Skyrme black holes in the isolated horizons formalism

We study static, spherically symmetric, Skyrme black holes in the context of the assumption that they can be viewed as bound states between ordinary bare black holes and solitons. This assumption and results stemming from the isolated horizons formalism lead to several conjectures about the static black hole solutions. These conjectures are tested against the Skyrme black hole solutions. It is shown that, while there is in general good agreement with the conjectures, a crucial aspect seems to violate one of the conjectures.

Figure 1

$\beta (x_{△})$ for the two branches of the $B\sim 1$ (solid line), $B\sim 2$ (dashed line) and $B\sim 3$ (dash-dotted line) Skyrme black holes with $\alpha =4\pi G{f}^2=0.001$. The portions of the curves with the lower values of $\beta (x_{△})$ are the unstable solutions.

Figure 2

The ADM masses for the two branches of the $B\sim 1$ (solid line), $B\sim 2$ (dashed line) and $B\sim 3$ (dash-dotted line) Skyrme black holes with $\alpha =4\pi G{f}^2=0.001$. The curves with the lower ADM masses are the stable solutions.

Figure 3

The function $A(x)$ versus dimensionless length $x=fgr$ for the two branches of the $B\sim 1$ (solid line), $B\sim 2$ (dashed line) and $B\sim 3$ (dash-dotted line) Skyrme black holes with $\alpha =4\pi G{f}^2=0.001$ and $x_{△}=0.03$. The curves with the lower horizon values of $A(x)$ are the unstable solutions.

Figure 4

The dimensionless mass function $\mu (x)=fgGm(r)$ versus the dimensionless length $x=fgr$ for the two branches of the $B\sim 1$ (solid line), $B\sim 2$ (dashed line) and $B\sim 3$ (dash-dotted line) Skyrme black holes with $\alpha =4\pi G{f}^2=0.001$ and $x_{△}=0.03$. The curves with the lower mass are the stable solutions.

Figure 5

The function $\chi (x)$ against dimensionless length $x=fgr$ for the two branches of the $B\sim 1$ (solid line), $B\sim 2$ (dashed line) and $B\sim 3$ (dash-dotted line) Skyrme black holes with $\alpha =4\pi G{f}^2=0.001$ and $x_{△}=0.03$. The curves with the lower value of $\chi (x)$ are the unstable solutions.