Naked Singularity Formation In f(R) Gravity

TL;DR

This paper investigates conditions under which gravitational collapse in f(R) gravity leads to naked singularities, challenging the cosmic censorship conjecture by analyzing specific functional forms and initial conditions.

Contribution

It demonstrates that certain f(R) gravity models can produce naked singularities during collapse, providing new insights into gravitational theory and cosmic censorship.

Findings

Naked singularities can form in f(R) gravity under specific conditions.

The ratio of mass function to area radius influences singularity visibility.

Weak energy condition can be maintained during collapse with appropriate parameters.

Abstract

We study the gravitational collapse of a star with barotropic equation of state $p=w\rho$ in the context of $f({\mathcal R})$ theories of gravity. Utilizing the metric formalism, we rewrite the field equations as those of Brans-Dicke theory with vanishing coupling parameter. By choosing the functionality of Ricci scalar as $f({\mathcal R})=\alpha{\mathcal R}^{m}$, we show that for an appropriate initial value of the energy density, if $\alpha$ and $m$ satisfy certain conditions, the resulting singularity would be naked, violating the cosmic censorship conjecture. These conditions are the ratio of the mass function to the area radius of the collapsing ball, negativity of the effective pressure, and the time behavior of the Kretschmann scalar. Also, as long as parameter $\alpha$ obeys certain conditions, the satisfaction of the weak energy condition is guaranteed by the collapsing configuration.