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

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.