The geometry of the Rindler black hole

Abstract

Using Einstein's equations for gravity for a spherically symmetric field in a static state and the mass function method, a general form of the metric for Schwarzschild-type black holes is proposed. A qualitative analysis of Schwarzschild, Reissner–Nordström and Rindler geometries is performed. In the paper, it is found that Rindler black hole geometry is structurally inverse to Reissner–Nordström geometry, i.e. it has two T-regions and one R-region. In this regard Rindler geometry is like geometry of the Kottler black hole, which does not have flat asymptotics. Potential curves in the gravitational field of the Rindler black hole are constructed, which makes it possible to calculate the limits of finite motion for a test particle in this field. In addition, a qualitative comparison with the known Schwarzschild field metric is performed. Their similarity in behavior at small distances and absolutely different behavior at large scales are shown. Using the known accelerations of the Pioneer spacecraft, limits are numerically found for the T- and R-regions of their motion in the gravitational field of the Solar System.