Einstein-Proca Model, Micro Black Holes, and Naked Singularities

TL;DR

This paper investigates the Einstein-Proca equations in static, spherically symmetric spacetime, revealing solutions that include naked singularities and relate to Reissner-Nordstrom black holes, with implications for micro black holes and singularities.

Contribution

It provides an analytical perturbative solution to the Einstein-Proca equations, connecting them to known black hole solutions and exploring the nature of naked singularities.

Findings

Proca field solutions approximate Reissner-Nordstrom metric as range parameter approaches zero.

Additional metric terms are positive, consistent with previous numerical results.

Solutions suggest the existence of naked singularities in the Einstein-Proca model.

Abstract

The Einstein-Proca equations, describing a spin-1 massive vector field in general relativity, are studied in the static, spherically-symmetric case. The Proca field equation is a highly nonlinear wave equation, but can be solved to good accuracy in perturbation theory, which should be very accurate for a wide range of mass scales. The resulting first order metric reduces to the Reissner-Nordstrom solution in the limit as the range parameter $\mu$ goes to zero. The additional terms in the $g_{00}$ metric are positive, as in Reissner-Nordstrom, in agreement with previous numerical solutions, and hence involve naked singularities.