Off-diagonal deformations of regular Schwarzschild black holes and general relativistic G. Perelman thermodynamics

TL;DR

This paper develops a method to generate off-diagonal deformations of regular Schwarzschild black holes in general relativity, exploring their thermodynamics through G. Perelman's entropy rather than traditional approaches.

Contribution

It introduces an anholonomic frame and connection deformation method to construct new off-diagonal black hole solutions and applies Perelman's entropy to analyze their thermodynamics.

Findings

Constructed new classes of off-diagonal black hole solutions.

Identified solutions with solitonic vacuum configurations.

Showed traditional thermodynamics does not apply to these solutions.

Abstract

We construct new classes of solutions describing generic off-diagonal deformations of regular Schwarzschild black holes (BHs) in general relativity (GR). Examples of such (primary) diagonal metrics reducing the Einstein equations to integrable systems of nonlinear ordinary differential equations were studied in a recent work by R. Casadio, A. Kamenshchik and J. Ovalle in Phys. Rev. D 111 (2025) 064036. We develop and apply our anholonomic frame and connection deformations method, which allows us to generate new classes of target off-diagonal solutions. Ansatz that reduces the gravitational field equations to systems of (exactly or parametric) integrable systems of nonlinear partial differential equations are used. We find and analyze certain families of deformed regular BHs containing an off-diagonal de Sitter condensate encoding solitonic vacuum configurations, with possible deformations of horizons and/or gravitational polarizations of constants. We emphasize that general off-diagonal solutions do not involve certain hypersurface or holographic configurations. This means that the Bekenstein-Hawking thermodynamic paradigm is not applicable for characterizing the physical properties of such target regular solutions. We argue that the concept of G. Perelman's entropy and relativistic geometric flow thermodynamics is more appropriate. Using nonlinear symmetries involving effective cosmological constants, we show how to compute thermodynamic variables for various classes of physically essential solutions in GR.