi.org/10.1103/PhysRevD.12.329

1975

Earlier work this paper cites.

Deser S, Isham C (1976) Canonical vierbein form of general relativity. Phys Rev D 14:2505–2510. https://doi.org/10.1103/PhysRevD.14.2505

1976

Earlier work this paper cites.

Kinoshita H (1978) Third-order solution of an artificial-satellite theory. In: Szebehely V (ed) Dynamics of planets and satellites and theories of their motion. Proceedings of the 41st Colloquium of the International Astronomical Union held in Cambridge, England, 17–19 August 1976. D. Reidel, Dordrecht, pp 241–257. https://doi.org/10.1007/978-94-009-9809-4˙30

1976

Earlier work this paper cites.

Nelson JE, Teitelboim C (1978) Hamiltonian formulation of the theory of interacting gravitational and electron fields. Ann Phys 116:86–104. https://doi.org/10.1016/0003-4916(78)90005-2

1978

Earlier work this paper cites.

Barker BM, O’Connell RF (1979) The gravitational interaction: Spin, rotation, and quantum effects — A review. Gen Relativ Gravit 11:149–175. https://doi.org/10.1007/BF00756587

1979

Earlier work this paper cites.

York JW (1979) Kinematics and dynamics of general relativity. In: Smarr L (ed) Sources of Gravitational Radiation. Cambridge University Press, Cambridge, pp 83–126

1979

Earlier work this paper cites.

Damour T (1980) Masses ponctuelles en relativité générale. C R Acad Sci Ser A 291:227–229

1980

Earlier work this paper cites.

Thorne KS (1980) Multipole expansion of gravitational radiation. Rev Mod Phys 52:299–339. https://doi.org/10.1103/RevModPhys.52.299

1980

Earlier work this paper cites.

Bel L, Damour T, Deruelle N, Ibañez J, Martin J (1981) Poincaré-invariant gravitational field and equations of motion for two pointlike objects: The postlinear approximation to general relativity. Gen Relativ Gravit 13:963–1004. https://doi.org/10.1007/BF00756073

1981

Earlier work this paper cites.

Damour T, Deruelle N (1981) Lagrangien généralisé du systèm de deux masses ponctuelles, á l’approximation post-post-newtonienne de la relativité générale. C R Acad Sci Ser II 293:537–540

1981

Earlier work this paper cites.

Goldstein H (1981) Classical Mechanics. Addison-Wesley, Reading, MA

1981

Earlier work this paper cites.

Damour T (1982) Problème des deux corps et freinage de rayonnement en relativité générale. C R Acad Sci Ser II 294:1355–1357

1982

Earlier work this paper cites.

Damour T (1983a) Gravitational radiation and the motion of compact objects. In: Deruelle N, Piran T (eds) Gravitational Radiation. Proceedings of the NATO Advanced Study Institute held in Les Houches, France, June 2–21, 1982. NATO ASI. North-Holland, Amsterdam, pp 59–144

1982

Earlier work this paper cites.

Faddeev LD (1982) The energy problem in Einstein’s theory of gravitation (Dedicated to the memory of V. A. Fock). Sov Phys Usp 25:130–142

1982

Earlier work this paper cites.

Schäfer G (1982) The equations of motion for an astrophysical binary with accuracy 1 / c 5 1/c^{5} . Prog Theor Phys 68:2191–2193. https://doi.org/10.1143/PTP.68.2191

1982

Earlier work this paper cites.

Thorne KS (1983) The theory of gravitational radiation: An introductory review. In: Deruelle N, Piran T (eds) Gravitational Radiation. Proceedings of the NATO Advanced Study Institute held in Les Houches, France, June 2–21, 1982. NATO ASI. North-Holland, Amsterdam, pp 1–57

1982

Earlier work this paper cites.

Fitchett MJ (1983) The influence of gravitational momentum losses on the centre of mass motion of a Newtonian binary system. Mon Not R Astron Soc 203:1049–1062. https://doi.org/10.1093/mnras/203.4.1049

1983

Earlier work this paper cites.

Barker BM, O’Connell RF (1984) Time transformations in post-Newtonian lagrangians. Phys Rev D 29:2721–2725. https://doi.org/10.1103/PhysRevD.29.2721

1984

Earlier work this paper cites.

Collins JC (1984) Renormalization: An Introduction to Renormalization, the Renormalization Group, and the Operator-Product Expansion. Cambridge University Press, Cambridge

1984

Earlier work this paper cites.

Schäfer G (1984) Acceleration-dependent Lagrangians in general relativity. Phys Lett 100A:128–129. https://doi.org/10.1016/0375-9601(84)90947-2

1984

Earlier work this paper cites.

Damour T, Deruelle N (1985) General relativistic celestial mechanics of binary systems I. The post-Newtonian motion. Ann Inst H Poincaré (Phys Théor) 43:107–132

1985

Earlier work this paper cites.

Damour T, Schäfer G (1985) Lagrangians for n n point masses at the second post-Newtonian approximation of general relativity. Gen Relativ Gravit 17:879–905. https://doi.org/10.1007/BF00773685

1985

Earlier work this paper cites.

Grishchuk LP, Kopeikin SM (1986) Equations of motion for isolated bodies with relativistic corrections including the radiation reaction force. In: Kovalevsky J, Brumberg VA (eds) Relativity in Celestial Mechanics and Astrometry: High Precision Dynamical Theories and Observational Verifications. Proceedings of the 114th Symposium of the International Astronomical Union held in Leningrad, U. S. S. R., May 28–31, 1985. D. Reidel, Dordrecht, pp 19–34

1985

Earlier work this paper cites.

Holm DD (1985) Hamiltonian formalism for general-relativistic adiabatic fluids. Physica D 17:1–36. https://doi.org/10.1016/0167-2789(85)90131-9

1985

Earlier work this paper cites.

Kopeikin SM (1985) General-relativistic equations of binary motion for extended bodies, with conservative corrections and radiation damping. Sov Astron 29:516–524

1985

Earlier work this paper cites.

Schäfer G (1985) The gravitational quadrupole radiation-reaction force and the canonical formalism of ADM. Ann Phys (N Y) 161:81–100. https://doi.org/10.1016/0003-4916(85)90337-9

1985

Earlier work this paper cites.

Thorne KS, Hartle JB (1985) Laws of motion and precession for black holes and other bodies. Phys Rev D 31:1815–1837. https://doi.org/10.1103/PhysRevD.31.1815

1985

Cited alongside, same era.

Westpfahl K (1985) High-speed scattering of charged and uncharged particles in general relativity. Fortschr Phys 33:417–493. https://doi.org/10.1002/prop.2190330802

1985

Cited alongside, same era.

Barker BM, O’Connell RF (1986) Gravitational two-body problem with acceleration-dependent spin terms. Gen Relativ Gravit 18:1055–1071. https://doi.org/10.1007/BF01090486

1986

Cited alongside, same era.

Damour T (1987a) An introduction to the theory of gravitational radiation. In: Carter B, Hartle JB (eds) Gravitation in Astrophysics. Proceedings of the NATO Advanced Study Institute held in Cargèse, Corse, France, July 15–31, 1986. NATO ASI Series B, vol 156. Plenum Press, New York, pp 3–62

1986

Cited alongside, same era.

Binnington T, Poisson E (2009) Relativistic theory of tidal Love numbers. Phys Rev D 80:084018. https://doi.org/10.1103/PhysRevD.80.084018 . arXiv:0906.1366

Original

2009

Later among the works it cites.

Bode T, Laguna P, Shoemaker DM, Hinder I, Herrmann F, Vaishnav B (2009) Binary black hole evolutions of approximate puncture initial data. Phys Rev D 80:024008. https://doi.org/10.1103/PhysRevD.80.024008 . arXiv:0902.1127

Original

2009

Later among the works it cites.

Henry Q, Faye G, Blanchet L (2020a) Hamiltonian for tidal interactions in compact binary systems to next-to-next-to-leading post-Newtonian order. Phys Rev D 102:124074. https://doi.org/10.1103/PhysRevD.102.124074 . arXiv:2009.12332

Original

2009

Later among the works it cites.

Itoh Y (2009) Third-and-a-half order post-Newtonian equations of motion for relativistic compact binaries using the strong field point particle limit. Phys Rev D 80:124003. https://doi.org/10.1103/PhysRevD.80.124003 . arXiv:0911.4232

Original

2009

Later among the works it cites.