Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Unifying Ordinary and Null Memory (2401.05936v2)

Published 11 Jan 2024 in gr-qc, astro-ph.CO, hep-ph, and hep-th

Abstract: Based on a recently proposed reinterpretation of gravitational wave memory that builds up on the definition of gravitational waves pioneered by Isaacson, we provide a unifying framework to derive both ordinary and null memory from a single well-defined equation at leading order in the asymptotic expansion. This allows us to formulate a memory equation that is valid for any unbound asymptotic energy-flux that preserves local Lorentz invariance. Using Horndeski gravity as a concrete example metric theory with an additional potentially massive scalar degree of freedom in the gravitational sector, the general memory formula is put into practice by presenting the first account of the memory correction sourced by the emission of massive field waves. Throughout the work, physical degrees of freedom are identified by constructing manifestly gauge invariant perturbation variables within an SVT decomposition on top of the asymptotic Minkowski background, which will in particular prove useful in future studies of gravitational wave memory within vector tensor theories.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (94)
  1. D. Lovelock, “The uniqueness of the Einstein field equations in a four-dimensional space,” Archive for Rational Mechanics and Analysis 33 no. 1, (1969) 54–70.
  2. R. H. Dicke, “Experimental relativity,” in Les Houches Summer Shcool of Theoretical Physics: Relativity, Groups and Topology, pp. 165–316. 1964.
  3. Cambridge University Press, 2014.
  4. T. P. Sotiriou, “Gravity and Scalar Fields,” in Modifications of Einstein’s Theory of Gravity at Large Distances, E. Papantonopoulos, ed., pp. 3–24. Springer International Publishing, Cham, 2015.
  5. C. M. Will, “The Confrontation between General Relativity and Experiment,” Living Rev. Rel. 17 (2014) 4, arXiv:1403.7377 [gr-qc].
  6. L. Heisenberg, “A systematic approach to generalisations of General Relativity and their cosmological implications,” Phys. Rept. 796 (2019) 1–113, arXiv:1807.01725 [gr-qc].
  7. C. M. Will, Theory and Experiment in Gravitational Physics. Cambridge University Press, 2 ed., 2018.
  8. M. Coleman Miller and N. Yunes, Gravitational Waves in Physics and Astrophysics. IOP, 12, 2021.
  9. L. Heisenberg, N. Yunes, and J. Zosso, “Gravitational wave memory beyond general relativity,” Phys. Rev. D 108 no. 2, (2023) 024010, arXiv:2303.02021 [gr-qc].
  10. G. W. Horndeski, “Second-order scalar-tensor field equations in a four-dimensional space,” Int. J. Theor. Phys. 10 (1974) 363–384.
  11. A. Nicolis, R. Rattazzi, and E. Trincherini, “The Galileon as a local modification of gravity,” Phys. Rev. D 79 (2009) 064036, arXiv:0811.2197 [hep-th].
  12. C. Deffayet, G. Esposito-Farese, and A. Vikman, “Covariant Galileon,” Phys. Rev. D 79 (2009) 084003, arXiv:0901.1314 [hep-th].
  13. C. Deffayet, S. Deser, and G. Esposito-Farese, “Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress-tensors,” Phys. Rev. D 80 (2009) 064015, arXiv:0906.1967 [gr-qc].
  14. T. Kobayashi, “Horndeski theory and beyond: a review,” Rept. Prog. Phys. 82 no. 8, (2019) 086901, arXiv:1901.07183 [gr-qc].
  15. M. Ostrogradsky, “Mémoires sur les équations différentielles, relatives au problème des isopérimètres,” Mem. Acad. St. Petersbourg 6 no. 4, (1850) 385–517.
  16. R. P. Woodard, “Ostrogradsky’s theorem on Hamiltonian instability,” Scholarpedia 10 no. 8, (2015) 32243, arXiv:1506.02210 [hep-th].
  17. 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].
  18. LIGO Scientific, Virgo Collaboration, B. P. Abbott et al., “Tests of general relativity with GW150914,” Phys. Rev. Lett. 116 no. 22, (2016) 221101, arXiv:1602.03841 [gr-qc]. [Erratum: Phys.Rev.Lett. 121, 129902 (2018)].
  19. Y. B. Zel’dovich and A. G. Polnarev, “Radiation of gravitational waves by a cluster of superdense stars,” Sov. Astron. 18 (1974) 17.
  20. M. Turner, “Gravitational radiation from point-masses in unbound orbits: Newtonian results,” Astrophysical Journal 216 (1977) 610–619.
  21. V. B. Braginsky and L. P. Grishchuk, “Kinematic Resonance and Memory Effect in Free Mass Gravitational Antennas,” Sov. Phys. JETP 62 (1985) 427–430.
  22. V. Braginsky and K. Thorne, “Gravitational-wave bursts with memory and experimental prospects,” Nature 327 (1987) 123–125.
  23. D. Christodoulou, “Nonlinear nature of gravitation and gravitational wave experiments,” Phys. Rev. Lett. 67 (1991) 1486–1489.
  24. M. Ludvigsen, “Geodesic deviation at null infinity and the physical effects of very long wave gravitational radiation,” General Relativity and Gravitation 21 (1989) 1205–1212.
  25. L. Blanchet and T. Damour, “Hereditary effects in gravitational radiation,” Phys. Rev. D 46 (1992) 4304–4319.
  26. J. Frauendiener, “Note on the memory effect,” Class. Quant. Grav. 9 (06, 1992) 1639–1641.
  27. K. S. Thorne, “Gravitational-wave bursts with memory: The Christodoulou effect,” Phys. Rev. D 45 no. 2, (1992) 520–524.
  28. A. G. Wiseman and C. M. Will, “Christodoulou’s nonlinear gravitational-wave memory: Evaluation in the quadrupole approximation,” Phys. Rev. D 44 (Nov, 1991) R2945–R2949.
  29. M. Favata, “Post-Newtonian corrections to the gravitational-wave memory for quasi-circular, inspiralling compact binaries,” Phys. Rev. D 80 (2009) 024002, arXiv:0812.0069 [gr-qc].
  30. M. Favata, “Gravitational-wave memory revisited: memory from the merger and recoil of binary black holes,” J. Phys. Conf. Ser. 154 (2009) 012043, arXiv:0811.3451 [astro-ph].
  31. M. Favata, “Nonlinear gravitational-wave memory from binary black hole mergers,” Astrophys. J. Lett. 696 (2009) L159–L162, arXiv:0902.3660 [astro-ph.SR].
  32. M. Favata, “The gravitational-wave memory effect,” Class. Quant. Grav. 27 (2010) 084036, arXiv:1003.3486 [gr-qc].
  33. L. Bieri and D. Garfinkle, “Perturbative and gauge invariant treatment of gravitational wave memory,” Phys. Rev. D 89 no. 8, (2014) 084039, arXiv:1312.6871 [gr-qc].
  34. A. Ashtekar, “Geometry and Physics of Null Infinity,” arXiv:1409.1800 [gr-qc].
  35. A. Strominger, “Lectures on the Infrared Structure of Gravity and Gauge Theory,” arXiv:1703.05448 [hep-th].
  36. G. Compère, Advanced Lectures on General Relativity. Springer Cham, 2019.
  37. D. Garfinkle, “Gravitational wave memory and the wave equation,” Class. Quant. Grav. 39 no. 13, (2022) 135010, arXiv:2201.05543 [gr-qc].
  38. F. D’Ambrosio, S. D. B. Fell, L. Heisenberg, D. Maibach, S. Zentarra, and J. Zosso, “Gravitational Waves in Full, Non-Linear General Relativity,” arXiv:2201.11634 [gr-qc].
  39. 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.
  40. R. K. Sachs, “Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times,” Proc. Roy. Soc. Lond. A 270 (1962) 103–126.
  41. Springer US, Boston, MA, 1977.
  42. 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.
  43. A. Strominger and A. Zhiboedov, “Gravitational Memory, BMS Supertranslations and Soft Theorems,” JHEP 01 (2016) 086, arXiv:1411.5745 [hep-th].
  44. A. Tolish and R. M. Wald, “Retarded Fields of Null Particles and the Memory Effect,” Phys. Rev. D 89 no. 6, (2014) 064008, arXiv:1401.5831 [gr-qc].
  45. A. Tolish, L. Bieri, D. Garfinkle, and R. M. Wald, “Examination of a simple example of gravitational wave memory,” Phys. Rev. D 90 no. 4, (2014) 044060, arXiv:1405.6396 [gr-qc].
  46. 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].
  47. A. D. Johnson, S. J. Kapadia, A. Osborne, A. Hixon, and D. Kennefick, “Prospects of detecting the nonlinear gravitational wave memory,” Phys. Rev. D 99 no. 4, (2019) 044045, arXiv:1810.09563 [gr-qc].
  48. H. Yang and D. Martynov, “Testing Gravitational Memory Generation with Compact Binary Mergers,” Phys. Rev. Lett. 121 no. 7, (2018) 071102, arXiv:1803.02429 [gr-qc].
  49. K. Islo, J. Simon, S. Burke-Spolaor, and X. Siemens, “Prospects for Memory Detection with Low-Frequency Gravitational Wave Detectors,” arXiv:1906.11936 [astro-ph.HE].
  50. M. Hübner, C. Talbot, P. D. Lasky, and E. Thrane, “Measuring gravitational-wave memory in the first LIGO/Virgo gravitational-wave transient catalog,” Phys. Rev. D 101 no. 2, (2020) 023011, arXiv:1911.12496 [astro-ph.HE].
  51. L. M. Burko and G. Khanna, “Climbing up the memory staircase: Equatorial zoom-whirl orbits,” Phys. Rev. D 102 no. 8, (2020) 084035, arXiv:2007.12545 [gr-qc].
  52. M. Ebersold and S. Tiwari, “Search for nonlinear memory from subsolar mass compact binary mergers,” Phys. Rev. D 101 no. 10, (2020) 104041, arXiv:2005.03306 [gr-qc].
  53. M. Hübner, P. Lasky, and E. Thrane, “Memory remains undetected: Updates from the second LIGO/Virgo gravitational-wave transient catalog,” Phys. Rev. D 104 no. 2, (2021) 023004, arXiv:2105.02879 [gr-qc].
  54. T. Islam, S. E. Field, G. Khanna, and N. Warburton, “Survey of gravitational wave memory in intermediate mass ratio binaries,” arXiv:2109.00754 [gr-qc].
  55. S. Sun, C. Shi, J.-d. Zhang, and J. Mei, “Detecting the gravitational wave memory effect with TianQin,” Phys. Rev. D 107 no. 4, (2023) 044023, arXiv:2207.13009 [gr-qc].
  56. LISA Collaboration, K. G. Arun et al., “New horizons for fundamental physics with LISA,” Living Rev. Rel. 25 no. 1, (2022) 4, arXiv:2205.01597 [gr-qc].
  57. A. M. Grant and D. A. Nichols, “Outlook for detecting the gravitational-wave displacement and spin memory effects with current and future gravitational-wave detectors,” Phys. Rev. D 107 no. 6, (2023) 064056, arXiv:2210.16266 [gr-qc]. [Erratum: Phys.Rev.D 108, 029901 (2023)].
  58. S. Gasparotto, R. Vicente, D. Blas, A. C. Jenkins, and E. Barausse, “Can gravitational-wave memory help constrain binary black-hole parameters? A LISA case study,” Phys. Rev. D 107 no. 12, (2023) 124033, arXiv:2301.13228 [gr-qc].
  59. S. Ghosh, A. Weaver, J. Sanjuan, P. Fulda, and G. Mueller, “Detection of the gravitational memory effect in LISA using triggers from ground-based detectors,” Phys. Rev. D 107 no. 8, (2023) 084051, arXiv:2302.04396 [gr-qc].
  60. B. Goncharov, L. Donnay, and J. Harms, “Inferring fundamental spacetime symmetries with gravitational-wave memory: from LISA to the Einstein Telescope,” arXiv:2310.10718 [gr-qc].
  61. M. Punturo et al., “The Einstein Telescope: A third-generation gravitational wave observatory,” Class. Quant. Grav. 27 (2010) 194002.
  62. M. Maggiore et al., “Science Case for the Einstein Telescope,” JCAP 03 (2020) 050, arXiv:1912.02622 [astro-ph.CO].
  63. D. Reitze et al., “Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO,” Bull. Am. Astron. Soc. 51 no. 7, (2019) 035, arXiv:1907.04833 [astro-ph.IM].
  64. M. Evans et al., “A Horizon Study for Cosmic Explorer: Science, Observatories, and Community,” arXiv:2109.09882 [astro-ph.IM].
  65. P. Amaro-Seoane et al., “Laser Interferometer Space Antenna,” arXiv:1702.00786 [astro-ph.IM].
  66. R. A. Isaacson, “Gravitational Radiation in the Limit of High Frequency. I. The Linear Approximation and Geometrical Optics,” Phys. Rev. 166 (Feb, 1968) 1263–1271.
  67. R. A. Isaacson, “Gravitational Radiation in the Limit of High Frequency. II. Nonlinear Terms and the Effective Stress Tensor,” Phys. Rev. 166 (Feb, 1968) 1272–1280.
  68. T. Kobayashi, M. Yamaguchi, and J. Yokoyama, “Generalized G-inflation: Inflation with the most general second-order field equations,” Prog. Theor. Phys. 126 (2011) 511–529, arXiv:1105.5723 [hep-th].
  69. C. Brans and R. H. Dicke, “Mach’s principle and a relativistic theory of gravitation,” Phys. Rev. 124 (1961) 925–935.
  70. R. H. Dicke, “Mach’s principle and invariance under transformation of units,” Phys. Rev. 125 (1962) 2163–2167.
  71. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley, 1972.
  72. P. G. Bergmann, “Comments on the scalar-tensor theory,” International Journal of Theoretical Physics 1 (1968) 25–36.
  73. T. V. Ruzmaǐkina and A. A. Ruzmaǐkin, “Quadratic Corrections to the Lagrangian Density of the Gravitational Field and the Singularity,” Soviet Journal of Experimental and Theoretical Physics 30 (Jan., 1969) 372.
  74. H. A. Buchdahl, “Non-linear Lagrangians and cosmological theory,” Monthly Notices of the Royal Astronomical Society 150 (Jan., 1970) 1.
  75. T. P. Sotiriou and V. Faraoni, “f(R) Theories Of Gravity,” Rev. Mod. Phys. 82 (2010) 451–497, arXiv:0805.1726 [gr-qc].
  76. A. De Felice and S. Tsujikawa, “f(R) theories,” Living Rev. Rel. 13 (2010) 3, arXiv:1002.4928 [gr-qc].
  77. B. Zwiebach, “Curvature Squared Terms and String Theories,” Phys. Lett. B 156 (1985) 315–317.
  78. D. J. Gross and E. Witten, “Superstring Modifications of Einstein’s Equations,” Nucl. Phys. B 277 (1986) 1.
  79. W. H. Freeman, San Francisco, 1973.
  80. J. M. Stewart and M. Walker, “Perturbations of spacetimes in general relativity,” Proc. Roy. Soc. Lond. A 341 (1974) 49–74.
  81. R. M. Wald, General Relativity. Chicago Univ. Pr., Chicago, USA, 1984.
  82. V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger, “Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions,” Phys. Rept. 215 (1992) 203–333.
  83. S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity. Cambridge University Press, 2019.
  84. E. E. Flanagan and S. A. Hughes, “The Basics of gravitational wave theory,” New J. Phys. 7 (2005) 204, arXiv:gr-qc/0501041.
  85. M. Maggiore, Gravitational Waves: Volume 1: Theory and Experiments. Oxford University Press, 10, 2007.
  86. L. C. Stein and N. Yunes, “Effective Gravitational Wave Stress-energy Tensor in Alternative Theories of Gravity,” Phys. Rev. D 83 (2011) 064038, arXiv:1012.3144 [gr-qc].
  87. S. Hou, Y. Gong, and Y. Liu, “Polarizations of Gravitational Waves in Horndeski Theory,” Eur. Phys. J. C 78 no. 5, (2018) 378, arXiv:1704.01899 [gr-qc].
  88. H. O. Silva, J. Sakstein, L. Gualtieri, T. P. Sotiriou, and E. Berti, “Spontaneous scalarization of black holes and compact stars from a Gauss-Bonnet coupling,” Phys. Rev. Lett. 120 no. 13, (2018) 131104, arXiv:1711.02080 [gr-qc].
  89. H. O. Silva, H. Witek, M. Elley, and N. Yunes, “Dynamical Descalarization in Binary Black Hole Mergers,” Phys. Rev. Lett. 127 no. 3, (2021) 031101, arXiv:2012.10436 [gr-qc].
  90. M. Elley, H. O. Silva, H. Witek, and N. Yunes, “Spin-induced dynamical scalarization, descalarization, and stealthness in scalar-Gauss-Bonnet gravity during a black hole coalescence,” Phys. Rev. D 106 no. 4, (2022) 044018, arXiv:2205.06240 [gr-qc].
  91. J. C. Degollado and C. A. R. Herdeiro, “Wiggly tails: a gravitational wave signature of massive fields around black holes,” Phys. Rev. D 90 no. 6, (2014) 065019, arXiv:1408.2589 [gr-qc].
  92. H. Okawa, H. Witek, and V. Cardoso, “Black holes and fundamental fields in Numerical Relativity: initial data construction and evolution of bound states,” Phys. Rev. D 89 no. 10, (2014) 104032, arXiv:1401.1548 [gr-qc].
  93. D. D. Doneva, K. V. Staykov, and S. S. Yazadjiev, “Gauss-Bonnet black holes with a massive scalar field,” Phys. Rev. D 99 no. 10, (2019) 104045, arXiv:1903.08119 [gr-qc].
  94. C. Richards, A. Dima, and H. Witek, “Black holes in massive dynamical Chern-Simons gravity: Scalar hair and quasibound states at decoupling,” Phys. Rev. D 108 no. 4, (2023) 044078, arXiv:2305.07704 [gr-qc].
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets