Boundary sources in the Doran - Lobo - Crawford spacetime

TL;DR

This paper investigates the boundary structure of the Doran-Lobo-Crawford spacetime using a null hypersurface as the boundary, analyzing the Brown-York quasilocal energy and stress tensors, revealing their dependence on time and impact parameter.

Contribution

It introduces a null hypersurface boundary in the Doran-Lobo-Crawford spacetime and computes the associated stress tensors and energy density, extending previous Rindler horizon results.

Findings

Stress tensors depend on time and impact parameter.

Surface energy density matches Rindler horizon results.

Boundary analysis provides insights into quasilocal energy in this spacetime.

Abstract

We take a null hypersurface (the causal horizon) generated by a congruence of null geodesics as the boundary of the Doran-Lobo-Crawford spacetime, to be the place where the Brown-York quasilocal energy is located. The components of the outer and inner stress tensors are computed and shown to depend on time and on the impact parameter $b$ of the test particle trajectory. The surface energy density $\sigma$ on the boundary is given by the same expression as that obtained previously for the energy stored on a Rindler horizon.