The positive energy conjecture for a class of AHM metrics on $\mathbb{R}^{2}\times\mathbb{T}^{n-2}$

TL;DR

This paper proves the positive energy conjecture for a class of asymptotically Horowitz-Myers metrics on certain product manifolds, extending previous results to a broader class of geometries.

Contribution

It generalizes the positive energy conjecture proof to a wider class of AHM metrics on  imes T^{n-2}, building on prior work by other researchers.

Findings

Confirmed the positive energy conjecture for specified AHM metrics.

Extended previous results to more general geometric settings.

Strengthened the theoretical foundation for energy positivity in these spacetimes.

Abstract

We prove the positive energy conjecture for a class of asymptotically Horowitz-Myers (AHM) metrics on $\mathbb{R}^{2}\times\mathbb{T}^{n-2}$.This generalizes the previous results of Barzegar-Chru\'{s}ciel-H\"{o}rzinger-Maliborski-Nguyen \cite{BCHMN} as well as the authors \cite{LZ}.