Einstein--Proca model: spherically symmetric solutions

TL;DR

This paper investigates the Einstein-Proca system, numerically finding spherically symmetric solutions and showing that such configurations do not form black holes, despite approaching Schwarzschild or Reissner-Nordström metrics at infinity.

Contribution

It provides the first numerical analysis of spherically symmetric solutions in the Einstein-Proca model, revealing the absence of black hole configurations.

Findings

Solutions approach Schwarzschild or Reissner-Nordström metrics at infinity

No black hole configurations are found in the Einstein-Proca system

Numerical methods successfully obtained spherically symmetric solutions

Abstract

The Proca wave equation describes a classical massive spin 1 particle. We analyze the gravitational interaction of this vector field. In particular, the spherically symmetric solutions of the Einstein-Proca coupled system are obtained numerically. Although at infinity the metric field approaches the usual Schwarzschild (Reissner-Nordstr\"om) limit, we demonstrate the absence of black hole type configurations.