Schwarzschild-de Sitter Metric And Inertial Beltrami Coordinates

Under consideration of coordinate conditions, we get Beltrami-de Sitter-Schwarzschild metric solution of the Einstein field equations with a cosmological constant A. A brief review to the de Sitter invariant special relativity (dS-SR), and de Sitter general relativity (dS-GR, or GR with a A) is presented. The Beltrami metric Bμv provides inertial reference frame for the dS-spacetime. By examining the de Sitter-Schwarzschild (dSS) metric gμv(M) existed in literatures since1918, we find that the existed dSS metric gμv(M) describes some mixing effects of gravity and inertial-force, instead of a pure gravity effect arisen from "solar mass" M in dS-GR. In this paper, we solve the vacuum Einstein equation of dS-GR, with the requirement of gravity-free metric gμv(M)|M→0=Bμv. In this way we find Beltrami-dSS, the dSS metric in inertial Beltrami coordinates of dS-GR. This is a new metric of dS-GR. Its physical meaning and possible applications are discussed.