Phys.Rev.D, 109, 084053 (2024)
Horizon as a natural boundary
Qi-Yuan Mao1, Liang Ma1 and Hong Lü1,2
1 Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University, Tianjin 300350, China.
2 Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Binhai New City, Fuzhou 350207, China.
* qiyuan_mao@tju.edu.cn, liangma@tju.edu.cn, mrhonglu@gmail.com
Abstract
We consider Einstein gravity extended with Riemann-squared term and construct the leading-order perturbative solution to the rotating black hole with all equal angular momenta in D=7. We find that in the extremal limit, the linear perturbation involves irrational powers in the near-horizon expansion. We argue that, despite that all curvature tensor invariants are regular on the horizon, the irrational power implies that the inside of the horizon is destroyed and the horizon becomes the natural boundary of the spacetime. We demonstrate that this vulnerability of the horizon regularity is an innate part of Einstein theory, and can arise in Einstein theory with minimally coupled matter. However, in fine-tuned theories such as supergravities, the black hole inside is preserved, which may be one of the criteria for a consistent theory of quantum gravity. We also show that the vulnerability occurs in general higher dimensions, which only a few sporadically distributed dimensions can evade.
