Marginally outer trapped surfaces in higher dimensions

TL;DR

This paper explores the properties of marginally outer trapped surfaces in higher-dimensional spacetimes, focusing on their behavior under Kaluza-Klein lifts and projections, and discusses related area inequalities.

Contribution

It demonstrates that marginally trapped surface properties are preserved under lift and projection with conformal scaling, extending understanding in higher-dimensional gravity theories.

Findings

Marginally trapped surfaces are preserved under Kaluza-Klein lift and projection.

Area inequalities for stable axially symmetric trapped surfaces are compared.

Behavior of Killing horizons under bundle transformations is analyzed.

Abstract

We review the basic setup of Kaluza-Klein theory, namely a 5-dimensional vacuum with a cyclic isometry, which corresponds to Einstein-Maxwell-dilaton theory in 4-dimensional spacetime. We first recall the behaviour of Killing horizons and its generators under bundle lift and projection. We then show that the property of compact surfaces of being (stably) marginally trapped is preserved under lift and projection provided the appropriate ("Pauli-") conformal scaling is used for the spacetime metric. We also discuss and compare recently proven area inequalities for stable axially symmetric 2-dimensional and 3-dimensional marginally outer trapped surfaces.