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Classical Kerr-Schild double copy in bigravity for maximally symmetric spacetimes

Published 28 Mar 2024 in gr-qc and hep-th | (2403.19608v3)

Abstract: A generalized Kerr-Schild ansatz for bigravity, already considered in the literature, which leads to linear interactions between the metrics is used to study the bigravity equations in the context of the double copy. By contracting the resulting spin-2 field bigravity equations of motion using Killing vector fields, as is usually carried out in general relativity, we arrive to the single and zeroth copy equations for the mentioned ansatz. For the case of stationary solutions, we obtain two Maxwell and two conformally coupled scalar field equations for the single and zeroth copies respectively, and the linear interactions are absent. In the time-dependent case we obtain equations for the fields which are coupled. By decoupling these equations and at the zeroth copy level, we recover a massless and a massive field whose mass is proportional to the Fierz-Pauli mass and depends on the coefficients of the interaction potential between the metrics. This has been also previously documented in the literature and is now reinterpreted within the context of the double copy proposal.

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References (45)
  1. S. N. Gupta, “Gravitation and Electromagnetism,” Phys. Rev. 96, 1683-1685 (1954) doi:10.1103/PhysRev.96.1683
  2. S. Weinberg, “Photons and gravitons in perturbation theory: Derivation of Maxwell’s and Einstein’s equations,” Phys. Rev. 138, B988-B1002 (1965) doi:10.1103/PhysRev.138.B988
  3. Z. Bern, J. J. M. Carrasco and H. Johansson, “New Relations for Gauge-Theory Amplitudes,” Phys. Rev. D 78, 085011 (2008) doi:10.1103/PhysRevD.78.085011 [arXiv:0805.3993 [hep-ph]].
  4. Z. Bern, T. Dennen, Y. t. Huang and M. Kiermaier, “Gravity as the Square of Gauge Theory,” Phys. Rev. D 82, 065003 (2010) doi:10.1103/PhysRevD.82.065003 [arXiv:1004.0693 [hep-th]].
  5. Z. Bern, J. J. M. Carrasco and H. Johansson, “Perturbative Quantum Gravity as a Double Copy of Gauge Theory,” Phys. Rev. Lett. 105, 061602 (2010) doi:10.1103/PhysRevLett.105.061602 [arXiv:1004.0476 [hep-th]].
  6. R. Monteiro, D. O’Connell and C. D. White, “Black holes and the double copy,” JHEP 12, 056 (2014) doi:10.1007/JHEP12(2014)056 [arXiv:1410.0239 [hep-th]].
  7. A. Luna, R. Monteiro, D. O’Connell and C. D. White, “The classical double copy for Taub–NUT spacetime,” Phys. Lett. B 750, 272-277 (2015) doi:10.1016/j.physletb.2015.09.021 [arXiv:1507.01869 [hep-th]].
  8. A. K. Ridgway and M. B. Wise, “Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy,” Phys. Rev. D 94, no.4, 044023 (2016) doi:10.1103/PhysRevD.94.044023 [arXiv:1512.02243 [hep-th]].
  9. A. Luna, R. Monteiro, I. Nicholson, D. O’Connell and C. D. White, “The double copy: Bremsstrahlung and accelerating black holes,” JHEP 06, 023 (2016) doi:10.1007/JHEP06(2016)023 [arXiv:1603.05737 [hep-th]].
  10. N. Bahjat-Abbas, A. Luna and C. D. White, “The Kerr-Schild double copy in curved spacetime,” JHEP 12, 004 (2017) doi:10.1007/JHEP12(2017)004 [arXiv:1710.01953 [hep-th]].
  11. M. Carrillo-González, R. Penco and M. Trodden, “The classical double copy in maximally symmetric spacetimes,” JHEP 04, 028 (2018) doi:10.1007/JHEP04(2018)028 [arXiv:1711.01296 [hep-th]].
  12. Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson and R. Roiban, “The duality between color and kinematics and its applications,” [arXiv:1909.01358 [hep-th]].
  13. G. Alkac, M. K. Gumus and M. Tek, “The Kerr-Schild Double Copy in Lifshitz Spacetime,” JHEP 05 (2021), 214 doi:10.1007/JHEP05(2021)214 [arXiv:2103.06986 [hep-th]].
  14. R. P. Kerr and A. Schild, “Some algebraically degenerate solutions of Einstein’s gravitational field equations,” Proc. Symp. Appl. Math. 17, 199 (1965)
  15. A. Luna, R. Monteiro, I. Nicholson and D. O’Connell, “Type D spacetimes and the Weyl double copy,” Class. Quant. Grav. 36, 065003 (2019) doi:10.1088/1361-6382/ab03e6 [arXiv:1810.08183 [hep-th]]. 98 citations counted in INSPIRE as of 21 Oct 2022
  16. S. Sabharwal and J. W. Dalhuisen, “Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor,” JHEP 07, 004 (2019) doi:10.1007/JHEP07(2019)004 [arXiv:1904.06030 [hep-th]].
  17. R. Alawadhi, D. S. Berman and B. Spence, “Weyl doubling,” JHEP 09, 127 (2020) doi:10.1007/JHEP09(2020)127 [arXiv:2007.03264 [hep-th]].
  18. H. Godazgar, M. Godazgar, R. Monteiro, D. Peinador Veiga and C. N. Pope, “Weyl Double Copy for Gravitational Waves,” Phys. Rev. Lett. 126, no.10, 101103 (2021) doi:10.1103/PhysRevLett.126.101103 [arXiv:2010.02925 [hep-th]].
  19. C. D. White, “Twistorial foundation for the classical double copy,” Phys. Rev. Lett. 126, no.6, 061602 (2021) doi:10.1103/PhysRevLett.126.061602 [arXiv:2012.02479 [hep-th]].
  20. E. Chacón, S. Nagy and C. D. White, “The Weyl double copy from twistor space,” JHEP 05, 2239 (2021) doi:10.1007/JHEP05(2021)239 [arXiv:2103.16441 [hep-th]].
  21. E. Chacón, A. Luna and C. D. White, “Double copy of the multipole expansion,” Phys. Rev. D 106, no.8, 086020 (2022) doi:10.1103/PhysRevD.106.086020 [arXiv:2108.07702 [hep-th]].
  22. E. Chacón, S. Nagy and C. D. White, “Alternative formulations of the twistor double copy,” JHEP 03, 180 (2022) doi:10.1007/JHEP03(2022)180 [arXiv:2112.06764 [hep-th]].
  23. A. Luna, N. Moynihan and C. D. White, “Why is the Weyl double copy local in position space?,” JHEP 12, 046 (2022) doi:10.1007/JHEP12(2022)046 [arXiv:2208.08548 [hep-th]].
  24. C. de Rham, “Massive Gravity,” Living Rev. Rel. 17, 7 (2014) doi:10.12942/lrr-2014-7 [arXiv:1401.4173 [hep-th]].
  25. S. F. Hassan and R. A. Rosen, “Bimetric Gravity from Ghost-free Massive Gravity,” JHEP 02, 126 (2012) doi:10.1007/JHEP02(2012)126 [arXiv:1109.3515 [hep-th]].
  26. S. F. Hassan and R. A. Rosen, “On Non-Linear Actions for Massive Gravity,” JHEP 07, 009 (2011) doi:10.1007/JHEP07(2011)009 [arXiv:1103.6055 [hep-th]].
  27. M. Banados, A. Gomberoff and M. Pino, “The bigravity black hole and its thermodynamics,” Phys. Rev. D 84, 104028 (2011) doi:10.1103/PhysRevD.84.104028 [arXiv:1105.1172 [gr-qc]].
  28. C. Deffayet and S. Randjbar-Daemi, “Non linear Fierz-Pauli theory from torsion and bigravity,” Phys. Rev. D 84, 044053 (2011) doi:10.1103/PhysRevD.84.044053 [arXiv:1103.2671 [hep-th]].
  29. L. Pilo, “Bigravity as a tool for massive gravity,” PoS EPS-HEP2011, 076 (2011) doi:10.22323/1.134.0076
  30. D. Comelli, M. Crisostomi, F. Nesti and L. Pilo, “Spherically Symmetric Solutions in Ghost-Free Massive Gravity,” Phys. Rev. D 85, 024044 (2012) doi:10.1103/PhysRevD.85.024044 [arXiv:1110.4967 [hep-th]].
  31. M. S. Volkov, “Hairy black holes in the ghost-free bigravity theory,” Phys. Rev. D 85, 124043 (2012) doi:10.1103/PhysRevD.85.124043 [arXiv:1202.6682 [hep-th]].
  32. D. Comelli, M. Crisostomi and L. Pilo, “FRW Cosmological Perturbations in Massive Bigravity,” Phys. Rev. D 90, 084003 (2014) doi:10.1103/PhysRevD.90.084003 [arXiv:1403.5679 [hep-th]].
  33. D. Comelli, M. Crisostomi, K. Koyama, L. Pilo and G. Tasinato, “Cosmology of bigravity with doubly coupled matter,” JCAP 04, 026 (2015) doi:10.1088/1475-7516/2015/04/026 [arXiv:1501.00864 [hep-th]].
  34. E. Ayón-Beato, D. Higuita-Borja and J. A. Méndez-Zavaleta, “Rotating (A)dS black holes in bigravity,” Phys. Rev. D 93, no.2, 024049 (2016) doi:10.1103/PhysRevD.93.024049 [arXiv:1511.01108 [hep-th]].
  35. E. Ayón-Beato, D. Higuita-Borja, J. A. Méndez-Zavaleta and G. Velázquez-Rodríguez, “Exact ghost-free bigravitational waves,” Phys. Rev. D 97, no.8, 084045 (2018) doi:10.1103/PhysRevD.97.084045 [arXiv:1801.06764 [hep-th]].
  36. D. Lust, C. Markou, P. Mazloumi and S. Stieberger, “Extracting bigravity from string theory,” JHEP 12, 220 (2021) doi:10.1007/JHEP12(2021)220 [arXiv:2106.04614 [hep-th]].
  37. A. Momeni, J. Rumbutis and A. J. Tolley, “Massive Gravity from Double Copy,” JHEP 12, 030 (2020) doi:10.1007/JHEP12(2020)030 [arXiv:2004.07853 [hep-th]].
  38. L. A. Johnson, C. R. T. Jones and S. Paranjape, “Constraints on a Massive Double-Copy and Applications to Massive Gravity,” JHEP 02, 148 (2021) doi:10.1007/JHEP02(2021)148 [arXiv:2004.12948 [hep-th]].
  39. M. C. González, A. Momeni and J. Rumbutis, “Massive double copy in three spacetime dimensions,” JHEP 08, 116 (2021) doi:10.1007/JHEP08(2021)116 [arXiv:2107.00611 [hep-th]].
  40. M. Carrillo González, A. Momeni and J. Rumbutis, “Cotton double copy for gravitational waves,” Phys. Rev. D 106, no.2, 025006 (2022) doi:10.1103/PhysRevD.106.025006 [arXiv:2202.10476 [hep-th]].
  41. D. Lüst, C. Markou, P. Mazloumi and S. Stieberger, “A stringy massive double copy,” JHEP 08, 193 (2023) doi:10.1007/JHEP08(2023)193 [arXiv:2301.07110 [hep-th]].
  42. H. Stephani, D. Kramer, M. A. H. MacCallum, C. Hoenselaers and E. Herlt, “Exact solutions of Einstein’s field equations,” Cambridge Univ. Press, 2003, ISBN 978-0-521-46702-5, 978-0-511-05917-9 doi:10.1017/CBO9780511535185
  43. E. Babichev and R. Brito, “Black holes in massive gravity,” Class. Quant. Grav. 32, 154001 (2015) doi:10.1088/0264-9381/32/15/154001 [arXiv:1503.07529 [gr-qc]].
  44. E. Babichev and A. Fabbri, “Rotating black holes in massive gravity,” Phys. Rev. D 90, 084019 (2014) doi:10.1103/PhysRevD.90.084019 [arXiv:1406.6096 [gr-qc]].
  45. P. Breitenlohner and D. Z. Freedman, “Stability in Gauged Extended Supergravity,” Annals Phys. 144 (1982), 249 doi:10.1016/0003-4916(82)90116-6

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