Kavli Affiliate: Lijing Shao
| First 5 Authors: Zhan-Feng Mai, Rui Xu, Dicong Liang, Lijing Shao,
| Summary:
Spherical black-hole (BH) solutions have been found in the bumblebee gravity
where a vector field nonminimally couples to the Ricci tensor. We study dynamic
(in)stability associated with the gravitational and vector perturbations of odd
parity against these bumblebee BHs. We find that bumblebee BHs do not suffer
ghost instability, but gradient instability and tachyonic instability exist
when the bumblebee charge exceeds certain values. The existence of the
instabilities also depends on the nonminimal coupling constant $xi$ that,
there is a minimal value $xi sim 4pi G$ with $G$ the gravitational constant
for the instabilities to happen. The theoretical consideration for bumblebee BH
stability turns out to place stronger constraints on the parameter space than
those from the recent observations of supermassive BH shadows by the Event
Horizon Telescope Collaboration. It is also reminiscent of Penrose’s cosmic
censorship conjecture since the charge of bumblebee BHs cannot be too large due
to the dynamic instabilities. Specifically, for $xi(xi-16pi G) > 0$, we find
that the charge of a bumblebee BH cannot be larger than its mass.
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