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Boundary terms and Brown-York quasi-local parameters for scalar-tensor theory: a study on both timelike and null hypersurfaces (2307.06674v2)

Published 13 Jul 2023 in gr-qc and hep-th

Abstract: Boundary term and Brown-York (BY) formalism, which is based on the Hamilton-Jacobi principle, are complimentary of each other as the gravitational actions are not, usually, well-posed. In scalar-tensor theory, which is an important alternative to GR, it has been shown that this complementarity becomes even more crucial in establishing the equivalence of the BY quasi-local parameters in the two frames which are conformally connected. Furthermore, Brown-York tensor and the corresponding quasi-local parameters are important from two important yet different aspects of gravitational theories: black hole thermodynamics and fluid-gravity correspondence. The investigation suggests that while the two frames are equivalent from the thermodynamic viewpoints, they are not equivalent from the perspective of fluid-gravity analogy or the membrane paradigm. In addition, the null boundary term and null Brown-York formalism are the recent developments (so far obtained only for GR) which is non-trivial owing to the degeneracy of the null surface. In the present analysis these are extended for scalar-tensor theory. The present analysis also suggests that, regarding the equivalence (or inequivalence) of the two frame, the null formalism draws the same inferences as of the timelike case, which in turn establishes the consistency of the newly developed null Brown-York formalism.

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References (99)
  1. J. F. Donoghue, “Introduction to the effective field theory description of gravity,” [arXiv:gr-qc/9512024 [gr-qc]].
  2. J. F. Donoghue, “The effective field theory treatment of quantum gravity,” AIP Conf. Proc. 1483, 73-94 (2012) [arXiv:1209.3511 [gr-qc]].
  3. C. P. Burgess, “Quantum gravity in everyday life: General relativity as an effective field theory,” Living Rev. Rel. 7, 5-56 (2004) [arXiv:gr-qc/0311082 [gr-qc]].
  4. T. Damour, F. Piazza and G. Veneziano, “Runaway dilaton and equivalence principle violations,” Phys. Rev. Lett. 89, 081601 (2002) [arXiv:gr-qc/0204094 [gr-qc]].
  5. S. Nojiri and S. D. Odintsov, “Introduction to modified gravity and gravitational alternative for dark energy,” eConf C0602061, 06 (2006) [arXiv:hep-th/0601213 [hep-th]].
  6. V. Faraoni, “Cosmology in scalar tensor gravity,”
  7. E. J. Copeland, M. Sami and S. Tsujikawa, “Dynamics of dark energy,” Int. J. Mod. Phys. D 15, 1753-1936 (2006) [arXiv:hep-th/0603057 [hep-th]].
  8. E. Elizalde, S. Nojiri, S. D. Odintsov, D. Saez-Gomez and V. Faraoni, “Reconstructing the universe history, from inflation to acceleration, with phantom and canonical scalar fields,” Phys. Rev. D 77 (2008), 106005 [arXiv:0803.1311 [hep-th]].
  9. S. Nojiri and S. D. Odintsov, “Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models,” Phys. Rept. 505, 59-144 (2011) [arXiv:1011.0544 [gr-qc]].
  10. S. Nojiri, S. D. Odintsov and V. K. Oikonomou, “Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution,” Phys. Rept. 692, 1-104 (2017). [arXiv:1705.11098 [gr-qc]]
  11. K. Hinterbichler, “Theoretical Aspects of Massive Gravity,” Rev. Mod. Phys. 84, 671-710 (2012) [arXiv:1105.3735 [hep-th]].
  12. L. Amendola and S. Tsujikawa, “Dark Energy: Theory and Observations,” Cambridge University Press, 2015, ISBN 978-1-107-45398-2
  13. T. Clifton, P. G. Ferreira, A. Padilla and C. Skordis, “Modified Gravity and Cosmology,” Phys. Rept. 513, 1-189 (2012) [arXiv:1106.2476 [astro-ph.CO]].
  14. K. Nordtvedt, Jr., “PostNewtonian metric for a general class of scalar tensor gravitational theories and observational consequences,” Astrophys. J. 161, 1059-1067 (1970)
  15. A. Billyard, A. Coley and J. Ibanez, “On the asymptotic behavior of cosmological models in scalar tensor theories of gravity,” Phys. Rev. D 59, 023507 (1999) [arXiv:gr-qc/9807055 [gr-qc]].
  16. J. D. Barrow and P. Parsons, “The Behavior of cosmological models with varying G,” Phys. Rev. D 55, 1906-1936 (1997) [arXiv:gr-qc/9607072 [gr-qc]].
  17. J. P. Mimoso and D. Wands, “Anisotropic scalar - tensor cosmologies,” Phys. Rev. D 52, 5612-5627 (1995) [arXiv:gr-qc/9501039 [gr-qc]].
  18. J. D. Barrow and J. P. Mimoso, “Perfect fluid scalar - tensor cosmologies,” Phys. Rev. D 50, 3746-3754 (1994)
  19. N. Banerjee and S. Sen, “Does Brans-Dicke theory always yield general relativity in the infinite omega limit?,” Phys. Rev. D 56, 1334-1337 (1997)
  20. V. Faraoni, “Illusions of general relativity in Brans-Dicke gravity,” Phys. Rev. D 59, 084021 (1999) [arXiv:gr-qc/9902083 [gr-qc]].
  21. T. Matsuda, “On the gravitational collapse in brans-dicke theory of gravity,” Prog. Theor. Phys. 47, 738-740 (1972)
  22. C. Romero and A. Barros, “Brans-Dicke cosmology and the cosmological constant: the spectrum of vacuum solutions,” Astrophys. Space Sci. 192, 263-274 (1992)
  23. C. Romero and A. Barros, “Does Brans-Dicke theory of gravity go over to the general relativity when omega —>>> infinity?,” Phys. Lett. A 173, 243-246 (1993)
  24. C. Romero and A. Barros, “Brans-Dicke vacuum solutions and the cosmological constant: A Qualitative analysis,” Gen. Rel. Grav. 25, 491-502 (1993)
  25. F. M. Paiva, M. J. Reboucas and M. A. H. MacCallum, “On limits of space-times: A Coordinate - free approach,” Class. Quant. Grav. 10, 1165-1178 (1993) [arXiv:gr-qc/9302005 [gr-qc]].
  26. F. M. Paiva and C. Romero, “On the limits of Brans-Dicke space-times: A Coordinate - free approach,” Gen. Rel. Grav. 25, 1305-1317 (1993) [arXiv:gr-qc/9304030 [gr-qc]].
  27. M. A. Scheel, S. L. Shapiro and S. A. Teukolsky, “Collapse to black holes in Brans-Dicke theory. 2. Comparison with general relativity,” Phys. Rev. D 51, 4236-4249 (1995) [arXiv:gr-qc/9411026 [gr-qc]].
  28. L. A. Anchordoqui, D. F. Torres, M. L. Trobo and S. E. Perez Bergliaffa, “Evolving wormhole geometries,” Phys. Rev. D 57, 829-833 (1998) [arXiv:gr-qc/9710026 [gr-qc]].
  29. B. Bertotti, L. Iess and P. Tortora, “A test of general relativity using radio links with the Cassini spacecraft,” Nature 425, 374-376 (2003).
  30. D. Bettoni, J. M. Ezquiaga, K. Hinterbichler and M. Zumalacárregui, “Speed of Gravitational Waves and the Fate of Scalar-Tensor Gravity,” Phys. Rev. D 95, no.8, 084029 (2017) [arXiv:1608.01982 [gr-qc]].
  31. T. Baker, E. Bellini, P. G. Ferreira, M. Lagos, J. Noller and I. Sawicki, “Strong constraints on cosmological gravity from GW170817 and GRB 170817A,” Phys. Rev. Lett. 119, no.25, 251301 (2017) [arXiv:1710.06394 [astro-ph.CO]].
  32. J. Sakstein and B. Jain, “Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories,” Phys. Rev. Lett. 119, no.25, 251303 (2017) [arXiv:1710.05893 [astro-ph.CO]].
  33. V. Faraoni and E. Gunzig, “Einstein frame or Jordan frame?,” Int. J. Theor. Phys.  38, 217 (1999) [astro-ph/9910176].
  34. A. Macias and A. Garcia, “Jordan frame or Einstein frame?,” Gen. Rel. Grav. 33, 889 (2001).
  35. V. Faraoni, E. Gunzig and P. Nardone, “Conformal transformations in classical gravitational theories and in cosmology,” Fund. Cosmic Phys.  20, 121 (1999) [gr-qc/9811047].
  36. V. Faraoni, “Black hole entropy in scalar-tensor and f(R) gravity: An Overview,” Entropy 12, 1246 (2010) [arXiv:1005.2327 [gr-qc]].
  37. V. Faraoni and S. Nadeau, “The (pseudo)issue of the conformal frame revisited,” Phys. Rev. D 75, 023501 (2007) [gr-qc/0612075].
  38. I. D. Saltas and M. Hindmarsh, “The dynamical equivalence of modified gravity revisited,” Class. Quant. Grav.  28, 035002 (2011) [arXiv:1002.1710 [gr-qc]].
  39. S. Capozziello, P. Martin-Moruno and C. Rubano, “Physical non-equivalence of the Jordan and Einstein frames,” Phys. Lett. B 689, 117 (2010) [arXiv:1003.5394 [gr-qc]].
  40. A. Padilla and V. Sivanesan, “Boundary Terms and Junction Conditions for Generalized Scalar-Tensor Theories,” JHEP 1208, 122 (2012) [arXiv:1206.1258 [gr-qc]].
  41. J. i. Koga and K. i. Maeda, “Equivalence of black hole thermodynamics between a generalized theory of gravity and the Einstein theory,” Phys. Rev. D 58, 064020 (1998) [gr-qc/9803086].
  42. T. Jacobson and G. Kang, “Conformal invariance of black hole temperature,” Class. Quant. Grav.  10, L201 (1993) [gr-qc/9307002].
  43. G. Kang, “On black hole area in Brans-Dicke theory,” Phys. Rev. D 54, 7483 (1996) [gr-qc/9606020].
  44. S. Deser and B. Tekin, “Conformal Properties of Charges in Scalar-Tensor Gravities,” Class. Quant. Grav. 23, 7479-7482 (2006) [arXiv:gr-qc/0609111 [gr-qc]].
  45. M. H. Dehghani, J. Pakravan and S. H. Hendi, “Thermodynamics of charged rotating black branes in Brans-Dicke theory with quadratic scalar field potential,” Phys. Rev. D 74, 104014 (2006) [hep-th/0608197].
  46. A. Sheykhi and M. M. Yazdanpanah, “Thermodynamics of charged Brans-Dicke AdS black holes,” Phys. Lett. B 679, 311 (2009) [arXiv:0904.1777 [hep-th]].
  47. C. F. Steinwachs and A. Y. Kamenshchik, “One-loop divergences for gravity non-minimally coupled to a multiplet of scalar fields: calculation in the Jordan frame. I. The main results,” Phys. Rev. D 84, 024026 (2011) [arXiv:1101.5047 [gr-qc]].
  48. A. Y. Kamenshchik and C. F. Steinwachs, “Question of quantum equivalence between Jordan frame and Einstein frame,” Phys. Rev. D 91, no. 8, 084033 (2015) [arXiv:1408.5769 [gr-qc]].
  49. N. Banerjee and B. Majumder, “A question mark on the equivalence of Einstein and Jordan frames,” Phys. Lett. B 754, 129 (2016) [arXiv:1601.06152 [gr-qc]].
  50. S. Pandey and N. Banerjee, “Equivalence of Jordan and Einstein frames at the quantum level,” arXiv:1610.00584 [gr-qc].
  51. M. S. Ruf and C. F. Steinwachs, “Quantum equivalence of f⁢(R)𝑓𝑅f(R)italic_f ( italic_R ) gravity and scalar-tensor theories,” Phys. Rev. D 97, no. 4, 044050 (2018) [arXiv:1711.07486 [gr-qc]].
  52. A. Karam, T. Pappas and K. Tamvakis, “Frame-dependence of higher-order inflationary observables in scalar-tensor theories,” Phys. Rev. D 96, no. 6, 064036 (2017) [arXiv:1707.00984 [gr-qc]].
  53. S. Bahamonde, S. D. Odintsov, V. K. Oikonomou and P. V. Tretyakov, “Deceleration versus acceleration universe in different frames of F⁢(R)𝐹𝑅F(R)italic_F ( italic_R ) gravity,” Phys. Lett. B 766, 225 (2017) [arXiv:1701.02381 [gr-qc]].
  54. A. Karam, A. Lykkas and K. Tamvakis, “Frame-invariant approach to higher-dimensional scalar-tensor gravity,” Phys. Rev. D 97, no. 12, 124036 (2018) [arXiv:1803.04960 [gr-qc]].
  55. K. Bhattacharya and B. R. Majhi, “Fresh look at the scalar-tensor theory of gravity in Jordan and Einstein frames from undiscussed standpoints,” Phys. Rev. D 95, no.6, 064026 (2017) [arXiv:1702.07166 [gr-qc]].
  56. K. Bhattacharya, A. Das and B. R. Majhi, “Noether and Abbott-Deser-Tekin conserved quantities in scalar-tensor theory of gravity both in Jordan and Einstein frames,” Phys. Rev. D 97, no.12, 124013 (2018) [arXiv:1803.03771 [gr-qc]].
  57. K. Bhattacharya, B. R. Majhi and D. Singleton, “Fluid-gravity correspondence in the scalar-tensor theory of gravity: (in)equivalence of Einstein and Jordan frames,” JHEP 07, 018 (2020) [arXiv:2002.04743 [hep-th]].
  58. K. Bhattacharya, “Thermodynamic aspects and phase transition of black holes,” http://gyan.iitg.ernet.in/bitstream/handle/123456789/1740/TH-2294_156121009.pdf?sequence=2&isAllowed=y .
  59. S. Dey, K. Bhattacharya and B. R. Majhi, “Thermodynamic structure of a generic null surface and the zeroth law in scalar-tensor theory,” Phys. Rev. D 104, no.12, 12 (2021) [arXiv:2105.07787 [gr-qc]].
  60. K. Bhattacharya, “Extended phase space thermodynamics of black holes: A study in Einstein’s gravity and beyond,” Nucl. Phys. B 989, 116130 (2023) [arXiv:2112.00938 [gr-qc]].
  61. K. Bhattacharya and B. R. Majhi, “Scalar–tensor gravity from thermodynamic and fluid-gravity perspective,” Gen. Rel. Grav. 54, no.9, 112 (2022) [arXiv:2209.07050 [gr-qc]].
  62. A. N. Seenivasan, S. Chakrabarti and B. R. Majhi, “Scalar fluid in scalar-tensor gravity from an equivalent picture of thermodynamic and fluid descriptions of gravitational dynamics,” Phys. Rev. D 107, no.10, 104027 (2023) [arXiv:2302.00373 [gr-qc]].
  63. J. M. Charap and J. E. Nelson, “Surface Integrals and the Gravitational Action,” J. Phys. A 16, 1661 (1983)
  64. T. Padmanabhan, “A short note on the boundary term for the Hilbert action,” Mod. Phys. Lett. A 29 (2014) no.08, 1450037 .
  65. K. Parattu, S. Chakraborty, B. R. Majhi and T. Padmanabhan, “A Boundary Term for the Gravitational Action with Null Boundaries,” Gen. Rel. Grav. 48, no.7, 94 (2016) [arXiv:1501.01053 [gr-qc]].
  66. K. Parattu, S. Chakraborty and T. Padmanabhan, “Variational Principle for Gravity with Null and Non-null boundaries: A Unified Boundary Counter-term,” Eur. Phys. J. C 76, no.3, 129 (2016) [arXiv:1602.07546 [gr-qc]]
  67. S. Chakraborty, K. Parattu and T. Padmanabhan, “A Novel Derivation of the Boundary Term for the Action in Lanczos-Lovelock Gravity,” Gen. Rel. Grav. 49, no.9, 121 (2017) [arXiv:1703.00624 [gr-qc]].
  68. S. Chakraborty and K. Parattu, “Null boundary terms for Lanczos–Lovelock gravity,” Gen. Rel. Grav. 51, no.2, 23 (2019) [erratum: Gen. Rel. Grav. 51, no.3, 47 (2019)] [arXiv:1806.08823 [gr-qc]].
  69. L. Lehner, R. C. Myers, E. Poisson and R. D. Sorkin, “Gravitational action with null boundaries,” Phys. Rev. D 94, no.8, 084046 (2016) [arXiv:1609.00207 [hep-th]].
  70. F. Hopfmüller and L. Freidel, “Gravity Degrees of Freedom on a Null Surface,” Phys. Rev. D 95, no.10, 104006 (2017) [arXiv:1611.03096 [gr-qc]].
  71. R. Oliveri and S. Speziale, “Boundary effects in General Relativity with tetrad variables,” Gen. Rel. Grav. 52, no.8, 83 (2020) [arXiv:1912.01016 [gr-qc]].
  72. S. Aghapour, G. Jafari and M. Golshani, “On variational principle and canonical structure of gravitational theory in double-foliation formalism,” Class. Quant. Grav. 36, no.1, 015012 (2019) [arXiv:1808.07352 [gr-qc]].
  73. V. Chandrasekaran and A. J. Speranza, “Anomalies in gravitational charge algebras of null boundaries and black hole entropy,” JHEP 01, 137 (2021) [arXiv:2009.10739 [hep-th]].
  74. J. D. Brown and J. W. York, Jr., “Quasilocal energy and conserved charges derived from the gravitational action,” Phys. Rev. D 47, 1407-1419 (1993) [arXiv:gr-qc/9209012 [gr-qc]].
  75. J. D. Brown, S. R. Lau and J. W. York, Jr., “Action and energy of the gravitational field,” [arXiv:gr-qc/0010024 [gr-qc]].
  76. J. D. E. Creighton and R. B. Mann, “Quasilocal thermodynamics of dilaton gravity coupled to gauge fields,” Phys. Rev. D 52, 4569-4587 (1995) [arXiv:gr-qc/9505007 [gr-qc]].
  77. S. Bose and D. Lohiya, “Behavior of quasilocal mass under conformal transformations,” Phys. Rev. D 59, 044019 (1999) [arXiv:gr-qc/9810033 [gr-qc]].
  78. J. Côté, M. Lapierre-Léonard and V. Faraoni, “Spacetime mappings of the Brown–York quasilocal energy,” Eur. Phys. J. C 79, no.8, 678 (2019) [arXiv:1908.02595 [gr-qc]].
  79. G. Jafari, “Stress Tensor on Null Boundaries,” Phys. Rev. D 99, no.10, 104035 (2019) [arXiv:1901.04054 [hep-th]].
  80. V. Chandrasekaran, E. E. Flanagan, I. Shehzad and A. J. Speranza, “Brown-York charges at null boundaries,” JHEP 01, 029 (2022) [arXiv:2109.11567 [hep-th]].
  81. C. Brans and R. H. Dicke, “Mach’s principle and a relativistic theory of gravitation,” Phys. Rev.  124, 925 (1961).
  82. Cambridge University Press, Cambridge, UK, 2010.
  83. T. Padmanabhan, “The Holography of gravity encoded in a relation between entropy, horizon area and action for gravity,” Gen. Rel. Grav. 34, 2029-2035 (2002) [arXiv:gr-qc/0205090 [gr-qc]].
  84. T. Padmanabhan, “Is gravity an intrinsically quantum phenomenon? Dynamics of gravity from the entropy of space-time and the principle of equivalence,” Mod. Phys. Lett. A 17, 1147-1158 (2002) [arXiv:hep-th/0205278 [hep-th]].
  85. T. Padmanabhan, “Gravity and the thermodynamics of horizons,” Phys. Rept. 406, 49-125 (2005) [arXiv:gr-qc/0311036 [gr-qc]].
  86. T. Padmanabhan, “Holographic gravity and the surface term in the Einstein-Hilbert action,” Braz. J. Phys. 35, 362-372 (2005) [arXiv:gr-qc/0412068 [gr-qc]].
  87. T. Padmanabhan, “Gravity: A New holographic perspective,” Int. J. Mod. Phys. D 15, 1659-1676 (2006) [arXiv:gr-qc/0606061 [gr-qc]].
  88. A. Mukhopadhyay and T. Padmanabhan, “Holography of gravitational action functionals,” Phys. Rev. D 74, 124023 (2006) [arXiv:hep-th/0608120 [hep-th]].
  89. S. Kolekar and T. Padmanabhan, “Holography in Action,” Phys. Rev. D 82, 024036 (2010) [arXiv:1005.0619 [gr-qc]].
  90. K. Bhattacharya, “A novel probe of Einstein-Hilbert action: Dynamic upgradation of metric parameters,” Gen. Rel. Grav. 54, no.8, 81 (2022) [arXiv:2207.08199 [gr-qc]].
  91. R. H. Price and K. S. Thorne, “Membrane Viewpoint on Black Holes: Properties and Evolution of the Stretched Horizon,” Phys. Rev. D 33, 915-941 (1986)
  92. M. Parikh and F. Wilczek, “An Action for black hole membranes,” Phys. Rev. D 58, 064011 (1998) [arXiv:gr-qc/9712077 [gr-qc]].
  93. J. D. Brown, J. Creighton and R. B. Mann, “Temperature, energy and heat capacity of asymptotically anti-de Sitter black holes,” Phys. Rev. D 50, 6394-6403 (1994) [arXiv:gr-qc/9405007 [gr-qc]].
  94. S. W. Hawking and W. Israel, “General Relativity: An Einstein Centenary Survey,” Univ. Pr., 1979, ISBN 978-0-521-29928-2
  95. H. Adami, A. Parvizi, M. M. Sheikh-Jabbari, V. Taghiloo and H. Yavartanoo, “Hydro & thermo dynamics at causal boundaries, examples in 3d gravity,” JHEP 07, 038 (2023) [arXiv:2305.01009 [hep-th]].
  96. E. Gourgoulhon and J. L. Jaramillo, “A 3+1 perspective on null hypersurfaces and isolated horizons,” Phys. Rept. 423, 159-294 (2006) [arXiv:gr-qc/0503113 [gr-qc]].
  97. T. P. Sotiriou and V. Faraoni, “f(R) Theories Of Gravity,” Rev. Mod. Phys. 82, 451-497 (2010). [arXiv:0805.1726 [gr-qc]].
  98. A. De Felice and S. Tsujikawa, “f(R) theories,” Living Rev. Rel. 13, 3 (2010). [arXiv:1002.4928 [gr-qc]].
  99. K. Bhattacharya, S. Dey, B. R. Majhi, K. Parattu “Revisiting fluid-gravity analogy in general relativity and beyond” (in preparation).
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