Spontaneous Vectorization in the Einstein-Maxwell-Vector Model

TL;DR

This paper explores spontaneous vectorization in the Einstein-Maxwell-Vector model, introducing a new coordinate approach to resolve divergences, extending solution domains, and proposing a combined charge concept that enhances understanding of black hole thermodynamics and observable features.

Contribution

It presents a novel mechanism for vectorization, resolves divergence issues near horizons, and introduces a combined charge framework for analyzing black hole solutions in the EMV model.

Findings

Extended the domain of vectorized Reissner-Nordstr"om black holes.

Proposed a combined charge that captures black hole physics more effectively.

Found enhanced thermodynamic preference and distinctive light ring features.

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-Nordstr\"om 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-Nordstr\"om 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.