Abstract
When starting with a static, spherically-symmetric ansatz, there are two types of black hole solutions in dRGT massive gravity: (i) exact Schwarzschild solutions which exhibit no Yukawa suppression at large distances and (ii) solutions in which the dynamical metric and the reference metric are simultaneously diagonal and which inevitably exhibit coordinate-invariant singularities at the horizon. In this work we investigate the possibility of black hole solutions which can accommodate both a nonsingular horizon and Yukawa asymptotics. In particular, by adopting a time-dependent ansatz, we derive perturbative analytic solutions which possess non-singular horizons. These black hole solutions are indistinguishable from Schwarzschild black holes in the limit of zero graviton mass. At finite graviton mass, they depend explicitly on time. However, we demonstrate that the location of the apparent horizon is not necessarily time-dependent, indicating that these black holes are not necessarily accreting or evaporating (classically). In deriving these results, we also review and extend known results about static black hole solutions in massive gravity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli Action, Phys. Rev. D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of massive gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].
D.G. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev. D 6 (1972) 3368 [INSPIRE].
S.F. Hassan and R.A. Rosen, Resolving the ghost problem in non-linear massive gravity, Phys. Rev. Lett. 108 (2012) 041101 [arXiv:1106.3344] [INSPIRE].
K. Hinterbichler, Theoretical aspects of massive gravity, Rev. Mod. Phys. 84 (2012) 671 [arXiv:1105.3735] [INSPIRE].
C. de Rham, Massive gravity, Living Rev. Rel. 17 (2014) 7 [arXiv:1401.4173] [INSPIRE].
K. Koyama, G. Niz and G. Tasinato, Analytic solutions in non-linear massive gravity, Phys. Rev. Lett. 107 (2011) 131101 [arXiv:1103.4708] [INSPIRE].
T.M. Nieuwenhuizen, Exact Schwarzschild-de Sitter black holes in a family of massive gravity models, Phys. Rev. D 84 (2011) 024038 [arXiv:1103.5912] [INSPIRE].
K. Koyama, G. Niz and G. Tasinato, Strong interactions and exact solutions in non-linear massive gravity, Phys. Rev. D 84 (2011) 064033 [arXiv:1104.2143] [INSPIRE].
A. Gruzinov and M. Mirbabayi, Stars and black holes in massive gravity, Phys. Rev. D 84 (2011) 124019 [arXiv:1106.2551] [INSPIRE].
D. Comelli, M. Crisostomi, F. Nesti and L. Pilo, Spherically symmetric solutions in ghost-free massive gravity, Phys. Rev. D 85 (2012) 024044 [arXiv:1110.4967] [INSPIRE].
L. Berezhiani et al., On black holes in massive gravity, Phys. Rev. D 85 (2012) 044024 [arXiv:1111.3613] [INSPIRE].
M.S. Volkov, Hairy black holes in the ghost-free bigravity theory, Phys. Rev. D 85 (2012) 124043 [arXiv:1202.6682] [INSPIRE].
F. Sbisa, G. Niz, K. Koyama and G. Tasinato, Characterising Vainshtein solutions in massive gravity, Phys. Rev. D 86 (2012) 024033 [arXiv:1204.1193] [INSPIRE].
P. Gratia, W. Hu and M. Wyman, Self-accelerating massive gravity: exact solutions for any isotropic matter distribution, Phys. Rev. D 86 (2012) 061504 [arXiv:1205.4241] [INSPIRE].
C.-I. Chiang, K. Izumi and P. Chen, Spherically symmetric analysis on open FLRW solution in non-linear massive gravity, JCAP 12 (2012) 025 [arXiv:1208.1222] [INSPIRE].
M. Mirbabayi and A. Gruzinov, Black hole discharge in massive electrodynamics and black hole disappearance in massive gravity, Phys. Rev. D 88 (2013) 064008 [arXiv:1303.2665] [INSPIRE].
M.S. Volkov, Self-accelerating cosmologies and hairy black holes in ghost-free bigravity and massive gravity, Class. Quant. Grav. 30 (2013) 184009 [arXiv:1304.0238] [INSPIRE].
G. Tasinato, K. Koyama and G. Niz, Exact solutions in massive gravity, Class. Quant. Grav. 30 (2013) 184002 [arXiv:1304.0601] [INSPIRE].
E. Babichev and A. Fabbri, Instability of black holes in massive gravity, Class. Quant. Grav. 30 (2013) 152001 [arXiv:1304.5992] [INSPIRE].
R. Brito, V. Cardoso and P. Pani, Black holes with massive graviton hair, Phys. Rev. D 88 (2013) 064006 [arXiv:1309.0818] [INSPIRE].
I. Arraut, On the black holes in alternative theories of gravity: the case of nonlinear massive gravity, Int. J. Mod. Phys. D 24 (2015) 1550022 [arXiv:1311.0732] [INSPIRE].
H. Kodama and I. Arraut, Stability of the Schwarzschild-de Sitter black hole in the dRGT massive gravity theory, PTEP 2014 (2014) 023E02 [arXiv:1312.0370] [INSPIRE].
S. Renaux-Petel, On the Vainshtein mechanism in the minimal model of massive gravity, JCAP 03 (2014) 043 [arXiv:1401.0497] [INSPIRE].
E. Babichev and A. Fabbri, Stability analysis of black holes in massive gravity: a unified treatment, Phys. Rev. D 89 (2014) 081502 [arXiv:1401.6871] [INSPIRE].
M.S. Volkov, Hairy black holes in theories with massive gravitons, Lect. Notes Phys. 892 (2015) 161 [arXiv:1405.1742].
E. Babichev and R. Brito, Black holes in massive gravity, Class. Quant. Grav. 32 (2015) 154001 [arXiv:1503.07529] [INSPIRE].
C. Deffayet and T. Jacobson, On horizon structure of bimetric spacetimes, Class. Quant. Grav. 29 (2012) 065009 [arXiv:1107.4978] [INSPIRE].
M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond. A 173 (1939) 211 [INSPIRE].
H. van Dam and M.J.G. Veltman, Massive and massless Yang-Mills and gravitational fields, Nucl. Phys. B 22 (1970) 397 [INSPIRE].
V.I. Zakharov, Linearized gravitation theory and the graviton mass, JETP Lett. 12 (1970) 312 [INSPIRE].
A.I. Vainshtein, To the problem of nonvanishing gravitation mass, Phys. Lett. 39B (1972) 393 [INSPIRE].
S.F. Hassan and R.A. Rosen, On non-linear actions for massive gravity, JHEP 07 (2011) 009 [arXiv:1103.6055] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1702.06543
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Rosen, R.A. Non-singular black holes in massive gravity: time-dependent solutions. J. High Energ. Phys. 2017, 206 (2017). https://doi.org/10.1007/JHEP10(2017)206
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2017)206