Solution of the deformed Schwarzschild metric by the Yang-Baxter equation

Abstract

In this article, an open-closed string map formulated by Seiberg & Whitten was used to solve problems of generalized supergravity, including the deformed Schwarzschild metric. For this task, found analytical supergravity solution (deformed metric and NSNS (Neveu – Schwarz) two-form Bμν-field). The solution was obtained from antisymmetric bivector constructed from antisymmetric products of Killing vectors used as components of the equation of motion. In the problem under consideration, the equations of motion are the CYBE (classical Yang-Baxter equation), whose general solution can be obtained using the r-matrix. As a result, for the deformed metric, the Hamilton — Jacobi equation is obtained, the particle motion on the plane is studied, with θ = π/2. So, we obtained several analytical solutions for the function r(φ), φ(r). Since these results are very voluminous for representations, we present the schedule the test particle from the function r(φ), which shows the centrally- symmetric motion of the particle in the Schwarchild field. As a continuation of this work, it is possible to obtain a numerical solution for a function r(t), that has a complex integral for the analytical solution of this problem. The theoretical meaning of the work is that CYBE derives from the equation of motion of the theory of gravity, thereby reducing the problem of determining the r-matrix, which is a CYBE solution for generalized supergravity.