Gauss-Bonnet scalarization of charged qOS-black holes

Abstract

The Gauss-Bonnet (GB) scalarization for charged quantum Oppenheimer-Snyder (cqOS)-black holes is investigated in the Einstein-Gauss-Bonnet-scalar theory with the nonlinear electrodynamics (NED) term. Here, the scalar coupling function to GB term is given by $f(φ)=2λφ^2$ with a coupling constant $λ$. Three parameters of mass ($M$), action parameter ($α$), and magnetic charge ($P$) are necessary to describe the cqOS-black hole, and it may become the qOS-black hole when $P=M$. The GB scalarization of cqOS-black holes comes into two cases GB$^\pm$, depending on the sign of GB term which triggers the different phenomena. For $α=0$ and $λ>0$, GB$^+$ scalarization is allowed, while for $α\not=0$ and $λ<0$, GB$^-$ scalarization appears for a narrow band of $3.5653\le α\le 4.6875$. After discussing the onset GB$^-$ scalarization, we construct scalarized qcOS-black holes which belong to the single branch. The scalar field is nonmonotonic near the horizon while it asymptotes to a finite value at infinity, indicating a distinct scalarization mechanism for negative coupling $λ$. Stability analysis shows these scalarized black holes are linearly stable under scalar perturbations.

Figures (13)

• Figure 1: (a) Two outer/inner horizons $r_\pm(M=1,\alpha,P=0.6)$ are functions of $\alpha\in[0,4.6875]$. The bouncing radius $r_{b}(1,\alpha,0.6)$ as function of $\alpha$ is inside the inner horizon. Here, $r_+(1,\alpha,0.6)$ involves the Davies point at [(2.29,1.88), black dot], critical onset point [(3.5653,1.7676), purple dot], and extremal point [(4.6875,1.5), red dot]. (b) Two horizons $r_{\pm}(M,\alpha=1,P=0.6)$ are functions of $M\in[M_{\rm rem}=0.6796,\infty]$, showing the lower mass bound [remnant point at (0.6796,1.02), red dot]. The black dot represents the Davies point at (0.81,1.52), while the purple dot denotes the critical onset point at (0.7277,1.286). The bouncing radius is located inside the inner horizon.
• Figure 2: Heat capacity $C(M,\alpha,P)/|C_S(1,0,0)|$ with $|C_S(1,0,0)|=25.13$ and temperature $T(M,\alpha,P)/0.04$. (a) Heat capacity $C(M=1,\alpha,P=0.6)$ blows up at Davies point ($\alpha_D=2.29,~\bullet$) and it is zero at the extremal point ($\alpha_e=4.6875,$ red dot). The shaded region represents $C\ge 0$ and it is divided at a line ($\alpha=\alpha_c=3.5653$). (b) Heat capacity $C(M,1,0.6)$ blows up at Davies point ($M_D=0.81,\bullet$). The heat capacity and temperature are zero at the remnant point ($M_{\rm rem}=0.6796,$ red dot). The shaded region denotes $C\ge 0$, but it is divided at a line ($M=M_c=0.7277$).
• Figure 3: (Left) $\bar{\mathcal{R}}^2_{\rm GB}(r,M=1,\alpha,P=0.6)$ as functions of $r\in [r_+(M=1,\alpha,P=0.6),2.2]$ and $\alpha\in[0,\alpha_e=4.6875]$ and its zero line is available, starting from $\alpha=\alpha_c(=3.5653)$ on the horizon. (Right) $\bar{\mathcal{R}}^2_{\rm GB}(r,M,\alpha=1,P=0.6)$ as functions of $r\in [r_+(M,\alpha=1,P=0.6),1.8]$ and $M\in[M_{\rm rem}=0.6796,0.81]$ and its zero line is available, ending at $M=M_c(=0.7277)$ on the horizon.
• Figure 4: Three different curves for $nc(M_e,\alpha_e,0.6)=0$, $dc(M_D,\alpha_D,0.6)=0$, and $rc(M_c,\alpha_c,0.6)=0$ for $M\in[0.6796,1.2]$ and $\alpha\in[0,4.6875]$, including extremal/remnant points (red dot), two Davies points (black dot), and two resonance points (purple dot) for $M=1$ and $\alpha=1$.
• Figure 5: (a) Sufficient condition of $\alpha_{\rm sc}(M=1,\lambda,P=0.6)$ with the critical onset parameter $\alpha=\alpha_c$ as the lower bound. A dashed line denotes the sufficient condition $\alpha=\alpha_{\rm sc}^{-\lambda\gg M,P}$. A top line denotes the extremal point at $\alpha=\alpha_e$ as the upper bound. (b) Graph for $M_{\rm sc}(\alpha=1,\lambda,P=0.6)$ with the critical onset mass $M=M_c$ as the upper bound and the sufficient condition $M=M_{\rm sc}^{-\lambda\gg \alpha,P}$. A bottom line represents the remnant point at $M=M_{\rm rem}$ as the lower bound.