Homothetic Killing horizons in generic Vaidya spacetimes

TL;DR

This paper investigates conformal Killing vectors in Vaidya spacetimes, revealing conditions for homothety, and explores their implications for horizons, thermodynamics, and particle creation in dynamic black hole models.

Contribution

It identifies unique homothetic conformal Killing vectors in Vaidya spacetimes and links them to conformal mappings and horizon thermodynamics.

Findings

Existence of a unique class of conformal Killing vectors in Vaidya spacetimes.

Homothetic Killing vectors enable conformal mapping to stationary spacetimes.

Defined homothetic Killing horizons and discussed their thermodynamic properties.

Abstract

We study the conformal Killing equation for generic Vaidya-like spacetimes, including those with rotation. We show that these spacetimes admit a unique class of conformal Killing vectors that are homothetic for mass, charge, or rotation parameters being linear functions of the advanced null-time. For the Kerr-Vaidya metric, the solution to the conformal Killing equation exists iff both mass and rotation parameters become dynamic. The presence of a homothetic Killing vector (HKV) for such a spacetime enables one to conformally map the original dynamical spacetime to a stationary spacetime, enabling access to the standard methods pertaining to a Killing horizon. The surface where an HKV becomes null is termed the homothetic Killing horizon. We discuss the thermodynamic properties of such homothetic Killing horizons and formulate a version of the first law (or flux balance law) for spherically symmetric Vaidya spacetimes. We further study the maximal analytic extension of a charged Vaidya metric and indicate its implications for studying particle creation in such backgrounds.