Unitary Constraints on Semiclassical Schwarzschild Black Holes in the Presence of Island

TL;DR

This paper refines the understanding of island solutions in higher-dimensional Schwarzschild black holes, establishing constraints on black hole size and boundary conditions to ensure unitarity in semiclassical gravity.

Contribution

It introduces a proper near-horizon condition that resolves tension in large dimensions and derives new constraints related to the existence of island solutions in any D≥4 dimensions.

Findings

Derived constraints on black hole size and boundary position for island existence.

Confirmed large D limit results align with previous findings.

Interpreted constraints as unitarity conditions in semiclassical gravity.

Abstract

We reconsider $D\geq4$ dimensional asymptotically flat eternal Schwarzschild black hole, and focus on the situation where the inner boundary of the radiation region is chosen to be near the horizon (i.e. $\beta \ll1$). The tension between the near-horizon condition and the short-distance approximation emerges in large dimensions in $[JHEP 06 (2020) 085]$. We remove this tension by introducing a more proper near horizon condition, thus the resulting island solution is well-behaved in any $D\geq4$ dimensional spacetime. Interestingly, a novel constraint is obtained in this situation as required by the existence of the island solution, which directly leads to the constraints on the size of the Schwarzschild black hole, the position of the inner boundary for the radiation region, or the value of $c\cdot\tilde{G}_{N}$ in any $D\geq4$ dimension. When considering the large $D$ limit, the constraint on the size of the Schwarzschild black hole obtained in this situation is in agreement with the result given in $[Phys.Rev.D 102 (2020) 2, 026016]$. We interpret these as the unitary constraints implied by the presence of island in semiclassical gravity.