PreprintCC BY 4.0arXiv
The Smarr Formula is Gauss's Law: A Kerr-Schild Single-Copy Perspective
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.
Versions
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BibTeX
@misc{alkac2026smarr,
title = {{The Smarr Formula is Gauss's Law: A Kerr-Schild Single-Copy Perspective}},
author = {Gokhan Alkac},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.14707},
eprint = {2605.14707},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.14707},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Smarr Formula is Gauss's Law: A Kerr-Schild Single-Copy Perspective
AU - Gokhan Alkac
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2605.14707
UR - https://arxiv.org/abs/2605.14707
AB - 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.
ER -