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. Under the plane-wave approximation, 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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