# Nakedly singular counterpart of Schwarzschild's incompressible star. A barotropic continuity condition in the center

## TL;DR

This paper explores a nakedly singular solution related to Schwarzschild's incompressible star, establishing initial conditions for barotropic equations of state and highlighting differences in central regularity.

## Contribution

It introduces a nakedly singular counterpart to Schwarzschild's interior solution with a new barotropic continuity condition at the center.

## Key findings

- Identifies a singular star-like solution with weakened central regularity.
- Establishes initial conditions for barotropic equations of state.
- Connects the solution to a nakedly singular spherical vacuum.

## Abstract

A static sphere of incompressible fluid with uniform proper energy density is considered as an example of exact star-like solution with weakened central regularity conditions characteristic of a nakedly singular spherical vaccuum solution. The solution is a singular counterpart of the Schwarzschild's interior solution. The initial condition in the center for general barotropic equations of state is established.