On a conformal Schwarzschild-de Sitter spacetime

Abstract

On the basis of the C-metric, we investigate the conformal Schwarzschild - deSitter spacetime and compute the source stress tensor and study its properties, including the energy conditions. Then we study its extremal version ($b^2=27m^2$, where $b$ is the deS radius and $m$ is the source mass), when the metric is nonstatic. The weak-field version is analyzed in several frames, and the metric becomes flat with the special choice $b=1/a$, $a$ being the constant acceleration of the Schwarzschild-like mass or black hole. This form is Rindler's geometry in disguise and is also conformal to a de Sitter metric where the acceleration plays the role of the Hubble constant. In its time dependent version, one finds that the proper acceleration of a static observer is constant everywhere, in contrast with the standard Rindler case. The timelike geodesics along the z-direction are calculated and proves to be hyperbolae.

11 pages, no figures. Version published in GRG 53:103 (2021)

References in corpus (3)

• Interpreting the C-metric
• Interior of a Schwarzschild black hole revisited
• Boundary sources in the Doran - Lobo - Crawford spacetime