Hawking Temperature of a Static Black Hole in Harmonic Coordinates

Hawking radiation is usually studied in standard coordinates. In this paper, we calculate the Hawking temperature of a Schwarzschild black hole in harmonic coordinates, as well as that of a Reissner-Nordström black hole. The action of a scalar field near the event horizon can be formulated exactly without omitting some high-order terms. We show dimensional reduction for Hawking temperature is also valid for harmonic coordinates, and verify further that the results are independent on concrete coordinates. With the help of Lorentz transformation, our work might also serve as a basis to investigate the thermal radiation from a moving black hole.     

Effect of the refractive index on the hawking temperature: an application of the Hamilton-Jacobi method

Hawking radiation of a non-asymptotically flat 4-dimensional spherically symmetric and static dilatonic black hole (BH) via the Hamilton-Jacobi (HJ) method is studied. In addition to the naive coordinates, we use four more different coordinate systems that are well-behaved at the horizon. Except for the isotropic coordinates, direct computation by the HJ method leads to the standard Hawking temperature for all coordinate systems. The isotropic coordinates allow extracting the index of refraction from the Fermat metric. It is explicitly shown that the index of refraction determines the value of the tunneling rate and its natural consequence, the Hawking temperature. The isotropic coordinates in the conventional HJ method produce a wrong result for the temperature of the linear dilaton. Here, we explain how this discrepancy can be resolved by regularizing the integral possessing a pole at the horizon.     

Coordinates Used in Derivation of Hawking Radiation via Hamilton-Jacobi Method

Coordinates used in derivation of Hawking radiation via Hamilton-Jacobi method are investigated more deeply. In the case of a 4-dimensional Schwarzschild black hole, a direct computation leads to a wrong result. In the meantime, making use of the isotropic coordinate or invariant radial distance, we can get the correct conclusion. More coordinates including Painleve and Eddington-Finkelstein are tried to calculate the semi-classical Hawking emission rate. The reason of the discrepancy between naive coordinate and well-behaved coordinates is also discussed.     

Hawking Temperature Calculation Using Tunneling Mechanism

Based on the black hole tunneling mechanism in which the ingoing particles should be absorbed absolutely, Hamilton-Jacobi method is modified to investigate Hawking radiation from a Schwarzschild black hole once again. The results are independent on the coordinates and the standard Hawking temperature is obtained without the factor of 2 problem. Moreover, it is also pointed out that the modified Hamilton-Jacobi method can be applied to investigate Hawking radiation from the general horizons in dynamical spacetimes.     

Which coordinate representations can give correct Hawking temperature of Kerr black hole by tunneling approach

Some authors found that, in different coordinates, the tunneling approach gives different Hawking temperature for the Schwarzschild black hole recently. In this paper, by studying the Hawking radiation of the Kerr black hole arising from the scalar and Dirac particles, we find that, to obtain the Hawking temperature by using tunneling effect, the coordinate representations for the stationary Kerr black hole should satisfy two conditions: (a) to keep the Killing vectors x_(t)^m{{\xi_{(t)}^\mu}} and x_(j)^m{{\xi_{(\varphi)}^\mu}} invariant; and (b) the radial coordinate transformation is a regular and non-zero function.     

The temperature in Hawking radiation as tunneling

The quasi-classical method of deriving Hawking radiation under the consideration of canonical invariance is investigated. We find that the horizon should be regarded as a two-way barrier and the ingoing amplitude should be calculated according to the negative energy particles tunneling into the black hole because of the whole space–time interchange and thus the standard Hawking temperature is recovered. We also discuss the advantage of the Painlevé coordinates in Hawking radiation as tunneling.     

Hawking Radiation of Scalar and Vector Particles from 5D Myers-Perry Black Holes

In the present paper we explore the Hawking radiation as a quantum tunneling effect from a rotating 5 dimensional Myers-Perry black hole (5D-MPBH) with two independent angular momentum components. First, we investigate the Hawking temperature by considering the tunneling of massive scalar particles and spin-1 vector particles from the 5D-MPBH in the Painlevé coordinates and then in the corotating frames. More specifically, we solve the Klein-Gordon and Proca equations by applying the WKB method and Hamilton-Jacobi equation in both cases. Finally, we recover the Hawking temperature and show that coordinates systems do not affect the Hawking temperature.     

A jet appearing when a black hole event horizon touches the rindler horizon

The Hawking effect of a nonuniformly rectilinearly accelerating Kinnersley black hole is studied. Its horizons are rotationally symmetric. Its Hawking temperature depends not only on the time, but also on the polar angle. When a Kinnersley black hole touches its Rindler horizon, the Hawking temperature at the contact point is reduced to zero. But at the opposite pole of the black hole, the Hawking temperature increases rapidly. A jet appears as a tail of the accelerating black hole.     

Quantum thermal effects of a radiating rotating charged black hole

Asymptotic solutions of the Klein-Gordon equation in a region near the event horizon of a radiating rotating charged black hole are obtained by using generalized tortoise coordinates. The location of the event horizon and the Hawking temperature of the black hole are given. Both the horizon and the temperature depend on the angle and time, due to radiation. However, they are independent of the angle if either rotation or radiation vanishes. The treatment encompasses as special cases the results on a number of well-known black holes.     

Tunneling of massive particles from noncommutative inspired Schwarzschild black hole

We apply the generalization of the Parikh–Wilczek method to the tunneling of massive particles from noncommutative inspired Schwarzschild black holes. By deriving the equation of radial motion of the tunneling particle directly, we calculate the emission rate which is shown to be dependent on the noncommutative parameter besides the energy and mass of the tunneling particle. After equating the emission rate to the Boltzmann factor, we obtain the modified Hawking temperature which relates to the noncommutativity and recovers the standard Hawking temperature in the commutative limit. We also discuss the entropy of the noncommutative inspired Schwarzschild black hole and its difference after and before a massive particle’s emission.     

Quantum tunneling and trace anomaly

We compute the corrections, using the tunneling formalism based on a quantum WKB approach, to the Hawking temperature and Bekenstein–Hawking entropy for the Schwarzschild black hole. The results are related to the trace anomaly and are shown to be equivalent to findings inferred from Hawking's original calculation based on path integrals using zeta function regularization. Finally, exploiting the corrected temperature and periodicity arguments we also find the modification to the original Schwarzschild metric which captures the effect of quantum corrections.     

Hawking temperature of Kerr anti-de-Sitter black hole affected by Lorentz symmetry violating

We studied the correction of the quantum tunneling radiation of fermions with spin 1/2 in Kerr anti-de-Sitter black hole. First, the dynamic equation of spin 1/2 fermions was corrected using Lorentz’s violation theory. Second, the new expressions of the fermions quantum tunneling rate,the Hawking temperature of the black hole and the entropy of the black hole were obtained according to the corrected fermions dynamic equation. Our results show that Hawking temperature increases with the enhancement of both the coupling strength and the radial component of ether-like field, but is independent of non-radial components of ether-like field.At last, some comments are made on the results of our work.     

Hawking temperature and higher order calculations

Hawking radiation has recently been explained by using solutions of wave equations across black hole horizons in a WKB approximation. Higher order calculations using both usual and non-singular coordinates are found to change the solution for zero spin, but this change is not an alteration of the Hawking temperature. For spin 1/2, there is no correction to the simplest form of the solution.     

Covariant Anomaly and Hawking Radiation from Kerr-Newman Black Hole in Dragging Coordinates Frame

In the light of Robinson and Wilczek's new idea, and motivated by Banerjee and Kulkarni's simplified method of using only the covariant anomaly to derive Hawking radiation from a black hole, we generally extend the work to Kerr-Newman black hole in dragging coordinates frame. It is shown that the flows introduced to cancel the anomaly at the event horizon are equal to the corresponding Hawking radiation in dragging coordinates frame, which supports and extends Robinson and Wilczek's opinion.     

缓变动态Kerr-Newman黑洞的量子热力学性质

引入局域热平衡概念，用Damour-Ruffini方法和薄膜模型研究了缓变动态Kerr-Newman黑洞的Hawking辐射和熵.得到了黑洞的Hawking温度和辐射谱公式，Hawking温度随时间和视界面上的位置而变化，辐射谱为准黑体谱；计算了黑洞熵，当取与静态球对称黑洞情况相同的截断关系时便得到了黑洞的Bekenstein-Hawking熵.结果表明，缓变动态黑洞的温度是局域量，缓变动态黑洞的熵与稳态黑洞情况一样正比于黑洞视界面面积. 关键词： 缓变动态黑洞 Hawking辐射 黑洞熵     

Hawking radiation of spin-1 particles from a three-dimensional rotating hairy black hole

We study the Hawking radiation of spin-1 particles (so-called vector particles) from a three-dimensional rotating black hole with scalar hair using a Hamilton–Jacobi ansatz. Using the Proca equation in the WKB approximation, we obtain the tunneling spectrum of vector particles. We recover the standard Hawking temperature corresponding to the emission of these particles from a rotating black hole with scalar hair.     

Hawking radiation and tunneling mechanism for a new class of black holes in Einstein–Gauss–Bonnet gravity

We study Hawking radiation in a new class of black hole solutions in Einstein–Gauss–Bonnet theory. The black hole has been argued to have vanishing mass and entropy, but finite Hawking temperature. To check if it really emits radiation, we analyze Hawking radiation using the original method of quantization of a scalar field in the black hole background and with the quantum tunneling method, and confirm that it emits radiation at the Hawking temperature. A general formula is derived for the Hawking temperature and backreaction in the tunneling approach. Physical implications of these results are discussed.     

Deriving the Hawking Temperature of (Massive) Global Monopole Spacetime via a Topological Formula

In this work, we study the Hawking temperature of the global monopole spacetime (non-spherical symmetrical black hole) based on the topological method proposed by Robson, Villari, and Biancalana (RVB). By connecting the Hawking temperature with the topological properties of black holes, the Hawking temperature of the global monopole spacetime can be obtained by the RVB method. We also discuss the Hawking temperature in massive gravity, and find that the effect of the mass term cannot be ignored in the calculation of the Hawking temperature; the corrected Hawking temperature in massive gravity can be derived by adding an integral constant, which can be determined by the standard definition.     

Hawking effect and quantum nonthermal radiation of an arbitrarily accelerating charged black hole using a new tortoise coordinate transformation

Using a new tortoise coordinate transformation, this paper investigates the Hawking effect from an arbitrarily accelerating charged black hole by the improved Damour-Ruffini method. After the tortoise coordinate transformation, the Klein-Gordon equation can be written as the standard form at the event horizon. Then extending the outgoing wave from outside to inside of the horizon analytically, the surface gravity and Hawking temperature can be obtained automatically. It is found that the Hawking temperatures of different points on the surface are different. The quantum nonthermal radiation characteristics of a black hole near the event horizon is also discussed by studying the Hamilton-Jacobi equation in curved spacetime and the maximum overlap of the positive and negative energy levels near the event horizon is given. There is a dimensional problem in the standard tortoise coordinate and the present results may be more reasonable.