Field dynamics on the trapping horizon in Vaidya spacetime

TL;DR

This paper investigates the field theoretic structure of trapping horizons in Vaidya spacetime, revealing a generalized Chern-Simons theory coupled to bulk sources, and emphasizes the importance of evolution equations over static cross-sections for quantum considerations.

Contribution

It introduces a generalized effective field theory for trapping horizons in Vaidya spacetime, incorporating matter-dependent couplings and highlighting the necessity of evolution equations for quantum analysis.

Findings

Effective field equations are of a Chern-Simons type coupled to bulk sources.

Standard cross-section analysis is insufficient to understand horizon nature.

Evolution equations are essential for quantum theory development.

Abstract

In this article, we shed some light on the field theoretic aspect of the spherically symmetric trapping horizon in Vaidya spacetime. The effective field equations are that of a Chern-Simons theory coupled to bulk sources through two different couplings, one is purely geometric and the other is matter dependent. This is an effective generalization of the equilibrium horizon scenario where the Chern-Simons theory is coupled to the bulk geometry through a constant matter-independent coupling. Further, we note that the field equations pulled-back to a cross-section of the horizon is inadequate to manifest the nature of the horizon. Hence, contrary to the usual practice, the evolution equation needs to be considered at least while passing on to the quantum theory.