Schwarzschild-de Sitter Metric and Inertial Beltrami Coordinates

Abstract

Under consideration of coordinate conditions, we get the Schwarzschild-Beltrami-de Sitter (S-BdS) metric solution of the Einstein field equations with a cosmological constant $\Lambda$. A brief review to the de Sitter invariant special relativity (dS-SR), and de Sitter general relativity (dS-GR, or GR with a $\Lambda$) is presented. The Beltrami metric $B_{\mu \nu }$ provides inertial reference frame for the dS-spacetime. By examining the Schwarzschild-de Sitter (S-dS) metric $g_{\mu \nu }^{(M)}$ existed in literatures since 1918, we find that the existed S-dS metric $g_{\mu \nu }^{(M)}$ 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 $g_{\mu \nu }^{(M)}{|}_{M\to 0}=B_{\mu \nu }$. In this way we find S-BdS solution of dS-GR, written in inertial Beltrami coordinates. This is a new form of S-dS metric. Its physical meaning and possible applications are discussed.

16 pages, 1 figure

References in corpus (3)

• Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity
• Yang's Model as Triply Special Relativity and the Snyder's Model--de Sitter Special Relativity Duality
• On de Sitter Invariant Special Relativity and Cosmological Constant as Origin of Inertia

Cited by in corpus (5)

• Thermodynamics of Higher Order Entropy Corrected Schwarzschild-Beltrami-de Sitter Black Hole
• Thermodynamics of Schwarzschild-Beltrami-de Sitter Black Hole
• Implication of Spatial and Temporal Variations of the Fine-Structure Constant
• Seeking for the observational manifestation of de Sitter Relativity
• Noether Charge, Thermodynamics and Phase Transition of a Black Hole in the Schwarzschild-Anti-de Sitter-Beltrami spacetime