Can the cosmological constant undergo abrupt changes?

TL;DR

This paper explores the possibility of abrupt changes in the cosmological constant by constructing solutions to Einstein's equations that transition between de Sitter and Schwarzschild space-times, suggesting potential discontinuities.

Contribution

It introduces a method to model spherically symmetric solutions with a variable cosmological constant that can change abruptly at a certain radius.

Findings

Solutions tend to zero external sources in the generalized functions sense.

The interior solution is de Sitter space, while the exterior is Schwarzschild space.

Demonstrates a mathematical framework for potential abrupt changes in the cosmological constant.

Abstract

The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of field configurations, which are solutions of the Einstein equations in the presence of the considered cosmological term and auxiliary external sources, is constructed. Then, it is shown that the associated succession of external sources tend to zero in the sense of the generalized functions. The type of weak solution that is found becomes the deSitter homogeneous space-time for the interior region, and the Schwartzschild space in the outside zone.