Curvature properties of Vaidya metric

Abstract

As a generalization of the Schwarzschild solution, Vaidya presented a radiating metric to develop a model of the exterior of a star including its radiation field, called Vaidya metric. The present paper deals with the investigation on the curvature properties of Vaidya metric. It is shown that Vaidya metric can be considered as a model of different pseudosymmetric type curvature conditions, namely, $C\cdot C = \frac{m}{r^3} Q(g, C)$, $R\cdot R - Q(S,R) = \frac{m}{r^3} Q(g,C)$ etc. It is also shown that Vaidya metric is Ricci simple, vanishing scalar curvature and its Ricci tensor is Riemann-compatible. As a special case of the main result, we obtain the curvature properties of Schwarzschild metric. Finally, we compare the curvature properties of Vaidya metric with another radiating metric, namely, Ludwig-Edgar pure radiation metric.