Nonsingular Rotating Black Holes in the Dark-Energy Dominated Universe

TL;DR

This work introduces a general stationary, axisymmetric metric for nonsingular rotating black holes in a dark-energy background, using a generalized Kerr-Schild construction on a de Sitter-like seed with a potentially running cosmological term $\Lambda(r)$. Regularity is achieved by imposing near-core conditions on the mass function $\mathcal{M}(r)$ and $\Lambda(r)$, yielding a scalar-regular (S-R) class that maps static regular seeds to rotating spacetimes and avoids the Newman–Janis algorithm’s pathologies in a $\Lambda$ background. A minimal-order, asymptotic-safety–inspired model demonstrates finite curvature invariants at the ring, analyzes horizons and causal structure, and shows that the weak energy condition is generically violated in the deep interior. The framework provides a controlled setting to confront rotating regular black holes with current and forthcoming gravitational-wave and horizon-scale imaging data, while noting unresolved issues like inner-horizon stability and dynamical robustness that merit further study.

Abstract

Motivated by quantum-gravity scenarios that replace the classical black hole singularity with a regular core, and by the possibility that the dark-energy sector may be scale dependent, we construct a broad class of nonsingular rotating black-hole spacetimes embedded in an improved de Sitter--like background with either constant or running $Λ$. Because the Newman--Janis algorithm is generically incompatible with a cosmological-constant fluid, we instead propose a generalized Kerr--Schild construction on a (possibly scale-dependent $Λ$) de Sitter seed, yielding a Carter-type metric characterized by a mass function and a $Λ$ function. Our construction provides a direct map from static, spherically symmetric regular models to their rotating counterparts. We derive sharp regularity conditions at the ring and we identify a minimal-order subclass. We analyze chronology and show that, for non-negative mass function and $Λ$ above a certain negative limit, the spacetimes are stably causal. For minimal-order geometries with non-negative mass, we prove that the weak energy condition must be violated. Finally, we illustrate the framework with an asymptotic-safety--inspired model and discuss horizon structure, surface gravities, and conformal diagrams. These results provide a controlled, observationally oriented arena to confront regular rotating black holes in dark-energy backgrounds with the rapidly improving gravitational-wave and horizon-scale imaging data.

Figures (3)

• Figure 4: A plot of the zeros of $\Delta_r$ showing the position of the horizon for the classical (dashed brown) case versus the quantum improved case (solid blue). Note that to improve the visualization, a logarithmic scale has been used in the $r$ axes. It can be verified that, even for $l=G_0 M/10$, the differences between the $\Delta_r$ functions are only appreciable in the quantum region below the inner horizon. Specifically, the displacement of the horizons was: $r_{IH}\simeq 0.991 r_{IH}^{Clas}$, $r_{OH}\simeq 1.002 r_{OH}^{Clas}$ and $r_{CH}\simeq 0.9999 r_{CH}^{Clas}$. The particular values used in this plot are $\{ l/l_P = 10, M/M_P = 100, a/M_P = 80, \Lambda_0 l_P^2 = 10^{-6}\}$.
• Figure 5: A portion of the conformal diagram for the regular rotating black hole. The grey regions are not part of the spacetime. A test particle initially outside the black hole at point $\mathcal{P}$ can traverse the event horizon and will not reach a singularity. Instead, it could traverse the black hole, as shown. It could even reach the disk at $(r=0,\theta\neq\pi/2)$ and traverse it (keeping $r(\tau)\geq 0$, $\theta\rightarrow\pi-\theta$ and $\phi\rightarrow\phi+\pi$ (mod $2\pi$), i.e., staying in the Ib region) or reach the ring at $(r=0,\theta=\pi/2)$ , where there are no singularities and continue its travel without any disruption.
• Figure 6: A plot of the zeros of $\Delta_r$ for significant cases where big quantum corrections are allowed (blue and green curves) versus the classical case (brown curve). In particular, for the value $l/M \simeq 0.845$ (blue curve) the inner horizon and the event horizon of the black hole combine into a single horizon, i.e., one gets an extreme black hole. If the value of $l$ is even bigger the black hole horizons disappear and only the cosmological horizon remains. This is illustrated for $l/M =1$ (green curve). The particular values used in this plot for the other parameters are $\{M/M_P = 100, a/M_P = 80, \Lambda_0 l_P^2 = 10^{-6}\}$.

Theorems & Definitions (6)

• Proposition 1
• Theorem 1
• Proposition 2
• Proposition 3
• Proposition 4
• Theorem 2