Causal description of marginally trapped surfaces in D-dimensions

TL;DR

This paper investigates the causal properties of marginally trapped surfaces in higher-dimensional spherically symmetric spacetimes, deriving formulas for their causal nature and proposing a new classification for degenerate horizons.

Contribution

It provides a novel analytical framework for understanding the causal structure of evolving horizons in D-dimensional spacetimes with perfect fluid and cosmological constant.

Findings

Derived a closed-form expression for the norm of the normal to the trapped surface.

Obtained simple formulas for the causal nature of horizons in homogeneous fluids.

Identified solutions with null causal signature despite evolving area, challenging standard horizon classification.

Abstract

In this paper, we analyse the causal aspects of evolving marginally trapped surfaces in a D-dimensional spherically symmetric spacetime, sourced by perfect fluid with a cosmological constant. The norm of the normal to the marginally trapped tube is shown to be the product of lie derivatives of the expansion parameter of future outgoing null rays along the incoming and outgoing null directions. We obtain a closed form expression for this norm in terms of principal density, pressure, areal radius and cosmological constant. For the case of a homogeneous fluid distribution, we obtain a simple formula for determining the causal nature of the evolving horizons. We obtain the causal phase portraits and highlight the critical radius. We identify many solutions where the causal signature of the marginally trapped tube or marginally anti-trapped tube is always null despite having an evolving area. These solutions don't comply with the standard inner and outer horizon classification for degenerate horizons. we propose an alternate prescription for this classification of these degenerate horizons.