Characterization of a distorted Schwarzschild black hole using curvature invariants

Abstract

One way to characterize spacetimes is by their curvature invariants. We expand upon the work of Abdelqader and Lake and apply their methods to a perturbed Schwarzschild spacetime---the Preston-Poisson spacetime. A set of curvature invariants may satisfy a syzygy from which one can construct a new dimensionless invariant which may provide an intuitive visualization of the deviation of two spacetimes. However, we point out some of the shortcomings of such an invariant. We also use the curvature invariants to obtain the approximate location of the horizon of the Preston-Poisson black hole.