Schwarzschild black hole, vacuum C-metric when m = 0 and Rindler metric

Abstract

In this paper, vacuum C-metric when m = 0 is derived from the metric of a Schwarzschild black hole if its mass and location approach to infinity in an appropriate way. Furthermore, by using coordinate transformation in which there is no acceleration, vacuum C-metric when m = 0 is transformed to Rindler metric. The result shows that an infinitesimal neighborhood of the horizon of an infinite Schwarzschild black hole is a Rindler space-time, and the acceleration in the Rindler space-time can arise from the in finite Schwarzschild black hole.