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Homothetic Killing horizons in generic Vaidya spacetimes

Ritwika Ghoshal1,*, Nilay Kundu1,†, and Srijit Bhattacharjee2,‡

  • *Contact author: ritwikaghoshal1997@gmail.com
  • †Contact author: nilayhep@iitk.ac.in
  • ‡Contact author: srijuster@gmail.com
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Phys. Rev. D 114, 024051 – Published 20 July, 2026

DOI: https://doi.org/10.1103/453t-xfmr

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 if and only if 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.

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Phys. Rev. D 114, 024051– Published 20 July, 2026
  • Received 23 April 2026
  • Accepted 29 June 2026
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