Spontaneous Vectorization in the Einstein-Maxwell-Vector Model

Abstract

We investigate spontaneous vectorization in the Einstein-Maxwell-Vector (EMV) model, introducing a novel mechanism driven by the interplay between electromagnetic and vector fields. A key innovation in our work is the resolution of an apparent divergence in the vector field near the event horizon, achieved by employing a generalized coordinate transformation. This not only extends the domain of existence for vectorized Reissner-Nordström black holes (VRNBHs), but also refines the theoretical understanding of such solutions. We introduce a new concept of combined charge $\sqrt{{\tilde{Q}}^2+{\tilde{P}}^2}$, which better captures the underlying physics of these black holes and provides a unified framework for analyzing thermodynamics and observable phenomena such as light ring structures. Our findings suggest that VRNBHs exhibit enhanced thermodynamic preference and distinctive light ring properties compared to Reissner-Nordström solutions. Moreover, we demonstrate how this combined charge approach reveals connections to two-charge black hole solutions, offering promising avenues for observational verification within the context of effective field theories.

31 pages, 11 figures Corrected typos. Revised the wording of the article, but the result unchanged