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

TL;DR

We show that a three-dimensional Yang–Mills/Manin gauge theory with a noncompact algebra $ ext{T}^*rak{sl}(2;\,b R)$, when coupled to Einstein gravity, admits a dual interpretation as Einstein gravity interacting with an emergent ersatz metric $oxed{\uhat{g}}$ that is a double copy of the gauge field, specifically $oxed{rac{g}{rac{e}}_{\mu u}\nolinebreak[0] \,oxdot rac{e}{rac{e}}_{ u}}$ and expressible as $rac{e}{rac{e}}^a rac{e}{rac{e}}^b \, olinebreak[0] \, eta_{ra{ab}}$. Under a duality to a bimetric theory, the gauge-field components $(A^a_\mu,B^a_\mu)$ swap with the gravitational dreibein and spin connection $(e^a_\mu,\omega^a_\mu)$, yielding a second metric $rac{rac{g}{rac{e}}}_{rac{rac{g}{rac{e}}}}$ and a coupling term between the metrics. When matter couples to the ersatz metric, the resulting black holes possess ersatz Hawking radiation and obey (approximately, in the low-energy limit) black-hole thermodynamics. The construction relies on a three-dimensional, noncompact-gauge-theory framework and admits higher-derivative corrections and various dualisations, with limitations on unitarity and applicability beyond three dimensions. This work thus connects the classical double copy, analogue gravity concepts, and bimetric gravity into a concrete gauge-theory realization of ersatz gravity and horizon thermodynamics.

Abstract

We show that a three-dimensional Manin gauge theory with gauge group $\operatorname{SL}(2;\mathbb R)$ (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 $\hat g_{μν}\sim\operatorname{tr}((\star F)_μ(\star F)_ν)$ is a classical double copy of the gauge field strength $F_{μν}$ (as opposed to the usual double copy of the gauge potential $A_μ$). If matter exclusively couples to $\hat g$ (for example, in a gravitational decoupling limit), then one can formulate black-hole thermodynamics with regards to the ersatz metric. In particular, a black-hole solution for the ersatz metric $\hat g_{μν}$ (made of Yang-Mills fields) radiates ersatz Hawking radiation and obeys the laws of black-hole thermodynamics.