We calculate the holographic entanglement entropy for the rotating cylindrical black holes in d +1 dimensions as perturbations over AdS d+1 . This is accomplished based on the first order variation of the area functional in arbitrary dimensions. For these types of black holes, the angular momentum appears at the first order of the perturbative expansion of the holographic entanglement entropy for spacetime dimensions of d +1 ≥ 4. We obtain a form of holographic entanglement first law in the presence of both energy and angular momentum.
We calculate the effects of the electromagnetic self-force on a charged particle outside a five dimensional Myers-Perry space-time. Based on our earlier work [1], we obtain the self-force using quaternions in Janis-Newman and Giampieri algorithms. In four dimensional rotating space-time the electromagnetic self-force is repulsive at any point, however, in five dimensional rotational spacetime, we find a point r0 where the electromagnetic self-force vanishes. For r < r0 (r > r0) the electromagnetic self-force is attractive (repulsive).
It is shown that adding hair like electric charge or angular momentum to the black hole decreases the amount of entropy emission. This motivates us to study the emission rate of entropy from black holes and conjecture a maximum limit (upper bound) on the rate of local entropy emission (Ṡ) for thermal systems in four dimensional space time and argue that this upper bound isṠ k B c 5 G . Also by considering Rènyi entropy, it is shown that Bekenstein-Hawking entropy leads to a maximum limit for the rate of entropy emission. We also suggest an upper bound on the surface gravity of the black holes which is called Planck surface gravity. Finally we obtain a relation between maximum rate of entropy emission, Planck surface gravity and Planck temperature of black holes.
We consider a holographic extended phase space in the presence of Reissner-Nordstrom-Anti-de Sitter (RN-AdS) and Born-Infeld-Anti-de Sitter (BI-AdS) black holes in the bulk. In this extended phase space the cosmological constant is investigated as pressure and volume is defined as the codimension one-time slice in the bulk geometry enclosed by the minimal area appearing in the computation of the holographic entanglement entropy. These thermodynamics quantities can serve as probes of the underlying phase transition dictated by black hole thermodynamics, but do not describe different structures. We find that the isocharges on the pressure-volume plane exhibit a Van der Waals-like structure, for RN-AdS black holes in the background. For BI-AdS black holes, we observe the analogy with a Van der Waals liquid-gas system for βQ > 1/2 and Reentrant phase transition for βQ < 1/2 in the holographic extended phase space. The same holographic thermodynamic behavior is observed when we use the fidelity susceptibility as the volume and the cosmological constant as the pressure for RN-AdS black hole in the background.
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