Charged spherically symmetric black holes in the Lyra geometry and a preliminary investigation on the overcharging process

This paper aims to investigate charged spherically symmetric static black holes in the Lyra geometry, in which a scale function naturally arises in the metric and affine structure of these types of manifolds. In particular, it utilizes the appropriate generalization of general relativity, the recently proposed Lyra scalartensor theory (LyST). The simplest generalization of Maxwell electrodynamics for Lyra manifolds is considered. An analytic solution for the line element of a Reissner-Nordstr & ouml;m LyST generalization is presented. It is shown that, due to the natural presence of a scale radius, it is possible to have three different extremal charges for positive or negative charge intervals. As a consequence, in natural units, the equality of the mass and charge defined on Lyra manifolds does not give rise to an extremal black hole, which allows the existence of solutions in which the charge is greater than the mass. An analysis with charged test particles indicates that a finite positive Lyra parameter, referred as the Lyra scale radius in this case, possibly allows for a violation of the weak cosmic censorship on Lyra manifolds. It is shown that an extremal black hole can be overcharged to the point that the emergence of a naked singularity becomes possible. The same behavior is observed for negative values of this parameter if its absolute value is greater than 4 times the black hole mass. Notably, this investigation also shows that an eternal black hole can exist for any charge increase if the Lyra parameter is sufficiently close to some critical values.