Energy density bounds for black strings

TL;DR

This paper investigates the positivity of energy density in black string spacetimes using Y-ADM mass density and spinorial techniques, extending previous results to include apparent horizons and providing conditions for positivity.

Contribution

It extends the positivity analysis of Y-ADM mass density to black strings with apparent horizons, offering new sufficient conditions for positive energy density.

Findings

Established conditions for positive Y-ADM mass density in black strings.

Extended positivity results to spacetimes with apparent horizons.

Utilized spinorial techniques for energy density analysis.

Abstract

The conserved charge called Y-ADM mass density associated with asymptotically translational Killing-Yano tensor gives us an appropriate physical meaning about the energy density of $p$ brane spacetimes or black strings. We investigated the positivity of energy density in black string spacetimes, using the spinorial technique introduced by Witten. Recently, the positivity of Y-ADM mass density in p brane spacetimes was discussed. In this paper, we will extend this discussion to the transversely asymptotically flat black string spacetimes containing an apparent horizon. We will give the sufficient conditions for the Y-ADM mass density to become positive in such spacetimes.