Anholonomic Soliton-Dilaton and Black Hole Solutions in General Relativity

TL;DR

This paper introduces a novel method for constructing exact solutions to Einstein's equations in 3D and 4D gravity using anholonomic frames, leading to new black hole and soliton solutions with anisotropic features.

Contribution

It presents a new approach to generate anisotropic black hole and soliton solutions in general relativity via anholonomic frames and nonlinear superpositions of 2D sine-Gordon solitons.

Findings

Existence of static and dynamic anisotropic black hole solutions.

Construction of solutions with horizons shaped as ellipsoids, tori, and cylinders.

Generation of multi-soliton dilaton-black hole configurations.

Abstract

A new method of construction of integral varieties of Einstein equations in three dimensional (3D) and 4D gravity is presented whereby, under corresponding redefinition of physical values with respect to anholonomic frames of reference with associated nonlinear connections, the structure of gravity field equations is substantially simplified. It is shown that there are 4D solutions of Einstein equations which are constructed as nonlinear superpositions of soliton solutions of 2D (pseudo) Euclidean sine-Gordon equations (or of Lorentzian black holes in Jackiw-Teitelboim dilaton gravity). The Belinski-Zakharov-Meison solitons for vacuum gravitational field equations are generalized to various cases of two and three coordinate dependencies, local anisotropy and matter sources. The general framework of this study is based on investigation of anholonomic soliton-dilaton black hole structures in general relativity. We prove that there are possible static and dynamical black hole, black torus and disk/cylinder like solutions (of non-vacuum gravitational field equations) with horizons being parametrized by hypersurface equations of rotation ellipsoid, torus, cylinder and another type configurations. Solutions describing locally anisotropic variants of the Schwarzschild-- Kerr (black hole), Weyl (cylindrical symmetry) and Neugebauer--Meinel (disk) solutions with anisotropic variable masses, distributions of matter and interaction constants are shown to be contained in Einstein's gravity. It is demonstrated in which manner locally anisotropic multi-soliton-- dilaton-black hole type solutions can be generated.