Radiative falloff in Einstein-Straus spacetime

TL;DR

This paper investigates the late-time behavior of a massless scalar field in Einstein-Straus spacetime, revealing that unlike in flat spacetime, the field does not decay as an inverse power-law due to curvature effects.

Contribution

It provides a numerical analysis of scalar field evolution in Einstein-Straus spacetime, highlighting the impact of curvature concentration and boundary discontinuities on late-time decay.

Findings

Scalar field does not decay as an inverse power-law in Einstein-Straus spacetime.

Curvature concentration near the black hole influences the field's evolution.

Discontinuity at the dust boundary affects late-time behavior.

Abstract

The Einstein-Straus spacetime describes a nonrotating black hole immersed in a matter-dominated cosmology. It is constructed by scooping out a spherical ball of the dust and replacing it with a vacuum region containing a black hole of the same mass. The metric is smooth at the boundary, which is comoving with the rest of the universe. We study the evolution of a massless scalar field in the Einstein-Straus spacetime, with a special emphasis on its late-time behavior. This is done by numerically integrating the scalar wave equation in a double-null coordinate system that covers both portions (vacuum and dust) of the spacetime. We show that the field's evolution is governed mostly by the strong concentration of curvature near the black hole, and the discontinuity in the dust's mass density at the boundary; these give rise to a rather complex behavior at late times. Contrary to what it would do in an asymptotically-flat spacetime, the field does not decay in time according to an inverse power-law.