Matching McVittie spacetimes

TL;DR

This paper develops a comprehensive framework for analyzing McVittie spacetimes, elucidating their junction conditions and evolution, which advances understanding of gravitational collapse and bubble dynamics in cosmological contexts.

Contribution

It introduces a novel function simplifying junction conditions and provides a unified analysis of static and dynamic McVittie spacetimes, including numerical evolution with various initial conditions.

Findings

Unified framework for McVittie junction conditions

Numerical insights into spacetime evolution

Deepened understanding of gravitational collapse

Abstract

Gravitational collapse and bubble evolution in the asymptotical Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe is an intriguing and intricate problem. We systematically analyze dynamics for contact \sch-FLRW (McVittie) spacetimes, focusing on their general junction conditions and introducing a novel function to simplify the extrinsic curvature and surface stress-energy tensor. We explore both static and dynamic scenarios, including special cases such as Schwarzschild, FLRW, and Einstein-Straus configurations by using our general framework. Numerical calculations further reveal the evolution of the concentric McVittie spacetimes with various initial conditions, offering deep insights into the interplay between the McVittie mass parameter and initial peculiar velocity. These results provide a unified perspective for understanding gravitational collapse and bubble evolution in cosmology and astrophysics.