Time dependent embedding of spherically symmetric Rindler-like spacetime

TL;DR

This paper studies a time-dependent Rindler-like spacetime embedded in a cosmological background, revealing unique horizon structures and energy conditions, with implications for understanding anisotropic cosmic fluids and horizon dynamics.

Contribution

It introduces a novel analysis of a time-dependent Rindler-like geometry within a cosmological setting, including energy conditions, horizon structure, and energy content.

Findings

Radial and transversal pressures are negative despite positive energy density.

Only one apparent horizon is inside the event horizon.

Weyl energy vanishes due to conformal flatness.

Abstract

An anisotropic cosmic fluid with radial heat flux which sources a time dependent Rindler-like geometry is investigated. Even though its energy density $\rho$ is positive, the radial and transversal pressures are negative and the strong energy condition is not satisfied. The congruence of "static" observers is not geodesic and the heat flux is oriented outward. We computed the Misner-Sharp energy associated with the Rindler-type metric embedded in a spatially flat FLRW universe and found that the Weyl energy is vanishing thanks to the conformally flat form of the spacetime. The null geodesic expansions are computed and one finds that only one of the two apparent horizons is located inside the event horizon. The properties of the Rindler-like geometry embedded in the conformally-flat de Sitter spacetime are investigated.