Stationary Einstein-vector-Gauss-Bonnet black holes

Abstract

We study spontaneously vectorized black holes in Einstein-vector-Gauss-Bonnet theory with a quadratic coupling function. Besides the static, spherically symmetric black holes carrying an electric charge, there are uncharged static, axially symmetric black holes that possess a magnetic dipole moment. Both types possess radial excitations. The magnetic black holes are prolate. They are hotter than the Schwarzschild black holes and possess lower free energy. The domain of existence of the rotating vectorized black holes is bounded by the Kerr black holes, the spherically and axially symmetric static black holes, and the critical solutions.

Figures (10)

• Figure 1: Static spherically symmetric EvGB black holes: (a) scaled electric charge $Q/M$ vs scaled coupling $\lambda/M^2$; (b) scaled entropy $4 S_{\rm H}/(16\pi M^2)$, scaled Hawking temperature $8 \pi T_{\rm H} M$ and scaled equatorial horizon radius $R_e/(2M)$ vs scaled coupling.
• Figure 2: Static spherically and axially symmetric EvGB black holes: Scaled free energy $F/M$ vs scaled Hawking temperature $8 \pi T_{\rm H} M$.
• Figure 3: Static axially symmetric EvGB black holes: (a) scaled magnetic dipole moment $\mu/M^2$ vs scaled coupling $\lambda/M^2$; (b) scaled entropy $4 S_{\rm H}/(16\pi M^2)$, scaled Hawking temperature $8 \pi T_{\rm H} M$, equatorial-to-polar horizon radius ratio $R_e/R_p$, scaled equatorial horizon radius $R_e/(2M)$, and scaled horizon area $A_{\rm H}/(16\pi M^2)$ vs scaled coupling.
• Figure 4: Static axially symmetric EvGB black holes: Approximation Eq. (\ref{['xpand_LegPol']}) (solid) and the numerical values (dots) at the horizon are shown as function of $\theta$ for $\lambda/M^2\approx (\lambda/M^2)_{\rm bif}$.
• Figure 5: Perturbative solutions: (a) Discrete values $\sqrt{\lambda}/M$ vs node number $n$, $n=0, \dots, 5$ and linear approximations (dotted). (b) Modes $\gamma$ for the spherically symmetric case vs compactified coordinate $x-1-r_H/r$ for node numbers $n=0,\dots,3$. (c) Same as (b) for the static axially symmetric case.