Negative Energy Condition and Black Holes on the Brane

TL;DR

This paper proposes a new perspective on energy conditions in brane-world black holes, suggesting that negative gravitational field energy defines the relevant energy condition, impacting the understanding of black holes influenced by bulk Weyl curvature.

Contribution

It introduces a novel energy condition based on gravitational field energy for non-localizable energies in brane-world scenarios, especially relevant for black holes influenced by bulk curvature.

Findings

Negative gravitational energy characterizes the energy condition for non-localizable energies.

Application to black holes on the brane with Weyl curvature effects.

Implications for energy conditions in higher-dimensional gravity theories.

Abstract

We propose that for non-localizable energy distribution the relevant energy condition is determined by the gravitational field energy which is negative for positive non-gravitational energy. That is negativity of the non-localized energy is the "positive" energy condition. This would have direct application and relevance for a black hole on the brane which would be sitting in a trace free stresses induced by the Weyl curvature of the bulk.