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 analyze 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 investigated 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.
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I am grateful to the anonymous referees for useful suggestions and comments which considerably improved the quality of the manuscript.
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Culetu, H. On a conformal Schwarzschild-de Sitter spacetime. Gen Relativ Gravit 53, 103 (2021). https://doi.org/10.1007/s10714-021-02876-2
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DOI: https://doi.org/10.1007/s10714-021-02876-2