Gravitational field of a slowly rotating black hole with phantom global monopole

We present a slowly rotating black hole with phantom global monopole by solving Einstein's field equation and find that presence of global monopole changes the structure of black hole. The metric coefficient $g_{t\phi}$ contains hypergeometric function of the polar coordinate $r$, which is more complex than that in the usual slowly rotating black hole. The energy scale of symmetry breaking $\eta$ affects the black hole horizon and a deficit solid angle. Especially, the solid angle is surplus rather than deficit for a black hole with the phantom global monopole. We also study the correction originating from the global monopole to the angular velocity of the horizon $\Omega_H$, the Kepler's third law, the innermost stable circular orbit and the radiative efficiency $\epsilon$ in the thin accretion disk model. Our results also show that for the phantom black hole the radiative efficiency $\epsilon$ is positive only for the case $\eta\leq \eta_c$. The threshold value $\eta_c$ increases with the rotation parameter $a$.Comment: 14 pages, 6 figure

Shadows of Bonnor black dihole by chaotic lensing

We have studied numerically the shadows of Bonnor black dihole through the technique of backward ray-tracing. The presence of magnetic dipole yields non-integrable photon motion, which affects sharply the shadow of the compact object. Our results show that there exists a critical value for the shadow. As the magnetic dipole parameter is less than the critical value, the shadow is a black disk, but as the magnetic dipole parameter is larger than the critical one, the shadow becomes a concave disk with eyebrows possessing a self-similar fractal structure. These behavior are very similar to those of the equal-mass and non-spinning Majumdar-Papapetrou binary black holes. However, we find that the two larger shadows and the smaller eyebrow-like shadows are joined together by the middle black zone for the Bonnor black dihole, which is different from that in the Majumdar-Papapetrou binary black holes spacetime where they are disconnected. With the increase of magnetic dipole parameter, the middle black zone connecting the main shadows and the eyebrow-like shadows becomes narrow. Our result show that the spacetime properties arising from the magnetic dipole yields the interesting patterns for the shadow casted by Bonnor black dihole.Comment: 18 pages, 9 figures; The title is changed and some discussion are added. The modified version for publication in PR

P−VP-V criticality of AdS black hole in f(R)f(R) gravity

We study thermodynamics of a charged AdS black hole in the special $f(R)$ correction with the constant Ricci scalar curvature. Our results show that the the $f(R)$ correction influences the Gibbs free energy and the phase transition of system. The ratio $\rho_c$ occurred at the critical point increases monotonically with the derivative term $f'(R_0)$. We also disclose that the critical exponents are the same as those of the liquid-gas phase transition in the Van der Waals model, which does not depend on the $f(R)$ correction considered here.Comment: 9 pages, 3 figure

Black hole entropy arising from massless scalar field with Lorentz violation induced by the coupling to Einstein tensor

We have investigated quantum entropy of a static black hole arising from the massless scalar field with Lorentz violation induced by the coupling to Einstein tensor. Our results show that the coupled massless scalar field contributes to the classical Bekenstein-Hawking term in the black hole entropy. The corrected classical Bekenstein-Hawking entropy is not one quarter of the event horizon area of the original background black hole, but of a corresponding effective metric related to the coupling. It means that the classical Bekenstein-Hawking entropy depends not only on the black hole parameter, but also on the coupling which reduces Lorentz violation.Comment: 5 pages, no figure. Accepted by PLB for publicatio