# An exact time-dependent interior Schwarzschild solution

## TL;DR

This paper introduces an exact, time-dependent interior Schwarzschild solution modeling gravitational collapse and the formation of a gravastar, revealing a curvature singularity at a critical radius.

## Contribution

It provides the first exact time-dependent interior solution describing collapse and gravastar formation within Einstein's equations.

## Key findings

- Describes collapse from infinite radius to a gravastar.
- Identifies a curvature singularity at 9/8 of Schwarzschild radius.
- Shows continuation beyond singularity to a gravastar.

## Abstract

We present a time-dependent uniform-density interior Schwarzschild solution, an exact solution to the Einstein field equations. Our solution describes the collapse (or the time-reversed expansion) of an object from an infinite radius to an intermediate radius of 9/8 of the Schwarzschild radius, at which time a curvature singularity appears at the origin, and then continues beyond the singularity to a gravastar with radius equal to the Schwarzschild radius.