Revisiting black holes and wormholes under Weyl transformations

TL;DR

This paper analyzes how black holes and wormholes transform under Weyl conformal transformations, providing a general derivation, exploring their behavior in various spacetimes, and demonstrating that such features can appear or change under these transformations.

Contribution

It offers a new, simplified derivation of horizon and wormhole transformations under Weyl conformal changes and explores their behavior in general spacetimes, revealing that such features can emerge or be altered.

Findings

Black holes and wormholes can appear in the conformal frame even if absent initially.

Some definitions of horizons and wormholes are transformable into each other under Weyl transformations.

Worked-out examples illustrate the transformation behavior of these spacetime features.

Abstract

The behavior of black holes horizon and wormholes under the Weyl conformal transformation is investigated. First, a shorter, but more general, derivation of the Weyl transformation of the simple prescription for detecting horizons and wormholes given recently in the literature for spherically symmetric spacetimes is provided. The derivation allows for a simple and intuitive way to understand why and when horizons and wormholes might arise in the conformal frame even if they were absent in the original frame. Then, the conformal behavior of black holes horizon and wormholes in more general spacetimes, based on more "sophisticated" definitions, is provided. The study shows that black holes and wormholes might always arise in the new frame even if they were absent in the original frame. Moreover, it is shown that some of the definitions found in the literature might be transformed into one another under such transformations. Worked-out examples are given.