Abstract
Recently it has been shown that quantum fields can be regular on the inner, Cauchy horizon of a rotating BTZ black hole, which appears to indicate a failure of strong cosmic censorship. We argue that, instead, what these results imply is that the inner horizon remains non-singular when leading-order backreaction of the quantum fields is computed, but, after next-order backreaction is accounted for, it will become singular. Then, strong cosmic censorship will be enforced in the BTZ black hole. We support our claims using a four-dimensional holographic dual of the system, which connects the instability of the inner horizon of the BTZ black hole to that of Kerr-type black holes.
Highlights
Quantum backreactionBackreaction from the quantum fields is accounted for by solving the Einstein equations for a perturbation of the BTZ black hole sourced by the renormalized stress-energy tensor
Recently it has been shown that quantum fields can be regular on the inner, Cauchy horizon of a rotating BTZ black hole, which appears to indicate a failure of strong cosmic censorship
Instead, what these results imply is that the inner horizon remains non-singular when leading-order backreaction of the quantum fields is computed, but, after next-order backreaction is accounted for, it will become singular
Summary
Backreaction from the quantum fields is accounted for by solving the Einstein equations for a perturbation of the BTZ black hole sourced by the renormalized stress-energy tensor. If this were divergent at the inner horizon, the correction to the geometry would become large. One may take the perturbative study to the order by solving for the quantum field theory in the first-order-corrected black hole geometry, and backreact again with the resulting renormalized stress tensor It is at this stage that the situation will change at the inner horizon of the BTZ black hole. We will follow a different approach to solving this problem, one which supports our arguments above, while casting them into a different, helpful light
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