Unitary constraints on semiclassical Schwarzschild black holes in the presence of island - INSPIRE

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Unitary constraints on semiclassical Schwarzschild black holes in the presence of island

Dong-Hui Du
(
- Zhongshan U.
)
,
Wen-Cong Gan
(
- Baylor U., Math. Dept.
)
,
Fu-Wen Shu
(
- Nanchang U. and
- Yangzhou U.
)
,
Jia-Rui Sun
(
- Zhongshan U.
)

Jun 21, 2022

21 pages

Published in:

Phys.Rev.D 107 (2023) 2, 026005

Published: Jan 5, 2023

e-Print:

2206.10339 [hep-th]

DOI:

10.1103/PhysRevD.107.026005 (publication)

View in:

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Abstract: (APS)

We reconsider

D \geq 4

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.,

β ≪ 1

). The tension between the near-horizon condition and the short-distance approximation emerges in large dimensions in [K. Hashimoto, N. Iizuka, and Y. Matsuo, J. High Energy Phys. 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 \geq 4

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 \geq 4

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 [F. Holdt-Sordrensen, D. A. McGady, and N. Wintergerst, Phys. Rev. D 102, 026016 (2020)]. We interpret these as the unitary constraints implied by the presence of island in semiclassical gravity.

Note:

21 pages, 4 figures; improvements to the expression; Footnote 2 added to show a new analytical island solution for $n\rightarrow\infty$ while $\alpha\sim \beta/n$; accepted for publication in PRD

black hole: Schwarzschild
unitarity: constraint
gravitation: semiclassical
tension
surface
space-time
horizon

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