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  • Open Access

Smarr formula is Gauss’s law: A Kerr-Schild single-copy perspective

Gökhan Alkaç*

  • *Contact author: alkac@mail.com
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Phys. Rev. D 114, 084052 – Published 19 October, 2026

DOI: https://doi.org/10.1103/qgy1-k9yl

Abstract

In the Kerr-Schild double copy, static and spherically symmetric black hole solutions of general relativity are mapped to purely electric solutions of Maxwell’s theory in flat spacetime. We demonstrate that, for these configurations, the thermodynamic Smarr formula is structurally identical to the single-copy Gauss’s law. Extending this to asymptotically anti–de Sitter spacetimes, we prove that the thermodynamic pressure-volume term naturally emerges from a gauge-theoretic background subtraction. This relationship establishes a novel connection between the classical double copy and black hole thermodynamics.

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Phys. Rev. D 114, 084052– Published 19 October, 2026
  • Received 25 May 2026
  • Accepted 23 September 2026
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