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

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.

Figures (18)

• Figure 1: Schematic representation of the equilibrium mechanism: gravitational attraction versus higher-order curvature and electromagnetic repulsive forces.
• Figure 2: (a): Relationship between the maximum value of the charge parameter $q$ and the coupling parameter $\alpha$ when the fixed frequency $\omega$ is 0.98. (b): Field functions at different $q$ when the $\omega$ is 0.98 and $\alpha$ is 0. The solid lines denote $f$, en-dash lines denote $h$, and dashed lines denote $V$. (c) and (d): The metric component $-g_{tt}$ and $1/g_{rr}$ vs. the radial coordinate $x$ when the $\omega$ is 0.98 and $\alpha$ is 0.
• Figure 3: (a): The ADM mass and conserved particle number, as functions of the field frequency $\omega$ with different $q$ under $\alpha = 0$. The solid lines represent $M$, and dashed lines represent $N_P$. (b): The corresponding binding energy.
• Figure 4: (a): The ADM mass and conserved particle number vs. $\alpha$ with different $q$ under $\omega = 0.98$. The solid lines represent $M$, and dashed lines represent $N_P$. (b): The corresponding binding energy.
• Figure 5: (a) and (b): The ADM mass and conserved particle number, as functions of the field frequency $\omega$ with different $q$ under $\alpha = 0.2$ and the corresponding binding energy. (c) and (d): The ADM mass and conserved particle number, as functions of the field frequency $\omega$ with different $q$ under $\alpha = 0.5$ and the corresponding binding energy. In (a) and (c), the solid lines represent $M$, and dashed lines represent $N_P$.