2018/01/31 by Ryotaro Kase, Masato Minamitsuji, Shinji Tsujikawa +1 · 33 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Black brane #Black hole (networking) #Cosmology and Gravitation Theories #Coupling (piping) #Instability #Pulsars and Gravitational Waves Research #Quartic function #Schwarzschild metric #Schwarzschild radius #Tensor (intrinsic definition) #astro-ph.CO #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1088/1475-7516/2018/02/048
published in Journal of Cosmology and Astroparticle Physics 2018(02), 048 (Institute of Physics) · 26 pages, 4 figures, published version
openalex created_date 2018/01/12 · openalex publication_date 2018/02/23 · arxiv created 2018/02/24 · arxiv updated 2018/02/27 · openalex updated_date 2026/08/06
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 G 3 ( X ), where X =− A μ A μ /2 with a vector field A μ , 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 A 1 , which originates from the coupling to the Einstein tensor G μν A μ A ν equivalent to the quartic coupling G 4 ( 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 G 4 ( X ) ⊃ β 4 X n with the nonvanishing A 1 , while the other branch with A 1 =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.