Skip to main content
Springer Nature Link
Account
Menu
Find a journal Publish with us Track your research
Search
Cart
  1. Home
  2. Journal of High Energy Physics
  3. Article

Black hole solutions to Einstein-Bel-Robinson gravity

  • Regular Article - Theoretical Physics
  • Open access
  • Published: 06 November 2024
  • Volume 2024, article number 41, (2024)
  • Cite this article
Download PDF

You have full access to this open access article

Journal of High Energy Physics Aims and scope Submit manuscript
Black hole solutions to Einstein-Bel-Robinson gravity
Download PDF
  • S. N. Sajadi  ORCID: orcid.org/0000-0001-6808-08261,2,
  • Robert B. Mann  ORCID: orcid.org/0000-0002-5859-22273,
  • H. Sheikhahmadi  ORCID: orcid.org/0000-0002-3307-137X4,5 &
  • …
  • M. Khademi  ORCID: orcid.org/0000-0002-2865-06924 

  • 302 Accesses

  • Explore all metrics

A preprint version of the article is available at arXiv.

Abstract

In this paper, we study the physical properties of black holes in the framework of the recently proposed Einstien-Bel-Robinson gravity. We show that interestingly the theory propagates a transverse and massless graviton on a maximally symmetric background with positive energy. There is also a single ghost-free branch that returns to the Einstein case when β → 0. We find new black hole solutions to the equations, both approximate and exact, the latter being a constant curvature black hole solution, and discuss inconsistencies with metrics that were previously claimed to be approximate solutions to the equations. We obtain the conserved charges of the theory and briefly study the thermodynamics of the black hole solutions.

Article PDF

Download to read the full article text

Similar content being viewed by others

Three-dimensional charged black holes in Gauss–Bonnet gravity

Article Open access 15 November 2023

A general study of regular and singular black hole solutions in Einstein’s conformal gravity

Article Open access 18 June 2018

Einstein–Yang–Mills–Lorentz black holes

Article Open access 11 December 2017

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.
  • Classical and Quantum Gravity
  • General Relativity
  • Gravitational Physics
  • Mathematical Methods in Physics
  • Newtonian Physics
  • Theoretical Astrophysics
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

References

  1. A. Einstein, Die Feldgleichungen der Gravitation, Sitzungsberichteder Preussischen Akademie der Wissenschaftenzu, Berlin (1915), p. 844–847.

  2. A. Einstein, Die Grundlage der allgemeinen Relativitätstheorie, Annalen Phys. 354 (1916) 769 [also published separately as Leipzig: Teubner (1916), p. 283–339].

  3. K. Schwarzschild, Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften 7 (1916) 189.

  4. J. Droste, On the field of a single centre in Einstein’s theory of gravitation, and the motion of a particle in that field, Proceedings Royal Academy Amsterdam 19-1 (1917) 197.

    Google Scholar 

  5. J. Smolic and M. Taylor, Higher derivative effects for 4d AdS gravity, JHEP 06 (2013) 096 [arXiv:1301.5205] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  6. K. S. Stelle, Renormalization of Higher Derivative Quantum Gravity, Phys. Rev. D16 (1977) 953.

  7. B. Zwiebach, Curvature Squared Terms and String Theories, Phys. Lett. B 156 (1985) 315 [INSPIRE].

    Article  ADS  Google Scholar 

  8. R.-G. Cai, Gauss-Bonnet black holes in AdS spaces, Phys. Rev. D 65 (2002) 084014 [hep-th/0109133] [INSPIRE].

  9. R.C. Myers and B. Robinson, Black Holes in Quasi-topological Gravity, JHEP 08 (2010) 067 [arXiv:1003.5357] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  10. R.C. Myers, M.F. Paulos and A. Sinha, Holographic studies of quasi-topological gravity, JHEP 08 (2010) 035 [arXiv:1004.2055] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  11. R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  12. M. Brigante et al., Viscosity Bound Violation in Higher Derivative Gravity, Phys. Rev. D 77 (2008) 126006 [arXiv:0712.0805] [INSPIRE].

  13. R.A. Hennigar and R.B. Mann, Black holes in Einsteinian cubic gravity, Phys. Rev. D 95 (2017) 064055 [arXiv:1610.06675] [INSPIRE].

  14. J. Oliva and S. Ray, A new cubic theory of gravity in five dimensions: Black hole, Birkhoff’s theorem and C-function, Class. Quant. Grav. 27 (2010) 225002 [arXiv:1003.4773] [INSPIRE].

  15. P. Bueno and P.A. Cano, Einsteinian cubic gravity, Phys. Rev. D 94 (2016) 104005 [arXiv:1607.06463] [INSPIRE].

  16. D.G. Boulware and S. Deser, String Generated Gravity Models, Phys. Rev. Lett. 55 (1985) 2656 [INSPIRE].

    Article  ADS  Google Scholar 

  17. D. Lovelock, The Einstein tensor and its generalizations, J. Math. Phys. 12 (1971) 498 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  18. M.B. Green and P. Vanhove, D instantons, strings and M theory, Phys. Lett. B 408 (1997) 122 [hep-th/9704145] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  19. J. Ahmed, R.A. Hennigar, R.B. Mann and M. Mir, Quintessential Quartic Quasi-topological Quartet, JHEP 05 (2017) 134 [arXiv:1703.11007] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  20. A.A. Tseytlin, R4 terms in 11 dimensions and conformal anomaly of (2,0) theory, Nucl. Phys. B 584 (2000) 233 [hep-th/0005072] [INSPIRE].

    Article  ADS  Google Scholar 

  21. S.V. Ketov, Starobinsky-Bel-Robinson Gravity, Universe 8 (2022) 351 [arXiv:2205.13172] [INSPIRE].

    Article  ADS  Google Scholar 

  22. K.S. Stelle, Classical Gravity with Higher Derivatives, Gen. Rel. Grav. 9 (1978) 353 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  23. A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].

  24. S. Ketov, On the large-field equivalence between Starobinsky and Higgs inflation in gravity and supergravity, PoS DISCRETE2020-2021 (2022) 014 [INSPIRE].

  25. I. Robinson, The Bel-Robinson tensor, Class. Quant. Grav. 14 (1997) A331.

    Article  ADS  MathSciNet  Google Scholar 

  26. R. Campos Delgado and S.V. Ketov, Schwarzschild-type black holes in Starobinsky-Bel-Robinson gravity, Phys. Lett. B 838 (2023) 137690 [arXiv:2209.01574] [INSPIRE].

  27. A. Belhaj et al., Deflection angle and Shadows by Black Holes in Starobinsky-Bel-Robinson Gravity from M-theory, arXiv:2304.03883 [INSPIRE].

  28. D. Arora et al., Exploring tidal force effects and shadow constraints for Schwarzschild-like black hole in Starobinsky-Bel-Robinson gravity, Eur. Phys. J. C 83 (2023) 995 [arXiv:2308.13901] [INSPIRE].

    Article  ADS  Google Scholar 

  29. A. Davlataliev et al., Probing the Starobinsky-Bel-Robinson gravity by photon motion around the Kerr-type black hole in non-uniform plasma, Phys. Dark Univ. 42 (2023) 101340 [INSPIRE].

  30. A. Belhaj et al., Optical behaviors of black holes in Starobinsky-Bel-Robinson gravity, Gen. Rel. Grav. 55 (2023) 110 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  31. S.V. Bolokhov, Black holes in Starobinsky-Bel-Robinson Gravity and the breakdown of quasinormal modes/null geodesics correspondence, Phys. Lett. B 856 (2024) 138879 [arXiv:2310.12326] [INSPIRE].

  32. B. Hamil and B.C. Lütfüoğlu, Black hole shadows in Einstein-Bel-Robinson gravity, Chin. Phys. C 48 (2024) 055102 [arXiv:2311.12354] [INSPIRE].

  33. G. Mustafa et al., Probing a black hole in Starobinsky-Bel-Robinson gravity with thermodynamical analysis, effective force and gravitational weak lensing, Chin. J. Phys. 90 (2024) 494 [arXiv:2401.08254] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  34. S.V. Ketov, E.O. Pozdeeva and S.Y. Vernov, On the superstring-inspired quantum correction to the Starobinsky model of inflation, JCAP 12 (2022) 032 [arXiv:2211.01546] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  35. T.Q. Do, D.H. Nguyen and T.M. Pham, Stability investigations of isotropic and anisotropic exponential inflation in the Starobinsky-Bel-Robinson gravity, Int. J. Mod. Phys. D 32 (2023) 2350087 [arXiv:2303.17283] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  36. P. Bueno et al., Generalized quasi-topological gravities: the whole shebang, Class. Quant. Grav. 40 (2023) 015004 [arXiv:2203.05589] [INSPIRE].

  37. S. Aminneborg, I. Bengtsson, S. Holst and P. Peldan, Making anti-de Sitter black holes, Class. Quant. Grav. 13 (1996) 2707 [gr-qc/9604005] [INSPIRE].

  38. R.B. Mann, Pair production of topological anti-de Sitter black holes, Class. Quant. Grav. 14 (1997) L109 [gr-qc/9607071] [INSPIRE].

  39. M. Crisostomi, K. Noui, C. Charmousis and D. Langlois, Beyond Lovelock gravity: Higher derivative metric theories, Phys. Rev. D 97 (2018) 044034 [arXiv:1710.04531] [INSPIRE].

  40. M. Ostrogradsky, Mémoires sur les équations différentielles, relatives au problème des isopérimètres, Mem. Ac. St. Petersbourg VI 4 (1850) 385.

  41. R.P. Woodard, Avoiding dark energy with 1/r modifications of gravity, Lect. Notes Phys. 720 (2007) 403 [astro-ph/0601672] [INSPIRE].

  42. S. Dyda, E.E. Flanagan and M. Kamionkowski, Vacuum Instability in Chern-Simons Gravity, Phys. Rev. D 86 (2012) 124031 [arXiv:1208.4871] [INSPIRE].

  43. S. Alexander and N. Yunes, Chern-Simons Modified General Relativity, Phys. Rept. 480 (2009) 1 [arXiv:0907.2562] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  44. M. Novello and R.P. Neves, The mass of the graviton and the cosmological constant, Class. Quant. Grav. 20 (2003) L67 [gr-qc/0210058] [INSPIRE].

  45. R.B. Mann, Topological black holes: Outside looking in, Annals Israel Phys. Soc. 13 (1997) 311 [gr-qc/9709039] [INSPIRE].

  46. K. Hajian and B. Tekin, Coupling Constants as Conserved Charges in Black Hole Thermodynamics, Phys. Rev. Lett. 132 (2024) 191401 [arXiv:2309.07634] [INSPIRE].

  47. R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].

  48. V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].

  49. B.R. Hull and R.B. Mann, Thermodynamics of exotic black holes in Lovelock gravity, Phys. Rev. D 104 (2021) 084032 [arXiv:2102.05282] [INSPIRE].

  50. D. Kubiznak and R.B. Mann, Black hole chemistry, Can. J. Phys. 93 (2015) 999 [arXiv:1404.2126] [INSPIRE].

    Article  ADS  Google Scholar 

  51. D. Kubiznak and R.B. Mann, P-V criticality of charged AdS black holes, JHEP 07 (2012) 033 [arXiv:1205.0559] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  52. D. Kubiznak, R.B. Mann and M. Teo, Black hole chemistry: thermodynamics with Lambda, Class. Quant. Grav. 34 (2017) 063001 [arXiv:1608.06147] [INSPIRE].

  53. J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  54. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  55. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  56. T. Sakai and S. Sugimoto, More on a holographic dual of QCD, Prog. Theor. Phys. 114 (2005) 1083 [hep-th/0507073] [INSPIRE].

    Article  ADS  Google Scholar 

  57. J. Casalderrey-Solana et al., Gauge/String Duality, Hot QCD and Heavy Ion Collisions, Cambridge University Press (2014) [https://doi.org/10.1017/9781009403504] [INSPIRE].

  58. D. Chernyavsky and K. Hajian, Cosmological constant is a conserved charge, Class. Quant. Grav. 35 (2018) 125012 [arXiv:1710.07904] [INSPIRE].

  59. S. Gunasekaran, R.B. Mann and D. Kubiznak, Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization, JHEP 11 (2012) 110 [arXiv:1208.6251] [INSPIRE].

    Article  ADS  Google Scholar 

  60. D. Kastor, S. Ray and J. Traschen, Smarr Formula and an Extended First Law for Lovelock Gravity, Class. Quant. Grav. 27 (2010) 235014 [arXiv:1005.5053] [INSPIRE].

  61. S. Deser and B. Tekin, Energy in generic higher curvature gravity theories, Phys. Rev. D 67 (2003) 084009 [hep-th/0212292] [INSPIRE].

  62. W.G. Brenna, R.B. Mann and M. Park, Mass and Thermodynamic Volume in Lifshitz Spacetimes, Phys. Rev. D 92 (2015) 044015 [arXiv:1505.06331] [INSPIRE].

  63. R.A. Hennigar, D. Kubizňák and R.B. Mann, Entropy Inequality Violations from Ultraspinning Black Holes, Phys. Rev. Lett. 115 (2015) 031101 [arXiv:1411.4309] [INSPIRE].

  64. S.N. Sajadi, R.B. Mann, N. Riazi and S. Fakhry, Analytically Approximation Solution to Higher Derivative Gravity, arXiv:2010.15039 [https://doi.org/10.1103/PhysRevD.102.124026] [INSPIRE].

  65. P.C.W. Davies, Thermodynamics of black holes, Rept. Prog. Phys. 41 (1978) 1313 [INSPIRE].

  66. P. Hut, Charged black holes and phase transitions, Mon. Not. Roy. Astron. Soc. 180 (1977) 379.

    Article  ADS  Google Scholar 

  67. S.N. Sajadi, L. Shahkarami, F. Charmchi and S.H. Hendi, Charged black holes in Einsteinian quartic gravity, Annals Phys. 447 (2022) 169162 [arXiv:2207.07374] [INSPIRE].

  68. M. Mir, R.A. Hennigar, J. Ahmed and R.B. Mann, Black hole chemistry and holography in generalized quasi-topological gravity, JHEP 08 (2019) 068 [arXiv:1902.02005] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  69. D. Kastor, S. Ray and J. Traschen, Enthalpy and the Mechanics of AdS Black Holes, Class. Quant. Grav. 26 (2009) 195011 [arXiv:0904.2765] [INSPIRE].

  70. D. Kubiznak and F. Simovic, Thermodynamics of horizons: de Sitter black holes and reentrant phase transitions, Class. Quant. Grav. 33 (2016) 245001 [arXiv:1507.08630] [INSPIRE].

  71. S. Mbarek, Explorations of Black Hole Thermodynamics in de Sitter Spacetime, Ph.D. thesis, University of Waterloo, Waterloo, Ontario, Canada (2019) [INSPIRE].

  72. F. Simovic and R.B. Mann, Critical Phenomena of Charged de Sitter Black Holes in Cavities, Class. Quant. Grav. 36 (2019) 014002 [arXiv:1807.11875] [INSPIRE].

  73. F. Simovic and R.B. Mann, Critical Phenomena of Born-Infeld-de Sitter Black Holes in Cavities, JHEP 05 (2019) 136 [arXiv:1904.04871] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  74. S. Haroon, R.A. Hennigar, R.B. Mann and F. Simovic, Thermodynamics of Gauss-Bonnet-de Sitter Black Holes, Phys. Rev. D 101 (2020) 084051 [arXiv:2002.01567] [INSPIRE].

  75. T. Ortín, Gravity and Strings, second edition, Cambridge University Press (2015) [https://doi.org/10.1017/cbo9781139019750].

Download references

Acknowledgments

SNS thanks the Strong Gravity Group of Silpakorn University. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada.

Author information

Authors and Affiliations

  1. School of Physics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5531, Tehran, Iran

    S. N. Sajadi

  2. Strong Gravity Group, Department of Physics, Faculty of Science, Silpakorn University, Nakhon Pathom, 73000, Thailand

    S. N. Sajadi

  3. Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Robert B. Mann

  4. School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5531, Tehran, Iran

    H. Sheikhahmadi & M. Khademi

  5. Center for Space Research, North-West University, Potchefstroom, South Africa

    H. Sheikhahmadi

Authors
  1. S. N. Sajadi
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Robert B. Mann
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. H. Sheikhahmadi
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. M. Khademi
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to S. N. Sajadi.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

ArXiv ePrint: 2308.01078

Rights and permissions

Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sajadi, S.N., Mann, R.B., Sheikhahmadi, H. et al. Black hole solutions to Einstein-Bel-Robinson gravity. J. High Energ. Phys. 2024, 41 (2024). https://doi.org/10.1007/JHEP11(2024)041

Download citation

  • Received: 31 January 2024

  • Revised: 09 September 2024

  • Accepted: 24 September 2024

  • Published: 06 November 2024

  • DOI: https://doi.org/10.1007/JHEP11(2024)041

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Black Holes
  • Classical Theories of Gravity

Profiles

  1. S. N. Sajadi View author profile
  2. Robert B. Mann View author profile
  3. H. Sheikhahmadi View author profile
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us
  • Track your research

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Journal finder
  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our brands

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Discover
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support
  • Legal notice
  • Cancel contracts here

Not affiliated

Springer Nature

© 2025 Springer Nature

pFad - Phonifier reborn

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.


Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy