Minimum mass-radius ratio for charged gravitational objects

TL;DR

This paper establishes a lower bound on the mass-radius ratio for charged compact objects in general relativity, considering effects of vacuum energy and stability, and provides bounds on charge, mass, and energy.

Contribution

It introduces a rigorous proof of a minimum mass-radius ratio for charged objects, extending Buchdahl's inequality to include charge and vacuum energy effects.

Findings

Derived lower bound for mass-radius ratio of charged objects

Obtained bounds on total charge, mass, and vacuum energy

Analyzed stability and energy of minimum ratio objects

Abstract

We rigorously prove that for compact charged general relativistic objects there is a lower bound for the mass-radius ratio. This result follows from the same Buchdahl type inequality for charged objects, which has been extensively used for the proof of the existence of an upper bound for the mass-radius ratio. The effect of the vacuum energy (a cosmological constant) on the minimum mass is also taken into account. Several bounds on the total charge, mass and the vacuum energy for compact charged objects are obtained from the study of the Ricci scalar invariants. The total energy (including the gravitational one) and the stability of the objects with minimum mass-radius ratio is also considered, leading to a representation of the mass and radius of the charged objects with minimum mass-radius ratio in terms of the charge and vacuum energy only.