The marginally trapped surfaces in spheroidal spacetimes

TL;DR

This paper investigates the placement of marginally trapped surfaces in spheroidal spacetimes, demonstrating that the Misner-Sharp mass from the undeformed spherical case accurately identifies the spheroidal horizon.

Contribution

It introduces a method to locate horizons in spheroidal spacetimes using the Misner-Sharp mass from the spherical case, extending horizon analysis beyond spherical symmetry.

Findings

Misner-Sharp mass correctly locates spheroidal horizons

Spheroidal deformations affect trapped surface locations

Method applies to axial deformations of static systems

Abstract

We study the location of marginally trapped surfaces in space-times resulting from an axial deformation of static isotropic systems, and show that the Misner-Sharp mass evaluated on the corresponding undeformed spherically symmetric space provides the correct gravitational radius to locate the spheroidal horizon.