Replica Trick Calculation for Entanglement Entropy of Static Black Hole Spacetimes

We calculate the entanglement entropy between two (maximally-extended) spacetime regions of static black hole, seperated by horizon. As a first case, we consider the Schwarzschild black hole, and then we extend the calculations to the charged Reissner- Nordstrom and Schwarzschild-de Sitter black holes with more than one horizon. The case for static and spherically-symmetric solution to the more general F (R) gravity is also considered. The calculation of the entanglement entropy is performed using the replica trick by obtaining the explicit form of the metric which corresponds to the replica spacetime for each black hole under consideration. The calculation of static and spherically-symmetric black holes result in the entanglement entropy that matches the Bekenstein-Hawking area law entropy.Comment: 41 pages, 12 figure

Chaos and fast scrambling delays of dyonic Kerr-Sen-AdS4_4 black hole and its ultra-spinning version

The scrambling time and its delay are calculated using holography in an asymptotically AdS black hole solution of the gauged Einstein-Maxwell-Dilaton-Axion (EMDA) theory, the dyonic Kerr-Sen-AdS$_4$ black hole, perturbed by rotating and charged shock waves along the equator. The leading term of the scrambling time for a black hole with large entropy is logarithmic in the entropy and hence supports the fast scrambling conjecture for this black hole solution, which implies that the system under consideration is chaotic. We also find that the instantaneous minimal Lyapunov index is bounded by $\kappa=2\pi T_H/(1-\mu\mathcal{L})$, which is analogous to the surface gravity but for the rotating shock waves, and becomes closer to equality for the near extremal black hole. For a small value of the AdS scale, we found that the Lyapunov exponent can exceed the bound for a large value of $\mathcal{L}$. Due to the presence of the electric and magnetic charge of the shock waves, we also show that the scrambling process of this holographic system is delayed by a time scale that depends on the charges of the shock waves. The calculations also hold for the ultra-spinning version of this black hole. The result of this paper generalizes the holographic calculations of chaotic systems which are described by an EMDA theory in the bulk.Comment: 19 page

Localized chaos in rotating and charged AdS black holes

The butterfly velocity and the Lyapunov exponent of four-dimensional rotating charged asymptotically AdS black holes are calculated to probe chaos using localized rotating and charged shock waves. The localized shocks also generate butterfly velocities which quickly vanish when we approach extremality, indicating no entanglement spread near extremality. One of the butterfly velocity modes is well bounded by both the speed of light and the Schwarzschild-AdS result, while the other may become superluminal. Aside from the logarithmic behavior of the scrambling time which indicates chaos, the Lyapunov exponent is also positive and bounded by $\kappa=2\pi T_H/(1-\mu\mathcal{L})$. The Kerr-NUT-AdS and Kerr-Sen-AdS solutions are used as examples to attain a better understanding of the chaotic phenomena in rotating black holes, especially the ones with extra conserved charges.Comment: 10 pages, 4 figures. Comments are welcom

Black-Body Radiation in a Uniformly Accelerated Frame

We derive Planck's radiation law in a uniformly accelerated frame expressed in Rindler coordinates. The black-body spectrum is time-dependent and Planckian at each instantaneous time, but it is scaled by an emissivity factor that depends on the Rindler spatial coordinate and the acceleration magnitude. The observer in an accelerated frame will perceive the black-body as black, hyperblack, or grey, depending on its position with respect to the source (moving away or towards), the acceleration magnitude, and the case of whether it is accelerated or decelerated. For an observer accelerating away from the source, there exists a threshold on the acceleration magnitude beyond which it stops receiving radiation from the black-body. Since the frequency and the number of modes in Planck's law evolve over time, the spectrum is continuously red or blue-shifted towards lower (or higher) frequencies as time progresses, and the radiation modes (photons) could be created or annihilated, depending on the observer's position and its acceleration or deceleration relative to the source of radiation.Comment: 21 pages, 14 figure