Causal dynamics of null horizons under linear perturbations

TL;DR

This paper investigates how null horizons in symmetric spacetimes change causally under linear perturbations, providing a new method to characterize these transitions and analyzing their behavior in Schwarzschild and homogeneous backgrounds.

Contribution

It introduces a simple procedure to characterize the causal transition of null horizons under linear perturbations in symmetric spacetimes, with detailed analysis of shear, vorticity, and stability properties.

Findings

The causal character of null horizons can be systematically characterized.

Shear and vorticity vectors are crucial in the horizon dynamics.

The stability operator's properties influence horizon behavior.

Abstract

We study the causal dynamics of an embedded null horizon foliated by marginally outer trapped surfaces (MOTS) for a locally rotationally symmetric background spacetime subjected to linear perturbations. We introduce a simple procedure which characterizes the transition of the causal character of the null horizon. We apply our characterization scheme to non-dissipative perturbations of the Schwarzschild and spatially homogeneous backgrounds. For the latter, a linear equation of state was imposed. Assuming a harmonic decomposition of the linearized field equations, we clarify the variables of a formal solution to the linearized system that determine how the null horizon evolves. For both classes of backgrounds, the shear and vorticity 2-vectors are essential to the characterization, and their roles are made precise. Finally, we discuss aspects of the relationship between the characterizing conditions. Various properties related to the self-adjointness of the MOTS stability operator are extensively discussed.