Marginally trapped and anti-trapped surfaces for matter evolution in D-dimensions

TL;DR

This paper analytically investigates the formation and evolution of marginally trapped and anti-trapped surfaces in D-dimensional dust cosmology, revealing differences from four-dimensional cases and extending horizon laws.

Contribution

It provides closed-form expressions for these surfaces and their causal nature, and extends the area-balance law to higher-dimensional dust evolution scenarios.

Findings

Derived analytical expressions for marginally trapped surfaces in D-dimensions.

Identified key differences from four-dimensional surface evolution.

Extended the horizon area-balance law to higher dimensions.

Abstract

In this paper, we explore the formation of the marginally trapped and marginally anti-trapped surfaces that arise from the evolution of homogeneous dust in D-dimensions with and without the cosmological constant, this is seen through the analytical expressions for such surfaces. We obtain closed form expressions for the Norm of the normal to the Horizon that decides their causal nature and also look at several interesting features of these surface evolution that are significantly different from the four dimensional counterpart. We obtain the expressions for the Ashtekar-Badrikrihnan's Area-balance law for dynamical horizon (spacelike surface) tailored for the case of spherically symmetric dust evolution in D-dimensions.