Abstract
This is a brief survey of the known black hole solutions in the theories of ghost-free bigravity and massive gravity. Various black holes exist in these theories, in particular those supporting a massive graviton hair. However, it seems that solutions which could be astrophysically relevant are the same as in General Relativity, or very close to them. Therefore, the no-hair conjecture essentially applies, and so it would be hard to detect the graviton mass by observing black holes.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
R. Ruffini, J.A. Wheeler, Introducing the black hole. Phys. Today 24, 30–41 (1971)
W. Israel, Event horizons in static vacuum space-times. Phys. Rev. 164, 1776–1779 (1967)
B. Carter, Black hole equilibrium states, in Black Holes, ed. by C. DeWitt, B.S. DeWit (Gordon and Breach, New York, 1973)
P.O. Mazur, Proof of uniqueness of the Kerr-Newman black hole solution. J. Phys. A15, 3173–3180 (1982)
J.D. Bekenstein, Transcendence of the law of baryon-number conservation in black hole physics. Phys. Rev. Lett. 28, 452–455 (1972)
J.D. Bekenstein, Nonexistence of baryon number for static black holes. Phys. Rev. D5, 1239–1246 (1972)
J.D. Bekenstein, Nonexistence of baryon number for black holes. II. Phys. Rev. D5, 2403–2412 (1972)
J.D. Bekenstein, Novel ‘no scalar hair’ theorem for black holes. Phys. Rev. D51, 6608–6611 (1995)
A.E. Mayo, J.D. Bekenstein, No hair for spherical black holes: charged and nonminimally coupled scalar field with selfinteraction. Phys. Rev. D54, 5059–5069 (1996)
J.D. Bekenstein, Black hole hair: 25 - years after (1996) [arXiv:gr-qc/9605059]
S. Hod, Stationary scalar clouds around rotating black holes. Phys. Rev. D86, 104026 (2012)
C.A.R. Herdeiro, E. Radu, Kerr black holes with scalar hair. Phys. Rev. Lett. 112, 221101 (2014)
P.B. Yasskin, Solutions for gravity coupled to massless gauge fields. Phys. Rev. D12, 2212–2217 (1975)
M.S. Volkov, D.V. Galtsov, Non-Abelian Einstein Yang-Mills black holes. JETP Lett. 50, 346–350 (1989)
M.S. Volkov, D.V. Galtsov, Black holes in Einstein Yang-Mills theory. Sov. J. Nucl. Phys. 51, 747–753 (1990)
M.S. Volkov, D.V. Gal’tsov, Gravitating non-Abelian solitons and black holes with Yang-Mills fields. Phys. Rept. 319, 1–83 (1999)
B. Kleihaus, J. Kunz, Static axially symmetric Einstein Yang-Mills dilaton solutions. 2. Black hole solutions. Phys. Rev. D57, 6138–6157 (1998)
S.S. Gubser, S.S. Pufu, The Gravity dual of a p-wave superconductor. J. High Energy Phys. 0811, 033 (2008)
M. Fierz, W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field. Proc. R. Soc. Lond. A173, 211–232 (1939)
C. de Rham, G. Gabadadze, A.J. Tolley, Resummation of massive gravity. Phys. Rev. Lett. 106, 231101 (2011)
K. Hinterbichler, Theoretical aspects of massive gravity. Rev. Mod. Phys. 84, 671–710 (2012)
C. de Rham, Massive gravity (2014) [arXiv:1401.4173]
D.G. Boulware, S. Deser, Can gravitation have a finite range? Phys. Rev. D6, 3368–3382 (1972)
S.F. Hassan, R.A. Rosen, Resolving the ghost problem in non-linear massive gravity. Phys. Rev. Lett. 108, 041101 (2012)
S.F. Hassan, R.A. Rosen, Confirmation of the secondary constraint and absence of ghost in massive gravity and bimetric gravity. J. High Energy Phys. 1204, 123 (2012)
J. Kluson, Non-linear massive gravity with additional primary constraint and absence of ghosts. Phys. Rev. D86, 044024 (2012)
D. Comelli, M. Crisostomi, F. Nesti, L. Pilo, Degrees of freedom in massive gravity. Phys. Rev. D86, 101502 (2012)
D. Comelli, F. Nesti, L. Pilo, Massive gravity: a general analysis (2013) [arXiv:1305.0236]
S.F. Hassan, R.A. Rosen, Bimetric gravity from ghost-free massive gravity. J. High Energy Phys. 1202, 126 (2012)
A.G. Riess et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116(3), 1009 (1998)
S. Perlmutter et al., Measurements of Omega and Lambda from 42 high-redshift supernovae. Astrophys. J. 517(2), 565 (1999)
T. Damour, I.I. Kogan, A. Papazoglou, Nonlinear bigravity and cosmic acceleration. Phys. Rev. D 66, 104025 (2002)
M.S. Volkov, Hairy black holes in the ghost-free bigravity theory. Phys. Rev. D85, 124043 (2012)
D. Comelli, M. Crisostomi, F. Nesti, L. Pilo, Spherically symmetric solutions in ghost-free massive gravity. Phys. Rev. D85, 024044 (2012)
R. Brito, V. Cardoso, P. Pani, Black holes with massive graviton hair. Phys. Rev. D88, 064006 (2013)
C.J. Isham, A. Salam, J.A. Strathdee, F-dominance of gravity. Phys. Rev. D3, 867–873 (1971)
M.S. Volkov, Self-accelerating cosmologies and hairy black holes in ghost-free bigravity and massive gravity. Class. Quant. Grav. 30, 184009 (2013)
A. Salam, J.A. Strathdee, A class of solutions for the strong gravity equations. Phys. Rev. D16, 2668 (1977)
C.J. Isham, D. Storey, Exact spherically symmetric classical solutions for the f-g theory of gravity. Phys. Rev. D18, 1047 (1978)
Z. Berezhiani, D. Comelli, F. Nesti, L. Pilo, Exact spherically symmetric solutions in massive gravity. J. High Energy Phys. 0807, 130 (2008)
E. Babichev, A. Fabbri, A class of charged black hole solutions in massive (bi)gravity. J. High. Energy Phys. 1407, 016 (2014)
Th.M. Nieuwenhuizen, Exact Schwarzschild-de Sitter black holes in a family of massive gravity models. Phys. Rev. D84, 024038 (2011)
L. Berezhiani, G. Chkareuli, C. de Rham, G. Gabadadze, A.J. Tolley, On black holes in massive gravity. Phys. Rev. D85, 044024 (2012)
K. Koyama, G. Niz, G. Tasinato, Analytic solutions in non-linear massive gravity. Phys. Rev. Lett. 107, 131101 (2011)
K. Koyama, G. Niz, G. Tasinato, Strong interactions and exact solutions in non-linear massive gravity. Phys. Rev. D84, 064033 (2011)
Y.-F. Cai, D.A. Easson, C. Gao, E.N. Saridakis, Charged black holes in nonlinear massive gravity. Phys. Rev. D87(6), 064001 (2013)
C. Deffayet, T. Jacobson, On horizon structure of bimetric spacetimes. Class. Quant. Grav. 29, 065009 (2012)
A.I. Vainshtein, To the problem of nonvanishing gravitation mass. Phys. Lett. B39, 393–394 (1972)
E. Babichev, C. Deffayet, R. Ziour, Recovering general relativity from massive gravity. Phys. Rev. Lett. 103, 201102 (2009)
E. Babichev, C. Deffayet, R. Ziour, The recovery of general relativity in massive gravity via the Vainshtein mechanism. Phys. Rev. D82, 104008 (2010)
A. Gruzinov, M. Mirbabayi, Stars and black holes in massive gravity. Phys. Rev. D84, 124019 (2011)
F. Sbisa, G. Niz, K. Koyama, G. Tasinato, Characterising Vainshtein solutions in massive gravity. Phys. Rev. D86, 024033 (2012)
E. Babichev, M. Crisostomi, Restoring general relativity in massive bi-gravity theory. Phys. Rev. D88, 084002 (2013)
E. Babichev, A. Fabbri, Instability of black holes in massive gravity. Class. Quant. Grav. 30, 152001 (2013)
R. Gregory, R. Laflamme, Black strings and p-branes are unstable. Phys. Rev. Lett. 70, 2837–2840 (1993)
R. Brito, V. Cardoso, P. Pani, Massive spin-2 fields on black hole spacetimes: instability of the Schwarzschild and Kerr solutions and bounds on the graviton mass. Phys. Rev. D88(2), 023514 (2013)
R. Brito, V. Cardoso, P. Pani, Partially massless gravitons do not destroy general relativity black holes. Phys. Rev. D87(12), 124024 (2013)
H. Kodama, I. Arraut, Stability of the Schwarzschild-de Sitter black hole in the dRGT massive gravity theory. Progr. Theor. Exp. Phys. 2014, 023E02 (2014)
E. Babichev, A. Fabbri, Stability analysis of black holes in massive gravity: a unified treatment. Phys. Rev. D89, 081502 (2014)
S. Deser, A. Waldron, Non-Einstein source effects in massive gravity. Phys. Rev. D89, 027503 (2014)
M. Mirbabayi, A. Gruzinov, Black hole discharge in massive electrodynamics and black hole disappearance in massive gravity. Phys. Rev. D88, 064008 (2013)
A. Nicolis, R. Rattazzi, E. Trincherini, The Galileon as a local modification of gravity. Phys. Rev. D79, 064036 (2009)
E. Babichev, C. Charmousis, Dressing a black hole with a time-dependent Galileon. J. High. Energy Phys. 1408, 106 (2014)
L. Hui, A. Nicolis, No-hair theorem for the Galileon. Phys. Rev. Lett. 110(24), 241104 (2013)
Acknowledgements
This work was partly supported by the Russian Government Program of Competitive Growth of the Kazan Federal University.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Volkov, M.S. (2015). Hairy Black Holes in Theories with Massive Gravitons. In: Papantonopoulos, E. (eds) Modifications of Einstein's Theory of Gravity at Large Distances. Lecture Notes in Physics, vol 892. Springer, Cham. https://doi.org/10.1007/978-3-319-10070-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-10070-8_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10069-2
Online ISBN: 978-3-319-10070-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)