Two-dimensional regular string black hole via complete α′\alpha^{\prime} corrections

In string theory, an important challenge is to show if the singularity of black holes can be smoothed out by the complete $\alpha^{\prime}$ corrections. The simplest case is to consider a 2D string black hole or 3D black string. This problem was discussed in a gauged Wess-Zumino-Witten (WZW) model and the results are supposed to be correct to all orders in $\alpha^{\prime}$ corrections. Based on the recent remarkable progress on classifying all the $\alpha^{\prime}$ corrections, in this work, we re-study this problem with the low energy effective spacetime action, and provide classes of exact non-perturbative and non-singular solutions of the 2D black hole via complete $\alpha^{\prime}$ corrections.Comment: V1: 6 pages, 2 figures; V2: 7 pages, 2 figures, typos corrected, version to appear in Eur. Phys. J.

Black Hole Radiation with Modified Dispersion Relation in Tunneling Paradigm: Free-fall Frame

Due to the exponential high gravitational red shift near the event horizon of a black hole, it might appear that the Hawking radiation would be highly sensitive to some unknown high energy physics. To study effects of any unknown physics at the Planck scale on the Hawking radiation, the dispersive field theory models have been proposed, which are variations of Unruh's sonic black hole analogy. In this paper, we use the Hamilton-Jacobi method to investigate the dispersive field theory models. The preferred frame is the free-fall frame of the black hole. The dispersion relation adopted agrees with the relativistic one at low energy but is modified near the Planck mass $m_{p}$. The corrections to the Hawking temperature are calculated for massive and charged particles to $\mathcal{O}\left( m_{p}^{-2}\right)$ and neutral and massless particles with $\lambda=0$ to all orders. The Hawking temperature of radiation agrees with the standard one at the leading order. After the spectrum of radiation near the horizon is obtained, we use the brick wall model to compute the thermal entropy of a massless scalar field near the horizon of a 4D spherically symmetric black hole and a 2D one. Finally, the luminosity of a Schwarzschild black hole is calculated by using the geometric optics approximation.Comment: 28 pages. arXiv admin note: substantial text overlap with arXiv:1505.0304

Phase transitions and thermodynamic geometry of a Kerr-Newman black hole in a cavity

Being placed in a cavity is an effective way of reaching thermodynamic equilibrium for black holes. We investigate a Kerr-Newman black hole in a cavity as well as compare it with two reduced cases, i.e., a RN black hole in a cavity and a Kerr black hole in a cavity. We derive the quasi-local energy from the Hamiltonian, and construct the first law of thermodynamics accordingly. In a canonical ensemble, these black holes could undergo a van der Waals-like phase transition, which is very similar to that in AdS space. We further investigate the black holes' thermodynamic geometry, which is a powerful tool to diagnose microscopic interactions of a thermodynamic system. Our results show that in a cavity, although phase structures of these black holes are similar, their thermodynamic geometry show strong dissimilarities, implying that the microstructure of a black hole is sensitive to its states.Comment: 25 pages, 8 figure