Extending the weak cosmic censorship conjecture to the charged Buchdahl star by employing the gedanken experiments

TL;DR

This paper investigates the weak cosmic censorship conjecture for Buchdahl stars, non-black hole objects, and finds that non-linear perturbations prevent overcharging, supporting the conjecture's validity for these stars.

Contribution

It extends the analysis of the weak cosmic censorship conjecture to Buchdahl stars and demonstrates that non-linear effects uphold the conjecture.

Findings

Overcharging possible at linear level

Non-linear perturbations prevent overcharging

WCCC holds for Buchdahl stars

Abstract

In this paper, we wish to investigate the weak cosmic censorship conjecture (WCCC) for the non black hole object, Buchdahl star and test its validity. It turns out that the extremal limit for the star is over-extremal for black hole, $Q^2/M^2 \leq 9/8 >1$; i.e., it could have $9/8 \geq Q^2/M^2 > 1$. By carrying out both linear and non-linear perturbations, we establish the same result for the Buchdahl star as well. That is, as for black hole it could be overcharged at the linear perturbation while the result is overturned when the non-linear perturbations are included. Thus WCCC is always obeyed by the Buchdahl star.