Hairy Reissner-Nordstrom Black Holes with Asymmetric Vacua

Abstract

We minimally coupled a scalar potential $V(φ)$ with asymmetric vacua to the Einstein gravity to numerically construct the hairy Reissner-Nordstrom black hole (RNBH) as a direct generalization of RNBHs to possess scalar hair. By fixing the electric charge to mass ratio $q$, a branch of hairy RNBHs bifurcates from the RNBH when the scalar field $φ_H$ is non-trivial at the horizon. The values of $q$ are bounded for $0 \leq q \leq 1$, which contrast to a class of hairy black holes with $q>1$ in the Einstein-Maxwell-scalar theory. We find that the profiles of solutions affected by the competition between the strength of $φ_H$ and $q$, for instance, the gradient of scalar field at the horizon can increase very sharply when $q \rightarrow 1$ and $φ_H$ is small but its gradient can be very small which independent of $q$ when $φ_H$ is large. Furthermore, the weak energy condition of hairy RNBHs, particularly at the horizon can be satisfied when $q>0$.

Figures (9)

• Figure 1: The authors have considered the scalar potential $V(\phi)$ with a false vacuum at $\phi=0$, a barrier at $\phi=\phi_0$ and a true vacuum at $\phi=\phi_1$ to construct the hairy black holes Chew:2022enh.
• Figure 2: The reduced area of horizon $a_H$ of the hairy RNBHs with $r_H=1$ and several $q$ for (a) $\phi_1=0.5$, (b) $\phi_1=1.0$.
• Figure 3: The reduced Hawking temperature $t_H$ of the hairy RNBHs with $r_H=1$ and several $q$ for (a) $\phi_1=0.5$, (b) $\phi_1=1.0$.
• Figure 4: The profiles of mass function $m(x)$ in the compactified coordinate $x$ for the hairy RNBHs with $r_H=1$, $\phi_1=1.0$ and several $q$ for (a) $\phi_H=0.5$, (b) $\phi_H=0.99$.
• Figure 5: The profiles of scalar field $\phi(x)$ in the compactified coordinate $x$ for the hairy RNBHs with $r_H=1$, $\phi_1=1.0$ and several $q$ for (a) $\phi_H=0.1$, (b) $\phi_H=0.99$.