Minimum mass–radius ratio for charged gravitational objects

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.