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arxiv: 2604.09760 · v1 · submitted 2026-04-10 · 🌀 gr-qc · hep-th

Recognition: unknown

Homothetic Killing horizons in generic Vaidya spacetimes

Ritwika Ghoshal , Nilay Kundu , Srijit Bhattacharjee
Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:07 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords Vaidya spacetimeconformal Killing vectorhomothetic Killing horizondynamical black holesblack hole thermodynamicsKerr-Vaidya metricanalytic extensionparticle creation
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The pith

Vaidya spacetimes admit unique homothetic Killing vectors when mass, charge or spin parameters vary linearly with advanced time.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper solves the conformal Killing equation throughout generic Vaidya geometries that may carry charge or rotation. It finds a unique family of solutions that are homothetic precisely when those parameters change linearly with the advanced null coordinate. The homothetic vector then permits a conformal rescaling that converts the original dynamical metric into a stationary one, so that ordinary Killing-horizon techniques become available on the surface where the vector is null. The authors use this construction to write a first-law relation for spherical cases and to sketch the maximal extension of the charged Vaidya metric together with its consequences for particle creation.

Core claim

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 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.

What carries the argument

The homothetic Killing vector, a solution of the conformal Killing equation whose conformal factor is constant and that becomes null on the homothetic Killing horizon, thereby furnishing the conformal map to a stationary geometry.

If this is right

  • The dynamical spacetime can be conformally transformed into a stationary spacetime possessing ordinary Killing horizons.
  • A first-law or flux-balance relation holds for the homothetic Killing horizons of spherically symmetric Vaidya metrics.
  • Both mass and angular-momentum parameters must vary with time for the homothetic vector to exist in the Kerr-Vaidya case.
  • Maximal analytic extensions of the charged Vaidya metric can be constructed, opening a route to particle-creation calculations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same linear-parameter condition may allow similar mappings in other classes of dynamical black-hole solutions.
  • Hawking-like radiation spectra could be computed by transporting the problem to the conformally related stationary geometry.
  • The homothetic horizons might serve as a controlled testing ground for comparing different dynamical horizon notions such as apparent or trapping horizons.

Load-bearing premise

The mass, charge, or rotation parameters must be linear functions of the advanced null time.

What would settle it

Explicit integration of the conformal Killing equation for a Vaidya metric whose mass parameter grows quadratically with advanced time, followed by verification that no homothetic solution exists.

Figures

Figures reproduced from arXiv: 2604.09760 by Nilay Kundu, Ritwika Ghoshal, Srijit Bhattacharjee.

Figure 2
Figure 2. Figure 2: FIG. 2. The region [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper solves the conformal Killing equation in generic Vaidya spacetimes (including charged and rotating Kerr-Vaidya cases). It establishes that a unique class of homothetic conformal Killing vectors exists precisely when the mass, charge, and/or rotation parameters are linear functions of advanced time v. This permits a conformal map to a stationary spacetime, the definition of a homothetic Killing horizon (the surface where the HKV is null), a flux-balance law for spherically symmetric Vaidya, and an analysis of the maximal analytic extension of charged Vaidya with implications for particle creation.

Significance. If the derivations hold, the result supplies an explicit, checkable condition under which dynamical Vaidya-type spacetimes possess a homothetic symmetry that reduces thermodynamic questions to the stationary case. The extension to Kerr-Vaidya (requiring both M(v) and a(v) linear) and the concrete flux-balance law are useful for modeling accreting or evaporating black holes; the maximal-extension discussion adds relevance to semiclassical effects.

minor comments (3)
  1. The abstract states that the solution exists 'iff both mass and rotation parameters become dynamic' for Kerr-Vaidya, but does not indicate the explicit form of the HKV or the coordinate components; adding one sentence or an equation reference would improve readability.
  2. The term 'homothetic Killing horizon' is introduced without an immediate equation; a short definition such as 'the locus where the HKV becomes null' placed early in §3 would help.
  3. In the discussion of the flux-balance law, the relation between the conformal factor and the surface gravity should be written explicitly (e.g., as an equation) rather than left implicit.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive assessment, including recognition of the utility of the homothetic Killing vector construction for dynamical Vaidya-type spacetimes and the extension to Kerr-Vaidya. The recommendation for minor revision is noted, but the report contains no specific major comments requiring point-by-point rebuttal.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The derivation proceeds by directly solving the conformal Killing equation componentwise in the given Vaidya-type metric ansatz (including Kerr-Vaidya). The requirement that mass, charge, or rotation parameters be linear in advanced time v emerges as a necessary condition for the existence of a homothetic solution, rather than being inserted by definition or fitted to data. No load-bearing step reduces to a self-citation, an ansatz smuggled via prior work, or a renaming of a known result; the subsequent conformal mapping, horizon definition, and flux-balance law are standard consequences once the vector field is obtained. The paper is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

The results depend on the specific form of the Vaidya metric and the linearity assumption for parameters, which are introduced to allow analytic solution of the conformal Killing equation.

axioms (2)
  • domain assumption The spacetime metric is of Vaidya form or Kerr-Vaidya form
    The paper studies these specific metrics as the background.
  • domain assumption Conformal Killing equation admits analytic solutions under linear parameter evolution
    Invoked to establish existence of the homothetic vectors.
invented entities (2)
  • Homothetic Killing vector (HKV) no independent evidence
    purpose: Conformal Killing vector that is homothetic for linear parameters
    Introduced to enable conformal mapping from dynamical to stationary spacetime.
  • Homothetic Killing horizon no independent evidence
    purpose: Surface where the HKV becomes null
    Defined to discuss thermodynamic properties and first law.

pith-pipeline@v0.9.0 · 5486 in / 1460 out tokens · 60111 ms · 2026-05-10T17:07:59.804744+00:00 · methodology

discussion (0)

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Reference graph

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