Accelerated motion in general relativity: fate of the singularity

Abstract

AbstractUnder general relativity, the paths of accelerated test particles are taken into account. It is examined whether such accelerations have any influence on the ‘singularity’ of the spacetime. The Raychaudhuri equation for the congruence of the time-like curves describing the paths of the accelerated particles is considered to calculate a few physical attributes. It is shown that if the acceleration of the test particles exceeds a particular value, then the congruences of the accelerated time-like curves do not encounter any singularity although the usual energy conditions are violated or modified. It is shown further that in the curved spacetime of general relativistic framework one may generate a system of transformations that is a generalization of the Rindler coordinates related to accelerated frame in the flat Minkowski spacetime. To show the influence of the acceleration of test particle on singularity of a particular spacetime the Schwarzschild spacetime is considered. Taking tidal deviation related acceleration term, it is shown that the acceleration may attain a specific value for which the modified Kretschmann scalar vanishes in a spherical neighbourhood of the singularity and thus the Schwarzschild singularity disappears. In the context of singularity as ‘geodesic incompleteness’ of the spacetime manifold it is also proved that prescribing an appropriate acceleration term on the maximal geodesic defined in a finite interval one may extend it up to infinite proper time and hence the spacetime becomes singularity free. Such results hold at the price of violating the usual energy conditions.