The No-Short Hair Theorem for Black Holes and Wormholes in Extra-Dimension

TL;DR

This paper extends the no-short hair theorem to black holes and wormholes in extra-dimensional theories, suggesting observational tests could reveal extra dimensions or support quantum gravity models like string theory.

Contribution

It generalizes the no-short hair theorem to extra-dimensional black holes and wormholes, linking observational signatures to theories beyond Einstein gravity.

Findings

The theorem applies to extra-dimensional black holes and wormholes.

Observational satisfaction of the theorem could indicate extra dimensions.

The theorem holds in quantum gravity theories excluding extra dimensions.

Abstract

The no-short hair theorem for static spherically symmetric black holes in general theory of relativity asserts that if a black hole has hair, that hair must extend beyond the lowest photon sphere radius of the black hole. This report generalizes the theorem to various extra-dimensional cases of black holes and wormholes in post-Einstein gravity and shows how the observational satisfaction of the no-short hair theorem may lead to a probe for the existence of extra-dimensions. We also show how we may lead to argue that this no-short hair theorem is satisfied for black holes in theories of quantum gravity that naturally precludes extra-dimensional cases, like string theory.