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Ersatz gravity and black-hole thermodynamics from Manin gauge theory with noncompact gauge group

Leron Borsten*, Dimitri Kanakaris†, and Hyungrok Kim (金炯錄)‡

  • Centre for Mathematics and Theoretical Physics Research, Department of Physics, Astronomy and Mathematics, University of Hertfordshire, Hatfield, Hertfordshire AL10 9AB, United Kingdom

  • *Contact author: l.borsten@herts.ac.uk
  • †Contact author: d.kanakaris-decavel@herts.ac.uk
  • ‡Contact author: h.kim2@herts.ac.uk
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Phys. Rev. D 113, 125017 – Published 15 June, 2026

DOI: https://doi.org/10.1103/mw7g-kjrw

Abstract

We show that a three-dimensional Manin gauge theory with gauge group SL(2;R) (i.e., Yang-Mills theory, the third-way theory, or the imaginary third-way theory) minimally coupled to Einstein gravity admits a dual interpretation as Einstein gravity with an exotic coupling to a Manin gauge theory, where the roles of dreibein/spin connection and field strength/gauge potential are interchanged. The dual, or ersatz, gravitational metric g^μν∼tr((⋆F)μ(⋆F)ν) is a classical double copy of the gauge-field strength Fμν (as opposed to the usual double copy of the gauge potential Aμ). If matter exclusively couples to g^ (for example, in a gravitational decoupling limit), then one can formulate black-hole thermodynamics with regard to the ersatz metric. In particular, a black-hole solution for the ersatz metric g^μν (made of Yang-Mills fields) radiates ersatz Hawking radiation and obeys the laws of black-hole thermodynamics.

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Phys. Rev. D 113, 125017– Published 15 June, 2026
  • Received 6 February 2026
  • Accepted 28 May 2026
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