Schwarzschild Solution in R-spacetime

Abstract

Here we construct new solutions from the Einstein Field equations -some analog of the Schwarzschild metric in anti-de Sitter-Beltrami spacetime in the c → ∞ limit (R-spacetime). In this case we derive an adiabatic invariant for finite movement of the massive point particle and separate variables Hamilton-Jacobi equation. Quasi orbital motion is analyzed and its radius time dependence is obtained.

Noether Charge, Thermodynamics and Phase Transition of the Schwarzschild Black Hole in Anti-de Sitter-Beltrami spacetime

“…This metric describes the spherically symmetric solution with negative cosmological constant in an inertial reference frame [39,40].…”

“…So it means that a zero-temperature state should be determined in (A)dSB spacetime [38]. The Schwarzschild solution in (Anti)-de Sitter-Beltrami spacetime was first studied in the works [39,40], which shows that the Schwarzschild-Anti-de Sitter metric in non-inertial or Beltrami coordinates can be constructed via the spherical coordinate transformation from the non-inertial or static Schwarzschild-Anti-de Sitter metric. Later thermodynamics of the Schwarzschild black hole in de Sitter-Beltrami (SdSB) was investigated in the work [41] and shown that the black hole with positive curvature appears only in unstable state in Beltrami coordinates.…”