Proca-Maxwell System in an Infinite Tower of Higher-Derivative Gravity

TL;DR

This paper constructs a five-dimensional Proca-Maxwell system coupled with higher-derivative gravity, demonstrating that higher-order corrections regularize spacetime and reveal a 'frozen state' that mimics extremal black holes, with charge influencing this behavior.

Contribution

It introduces a novel higher-derivative gravity model that produces regular, physically viable black hole mimickers without exotic matter.

Findings

Higher-order corrections regularize spacetime singularities.

A 'frozen state' emerges with matter concentrated at a critical radius.

Electric charge prevents the formation of the critical core.

Abstract

We numerically construct a five-dimensional Proca-Maxwell system coupled to an infinite tower of higher-derivative gravity, parameterized by the correction order and coupling constant. While the first-order correction case recovers standard Einstein gravity results, and the second-order correction (Gauss-Bonnet) case fails to resolve the central singularity in the vanishing frequency limit, we demonstrate that higher-order corrections effectively regularize the spacetime, yielding globally regular solutions. A key finding is the emergence of a ``frozen state'' in the supercritical regime: as the field frequency approaches zero, matter concentrates entirely within a critical radius, creating a regular core that externally mimics an extremal black hole. We further reveal that introducing the electric charge fundamentally alters this behavior; the electrostatic repulsion counteracts the gravitational collapse, effectively ``unfreezing'' the system and preventing the formation of the critical core. Significantly, unlike models relying on exotic matter, our solutions satisfy all standard energy conditions across the entire parameter space, establishing a physically viable pathway for constructing regular black hole mimickers.