Nonsingular hairy black holes by gravitational decoupling

Abstract

Using gravitational decoupling under the requirements of a well-defined event horizon and the source matter satisfying the weak energy condition, we construct nonsingular hairy black holes with spherical or axial symmetry. These solutions emerge from a deformation of the Minkowski vacuum, bridging the novel hairy geometries and the classical Schwarzschild and Kerr solutions at the maximum deformation in their respective sectors.

Figures (3)

• Figure 1: The structure of the spherically symmetric metric function \ref{['9g']}: no horizons, one horizon, or two horizons if taking $l=2$ and $\eta=1$ (the top left panel), or $\mathcal{M}=1$ and $\eta=2$ (the top right panel), or $\mathcal{M}=1$ and $\omega=2$ (the bottom right panel); and there is no horizon for $\mathcal{M}=1$ and $l=2$ (the bottom left panel)
• Figure 2: The source terms $\tilde{\epsilon}$, $\tilde{p}_{r}$, $\tilde{p}_{t}$ in the sphericity metric case for $l=2$, $\eta=1$ and $\omega=0.9$ (the top left panel); for $\mathcal{M}=1$, $\eta=2$ and $\omega=102$ (the top right panel); for $\mathcal{M}=1$ and $l=2$ (the bottom left panel); and for $\mathcal{M}=1$, $\omega=2$ and $l=0.3$ (the bottom right panel). The vertical dashed lines represent the event horizons, which are located, respectively, at $r_{\rm h}\sim14$, $r_{\rm h}\sim1.8$, and $r_{\rm h}\sim1.9$
• Figure 3: Axially symmetric solutions of the metric function \ref{['6g']}: There are no horizons, one horizon, and two horizons for $l=2$, $\eta=1$, and $a=0.3$ (the top left panel), or for $\mathcal{M}=1$, $\eta=2$, $a=0.3$ (the top right panel), or for $\mathcal{M}=1$, $\omega=2$, $a=0.3$ (the bottom right panel). There are no horizons for $\mathcal{M}=1$, $l=2$, and $a=0.3$ (the bottom left panel).