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

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.

💡 Research Summary

The paper investigates a three‑dimensional Manin gauge theory with gauge group SL(2;ℝ) and shows that, when minimally coupled to Einstein gravity, it admits a dual description in which the usual dreibein and spin connection are exchanged with the gauge potential A and its dual field B. This exchange leads to a second, gauge‑invariant metric – the “ersatz metric’’ (\hat g_{\mu\nu}) – defined as a double copy of the field strength rather than the potential: \