For BTZ-like black holes in Einstein-bumblebee gravity, the conserved charges, central charges, and entropy all acquire factors of the Lorentz-violating parameter, and the near-horizon extremal case admits a Virasoro-Kac-Moody U(1) algebra.
Asymmetrically warped compactifications and gravitational Lorentz violation
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In a variant of the Randall-Sundrum braneworld model which has a charged black hole in an anti-de Sitter bulk, the 4D speed of gravity depends upon one's location in the bulk, and in general differs from the speed of light on a given 3-brane. We apply phenomenological constraints on the difference in the speeds of light and gravity to models which use the warping to solve the hierarchy problem. In particular, consideration of the gravi-Cerenkov radiation of Kaluza-Klein gravitons by ultra-high energy cosmic rays leads to a stringent limit on the fractional difference between the graviton and photon speeds in RS-like models: it must be less than a part in 10^{23}.
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Conserved charges and asymptotic symmetries of BTZ-like black holes in Einstein-bumblebee gravity
For BTZ-like black holes in Einstein-bumblebee gravity, the conserved charges, central charges, and entropy all acquire factors of the Lorentz-violating parameter, and the near-horizon extremal case admits a Virasoro-Kac-Moody U(1) algebra.