TY - JOUR
T1 - Black hole perturbations in vector-tensor theories
T2 - The odd-mode analysis
AU - Kase, Ryotaro
AU - Minamitsuji, Masato
AU - Tsujikawa, Shinji
AU - Zhang, Ying Li
N1 - Funding Information:
We thank Lavinia Heisenberg for useful discussions. RK is supported by the Grant-in-Aid for Young Scientists B of the JSPS No. 17K14297. MM is supported by FCT-Portugal through Grant No. SFRH/BPD/88299/2012. ST is supported by the Grant-in-Aid for Scientific Research Fund of the JSPS No. 16K05359 and MEXT KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas Cosmic Acceleration (No. 15H05890). YZ is supported by the NSFC grant No. 11605228, 11673025 and 1171001024.
Publisher Copyright:
© 2018 IOP Publishing Ltd and Sissa Medialab.
PY - 2018/2/23
Y1 - 2018/2/23
N2 - In generalized Proca theories with vector-field derivative couplings, a bunch of hairy black hole solutions have been derived on a static and spherically symmetric background. In this paper, we formulate the odd-parity black hole perturbations in generalized Proca theories by expanding the corresponding action up to second order and investigate whether or not black holes with vector hair suffer ghost or Laplacian instabilities. We show that the models with cubic couplings G3(X), where X=-AμAμ/2 with a vector field Aμ, do not provide any additional stability condition as in General Relativity. On the other hand, the exact charged stealth Schwarzschild solution with a nonvanishing longitudinal vector component A1, which originates from the coupling to the Einstein tensor GμνAμ Aν equivalent to the quartic coupling G4(X) containing a linear function of X, is unstable in the vicinity of the event horizon. The same instability problem also persists for hairy black holes arising from general quartic power-law couplings G4(X) β4 Xn with the nonvanishing A1, while the other branch with A1=0 can be consistent with conditions for the absence of ghost and Laplacian instabilities. We also discuss the case of other exact and numerical black hole solutions associated with intrinsic vector-field derivative couplings and show that there exists a wide range of parameter spaces in which the solutions suffer neither ghost nor Laplacian instabilities against odd-parity perturbations.
AB - In generalized Proca theories with vector-field derivative couplings, a bunch of hairy black hole solutions have been derived on a static and spherically symmetric background. In this paper, we formulate the odd-parity black hole perturbations in generalized Proca theories by expanding the corresponding action up to second order and investigate whether or not black holes with vector hair suffer ghost or Laplacian instabilities. We show that the models with cubic couplings G3(X), where X=-AμAμ/2 with a vector field Aμ, do not provide any additional stability condition as in General Relativity. On the other hand, the exact charged stealth Schwarzschild solution with a nonvanishing longitudinal vector component A1, which originates from the coupling to the Einstein tensor GμνAμ Aν equivalent to the quartic coupling G4(X) containing a linear function of X, is unstable in the vicinity of the event horizon. The same instability problem also persists for hairy black holes arising from general quartic power-law couplings G4(X) β4 Xn with the nonvanishing A1, while the other branch with A1=0 can be consistent with conditions for the absence of ghost and Laplacian instabilities. We also discuss the case of other exact and numerical black hole solutions associated with intrinsic vector-field derivative couplings and show that there exists a wide range of parameter spaces in which the solutions suffer neither ghost nor Laplacian instabilities against odd-parity perturbations.
KW - astrophysical black holes
KW - dark energy theory
KW - modified gravity
UR - http://www.scopus.com/inward/record.url?scp=85043593684&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85043593684&partnerID=8YFLogxK
U2 - 10.1088/1475-7516/2018/02/048
DO - 10.1088/1475-7516/2018/02/048
M3 - Article
AN - SCOPUS:85043593684
VL - 2018
JO - Journal of Cosmology and Astroparticle Physics
JF - Journal of Cosmology and Astroparticle Physics
SN - 1475-7516
IS - 2
M1 - 048
ER -