Gravitational Collapse of Self-similar Perfect fluid with Scalar function

TL;DR

This paper investigates the gravitational collapse of a self-similar perfect fluid with a scalar function, revealing conditions under which collapse results in black holes or naked singularities.

Contribution

It introduces a model with a scalar function in self-similar perfect fluid spacetime and analyzes collapse outcomes based on initial data and equations of state.

Findings

Scalar function has an imaginary form during collapse

Collapse outcomes depend on initial data and equation of state

Black hole or naked singularity formation determined by model parameters

Abstract

The self-similar spherically symmetric perfect fluid space-time with scalar function incorporating linear equation of state is studied. The investigation of gravitational collapse conditions on the space-time determines that scalar function has an imaginary form $\phi(X) = i \; \alpha_o \; \varphi(X)$, $\varphi(X)$ being a non-zero real valued function of self-similar variable $X$. The gravitational collapse of cloud ends into the formation of black hole or naked singularity according to the choice of physically reasonable initial data relative to the linear equation of state.