2000 character limit reached
Note on post-Minkowskian expansion and Bondi coordinates
Published 20 May 2024 in gr-qc and hep-th | (2405.11953v1)
Abstract: In this note, we transform the linear order (first order in $G$) metric from a system of pointlike bodies source to the Bondi coordinates. We confirm that the Bondi 4-momentum and angular momentum of the system computed at null infinity in Bondi coordinates coincide with the relativistic definitions of 4-momentum and angular momentum for the system of pointlike bodies.
- LIGO Scientific, Virgo Collaboration, B. P. Abbott et al., “Observation of Gravitational Waves from a Binary Black Hole Merger,” Phys. Rev. Lett. 116 no. 6, (2016) 061102, arXiv:1602.03837 [gr-qc].
- A. Buonanno, M. Khalil, D. O’Connell, R. Roiban, M. P. Solon, and M. Zeng, “Snowmass White Paper: Gravitational Waves and Scattering Amplitudes,” in Snowmass 2021. 4, 2022. arXiv:2204.05194 [hep-th].
- T. Damour, A. Nagar, D. Pollney, and C. Reisswig, “Energy versus Angular Momentum in Black Hole Binaries,” Phys. Rev. Lett. 108 (2012) 131101, arXiv:1110.2938 [gr-qc].
- L. Blanchet, “Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries,” Living Rev. Rel. 17 (2014) 2, arXiv:1310.1528 [gr-qc].
- L. Blanchet and G. Faye, “Flux-balance equations for linear momentum and center-of-mass position of self-gravitating post-Newtonian systems,” Class. Quant. Grav. 36 no. 8, (2019) 085003, arXiv:1811.08966 [gr-qc].
- A. Ashtekar, T. De Lorenzo, and N. Khera, “Compact binary coalescences: Constraints on waveforms,” Gen. Rel. Grav. 52 no. 11, (2020) 107, arXiv:1906.00913 [gr-qc].
- T. Damour, “Radiative contribution to classical gravitational scattering at the third order in G𝐺Gitalic_G,” Phys. Rev. D 102 no. 12, (2020) 124008, arXiv:2010.01641 [gr-qc].
- G. U. Jakobsen, G. Mogull, J. Plefka, and J. Steinhoff, “Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory,” Phys. Rev. Lett. 126 no. 20, (2021) 201103, arXiv:2101.12688 [gr-qc].
- S. Mougiakakos, M. M. Riva, and F. Vernizzi, “Gravitational Bremsstrahlung in the post-Minkowskian effective field theory,” Phys. Rev. D 104 no. 2, (2021) 024041, arXiv:2102.08339 [gr-qc].
- E. Herrmann, J. Parra-Martinez, M. S. Ruf, and M. Zeng, “Gravitational Bremsstrahlung from Reverse Unitarity,” Phys. Rev. Lett. 126 no. 20, (2021) 201602, arXiv:2101.07255 [hep-th].
- E. Herrmann, J. Parra-Martinez, M. S. Ruf, and M. Zeng, “Radiative classical gravitational observables at 𝒪𝒪\mathcal{O}caligraphic_O(G3) from scattering amplitudes,” JHEP 10 (2021) 148, arXiv:2104.03957 [hep-th].
- D. Bini, T. Damour, and A. Geralico, “Radiative contributions to gravitational scattering,” Phys. Rev. D 104 no. 8, (2021) 084031, arXiv:2107.08896 [gr-qc].
- M. M. Riva and F. Vernizzi, “Radiated momentum in the post-Minkowskian worldline approach via reverse unitarity,” JHEP 11 (2021) 228, arXiv:2110.10140 [hep-th].
- G. Veneziano and G. A. Vilkovisky, “Angular momentum loss in gravitational scattering, radiation reaction, and the Bondi gauge ambiguity,” Phys. Lett. B 834 (2022) 137419, arXiv:2201.11607 [gr-qc].
- A. V. Manohar, A. K. Ridgway, and C.-H. Shen, “Radiated Angular Momentum and Dissipative Effects in Classical Scattering,” Phys. Rev. Lett. 129 no. 12, (2022) 121601, arXiv:2203.04283 [hep-th].
- P. Di Vecchia, C. Heissenberg, and R. Russo, “Angular momentum of zero-frequency gravitons,” JHEP 08 (2022) 172, arXiv:2203.11915 [hep-th].
- D. Bini, T. Damour, and A. Geralico, “Radiated momentum and radiation reaction in gravitational two-body scattering including time-asymmetric effects,” Phys. Rev. D 107 no. 2, (2023) 024012, arXiv:2210.07165 [gr-qc].
- D. Bini and T. Damour, “Radiation-reaction and angular momentum loss at the second post-Minkowskian order,” Phys. Rev. D 106 no. 12, (2022) 124049, arXiv:2211.06340 [gr-qc].
- C. Heissenberg, “Angular Momentum Loss due to Tidal Effects in the Post-Minkowskian Expansion,” Phys. Rev. Lett. 131 no. 1, (2023) 011603, arXiv:2210.15689 [hep-th].
- C. Heissenberg, “Angular momentum loss due to spin-orbit effects in the post-Minkowskian expansion,” Phys. Rev. D 108 no. 10, (2023) 106003, arXiv:2308.11470 [hep-th].
- H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, “Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems,” Proc. Roy. Soc. Lond. A 269 (1962) 21–52.
- R. K. Sachs, “Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times,” Proc. Roy. Soc. Lond. A 270 (1962) 103–126.
- E. T. Newman and R. Penrose, “10 exact gravitationally-conserved quantities,” Phys. Rev. Lett. 15 (1965) 231–233.
- E. T. Newman and R. Penrose, “New conservation laws for zero rest-mass fields in asymptotically flat space-time,” Proc. Roy. Soc. Lond. A 305 (1968) 175–204.
- J. Winicour, “Some Total Invariants of Asymptotically Flat Space‐Times,” J. Math. Phys. 9 (1968) 861–867.
- R. Geroch, “Asymptotic Structure of Space-Time,” in Symposium on Asymptotic Structure of Space-Time. 1977.
- C. R. Prior, “Angular Momentum in General Relativity. I. Definition and Asymptotic Behaviour,” Proc. Roy. Soc. Lond. A 354 (1977) 379–405.
- A. Ashtekar and R. O. Hansen, “A unified treatment of null and spatial infinity in general relativity. I - Universal structure, asymptotic symmetries, and conserved quantities at spatial infinity,” J. Math. Phys. 19 (1978) 1542–1566.
- A. Ashtekar and A. Magnon-Ashtekar, “Energy-Momentum in General Relativity,” Phys. Rev. Lett. 43 no. 3, (1979) 181.
- A. Ashtekar and M. Streubel, “On angular momentum of stationary gravitating systems,” J. Math. Phys. 20 no. 7, (1979) 1362–1365.
- A. Ashtekar and M. Streubel, “Symplectic Geometry of Radiative Modes and Conserved Quantities at Null Infinity,” Proc. Roy. Soc. Lond. A 376 (1981) 585–607.
- R. P. Geroch and J. Winicour, “Linkages in general relativity,” J. Math. Phys. 22 (1981) 803–812.
- T. Dray and M. Streubel, “Angular momentum at null infinity,” Class. Quant. Grav. 1 no. 1, (1984) 15–26.
- G. Barnich and C. Troessaert, “BMS charge algebra,” JHEP 12 (2011) 105, arXiv:1106.0213 [hep-th].
- E. E. Flanagan and D. A. Nichols, “Conserved charges of the extended Bondi-Metzner-Sachs algebra,” Phys. Rev. D 95 no. 4, (2017) 044002, arXiv:1510.03386 [hep-th]. [Erratum: Phys.Rev.D 108, 069902 (2023)].
- G. Compère, R. Oliveri, and A. Seraj, “The Poincaré and BMS flux-balance laws with application to binary systems,” JHEP 10 (2020) 116, arXiv:1912.03164 [gr-qc].
- L. Blanchet, G. Compère, G. Faye, R. Oliveri, and A. Seraj, “Multipole expansion of gravitational waves: from harmonic to Bondi coordinates,” JHEP 02 (2021) 029, arXiv:2011.10000 [gr-qc].
- L. Blanchet, G. Compère, G. Faye, R. Oliveri, and A. Seraj, “Multipole expansion of gravitational waves: memory effects and Bondi aspects,” JHEP 07 (2023) 123, arXiv:2303.07732 [gr-qc].
- R. Javadinezhad and M. Porrati, “Supertranslation-Invariant Formula for the Angular Momentum Flux in Gravitational Scattering,” Phys. Rev. Lett. 130 no. 1, (2023) 011401, arXiv:2211.06538 [gr-qc].
- A. Ashtekar and N. Khera, “Unified treatment of null and spatial infinity III: asymptotically minkowski space-times,” JHEP 02 (2024) 210, arXiv:2311.14130 [gr-qc].
- A. Ashtekar and N. Khera, “Unified treatment of null and spatial infinity IV: angular momentum at null and spatial infinity,” JHEP 01 (2024) 085, arXiv:2311.14190 [gr-qc].
- G. Compère, S. E. Gralla, and H. Wei, “An asymptotic framework for gravitational scattering,” Class. Quant. Grav. 40 no. 20, (2023) 205018, arXiv:2303.17124 [gr-qc].
- B. Bonga and E. Poisson, “Coulombic contribution to angular momentum flux in general relativity,” Phys. Rev. D 99 no. 6, (2019) 064024, arXiv:1808.01288 [gr-qc].
- R. Sachs, “Asymptotic symmetries in gravitational theory,” Phys. Rev. 128 (1962) 2851–2864.
- G. Barnich and F. Brandt, “Covariant theory of asymptotic symmetries, conservation laws and central charges,” Nucl. Phys. B 633 (2002) 3–82, arXiv:hep-th/0111246.
- R. Penrose, “Some unsolved problems in classical general relativity,” in Seminar on Differential Geometry, S.-T. Yau, ed., pp. 631–668. Princeton Univ. Press, Princeton, 1982.
- J. Winicour, “Angular momentum in general relativity,” in General Relativity and Gravitation:One Hundred Years After the Birth of Albert Einstein. Volume 2, A. Held, ed., pp. 71–96. Plenum Press, New York, 1980.
- A. Ashtekar, T. De Lorenzo, and N. Khera, “Compact binary coalescences: The subtle issue of angular momentum,” Phys. Rev. D 101 no. 4, (2020) 044005, arXiv:1910.02907 [gr-qc].
- P. Mao, J.-B. Wu, and X. Wu, “Angular momentum and memory effect,” Phys. Rev. D 107 no. 10, (2023) L101501, arXiv:2301.08032 [gr-qc].
- M. M. Riva, F. Vernizzi, and L. K. Wong, “Angular momentum balance in gravitational two-body scattering: Flux, memory, and supertranslation invariance,” Phys. Rev. D 108 no. 10, (2023) 104052, arXiv:2302.09065 [gr-qc].
- R. Javadinezhad and M. Porrati, “Three Puzzles with Covariance and Supertranslation Invariance of Angular Momentum Flux and Their Solutions,” Phys. Rev. Lett. 132 no. 15, (2024) 151604, arXiv:2312.02458 [hep-th].
- G. Compère and J. Long, “Vacua of the gravitational field,” JHEP 07 (2016) 137, arXiv:1601.04958 [hep-th].
- P. Mao, “Gravitational vacua in Newman-Penrose formalism,” arXiv:2402.12131 [hep-th].
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.