Conformal scalar propagation inside the Schwarzschild black hole

The analytic expression obtained in the preceding project for the massless conformal scalar propagator in the Hartle–Hawking vacuum state for small values of the Schwarzschild radial coordinate above r = 2M is analytically extended into the interior of the Schwarzschild black hole. The result of the analytical extension coincides with the exact propagator for a small range of values of the Schwarzschild radial coordinate below r = 2M and is an analytic expression which manifestly features its dependence on the background space–time geometry. This feature as well as the absence of any assumptions and prerequisites in the derivation render this Hartle–Hawking scalar propagator in the interior of the Schwarzschild black-hole geometry distinct from previous results. The two propagators obtained in the interior and in the exterior region of the Schwarzschild black hole are matched across the event horizon. The result of that match is a massless conformal scalar propagator in the Hartle–Hawking vacuum state which is shown to describe particle production by the Schwarzschild black hole.

“The future is not what it used to be!” From Alan Parker’s film “Angel Heart”     

Confluent Heun functions and the physics of black holes: Resonant frequencies,Hawking radiation and scattering of scalar waves

We apply the confluent Heun functions to study the resonant frequencies (quasispectrum), the Hawking radiation and the scattering process of scalar waves, in a class of spacetimes, namely, the ones generated by a Kerr–Newman–Kasuya spacetime (dyon black hole) and a Reissner–Nordström black hole surrounded by a magnetic field (Ernst spacetime). In both spacetimes, the solutions for the angular and radial parts of the corresponding Klein–Gordon equations are obtained exactly, for massive and massless fields, respectively. The special cases of Kerr and Schwarzschild black holes are analyzed and the solutions obtained, as well as in the case of a Schwarzschild black hole surrounded by a magnetic field. In all these special situations, the resonant frequencies, Hawking radiation and scattering are studied.     

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.     

Anomalous behavior of a scalar particle in a globally regular space-time of a Schwarzschild black hole

The curved space-time Klein-Gordon equation in a globally regular space-time of a Schwarzschild black hole is solved, and its exact solution is obtained. The wave functions of a scalar particle inside the black hole are discussed by means of numerical analysis. The anomalous behaviors of the scalar particle in the central region of the black hole and in the interior neighborhood of the Schwarzschild event horizon are studied with the help of approximate solutions, which are compared with the exact one in these two regions.     

Entangled Particles Tunneling From a Schwarzschild Black Hole immersed in an Electromagnetic Universe with GUP

Quantum gravity has exciting peculiarities on the Planck scale.The effect of generalized uncertainty principle (GUP) to the entangled scalar/fermion particles’ tunneling from a Schwarzschild black hole immersed in an electromagnetic Universe is investigated by the help of semi-classical tunneling method. The quantum corrected Hawking temperature of this black hole with an external parameter “a” modifies the Hawking temperature for the entangled particles.     

Black Hole Fluctuations and Backreaction in Stochastic Gravity

We present a framework for analyzing black hole backreaction from the point of view of quantum open systems using influence functional formalism. We focus on the model of a black hole described by a radially perturbed quasi-static metric and Hawking radiation by a conformally coupled massless quantum scalar field. It is shown that the closed-time-path (CTP) effective action yields a non-local dissipation term as well as a stochastic noise term in the equation of motion, the Einstein–Langevin equation. Once the thermal Green's function in a Schwarzschild background becomes available to the required accuracy, the strategy described here can be applied to obtain concrete results on backreaction. We also present an alternative derivation of the CTP effective action in terms of the Bogolyubov coefficients, thus making a connection with the interpretation of the noise term as measuring the difference in particle production in alternative histories.     

Scalar resonant frequencies and Hawking effect of an f(R) global monopole

Massive scalar fields are considered in the gravitational field produced by a Schwarzschild black hole with a global monopole in f(R) gravity.The exact solution of the radial part of the Klein-Gordon equation in this background is obtained and is given in terms of the general Heun functions.We apply the properties of the general Heun functions to study the Hawking radiation and the resonant frequencies of scalar particles.     

Conformal scalar propagation on the Schwarzschild black-hole geometry

The vacuum activity generated by the curvature of the Schwarzschild black-hole geometry close to the event horizon is studied for the case of a massless, conformal scalar field. The associated approximation to the unknown, exact propagator in the Hartle–Hawking vacuum state for small values of the radial coordinate above r = 2M results in an analytic expression which manifestly features its dependence on the background space–time geometry. This approximation to the Hartle–Hawking scalar propagator on the Schwarzschild black-hole geometry is, for that matter, distinct from all other. It is shown that the stated approximation is valid for physical distances which range from the event horizon to values which are orders of magnitude above the scale within which quantum and backreaction effects are comparatively pronounced. An expression is obtained for the renormalised \({ \langle\phi^2(x)\rangle}\) in the Hartle–Hawking vacuum state which reproduces the established results on the event horizon and in that segment of the exterior geometry within which the approximation is valid. In contrast to previous results the stated expression has the superior feature of being entirely analytic. The effect of the manifold’s causal structure to scalar propagation is also studied.     

From Schwarzschild to Kerr due to Black Hole Quantum Tunnelling

Hawking radiation can be viewed as a process of quantum tunnelling near black hole horizon. When a particle with angular momentum tunnels across the event horizon of Schwarzschild black hole, the black hole will change into a Kerr black hole. The emission rate of the massless particles with angular momentum is calculated, and the result is consistent with an underlying unitary theory.     

Finite motion of massive particles in the Kerr and Schwarzschild fields

In the weakly relativistic limit, an expression is obtained for the damping of quasistationary energy levels in Schwarzschild and Kerr fields due to capture by a collapsar. The strength of the damping in the Schwarzschild field decreases strongly with increasing angular momentum of the particle. If the condition < m_H is satisfied in the case of a rotating black hole, the damping can be replaced by excitation. A particle production process (Hawking process) is considered that leads to the accumulation of particles on quasistationary levels near the black hole. Dynamical equilibrium can be established in the system between the processes of production and capture of particles by the black hole.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, 109–114, September, 1978.     

Massive Particles' Tunneling Effect from An Arbitrarily Dimensional Schwarzschild Black Hole

According to Parikh's recent work, Hawking radiation is viewed as a tunneling process and the barrier is created just by the outgoing particle itself. In this paper, we extend Parikh's work to the case of massive particles' tunneling, and calculate the emission rate at which massive particles tunnel across the event horizon of an arbitrarily dimensional Schwarzschild black hole. The result is also consistent with an underlying unitary theory and takes the same functional form as that of massless particles. Moreover, our result also shows that Hawking radiation is an intrinstic property of the black hole.     

Non-equilibrium Landauer transport model for Hawking radiation from a Reissner—Nordstrom black hole

The recent work of Nation et al., in which the Hawking radiation energy and entropy flow from a black hole is considered to be produced in a one-dimensional Landauer transport process, is extended to the case of a Reissner- Nordstrom black hole. The energy flow contains not only the contribution of the thermal flux but also that of the particle flux. It is found that the charge can also be transported via the one-dimensional quantum tunnel. Because of the existence of the electrostatic potential, the entropy production rate is shown to be smaller than that of the Schwarzschild black hole.     

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.     

Hawking radiation from gravity''s rainbow via gravitational anomaly

Based on the anomaly cancellation method, initiated by Robinson and Wilczek, we investigates Hawking radiation from the modified Schwarzschild black hole from gravity＇s rainbow from the anomaly point of view. Unlike the general Schwarzschild space-time, the metric of this black hole depends on the energies of probes. The obtained result shows to restore the underlying general covariance at the quantum level in the effective field, the covariant compensating flux of energy-momentum tensor, which is related to the energies of the probes, should precisely equal to that of a （1 ＋ 1）-dimensional blackbody at the Hawking temperature.     

洛仑兹破缺标量场的霍金隧穿辐射

把洛仑兹破缺的标量场方程推广到弯曲时空中,并通过Aether-like项对标量场方程进行修正,该项所产生的效应也会影响到黑洞时空视界附近处的物理效应.接着,进一步在半经典近似下得到了修正的Hamilton-Jacobi方程,然后用这一修正的Hamilton-Jacobi方程研究了史瓦西黑洞的隧穿辐射特征,并讨论了洛仑兹破缺对黑洞霍金辐射和黑洞熵的影响.结果表明,u~α=δ_t~αu~t,δ_r~αu~r形式的Aether-like项的效应可能使黑洞温度增加,而黑洞熵降低.该工作可以帮助我们更深刻地理解弯曲时空中的洛仑兹破缺效应的物理性质.     

Entropy Quantization of Schwarzschild Black Hole

The surface gravity of Schwarzschild black hole can be quantized from the test particle moving around different energy states analog to the Bohr's atomic model. We have quantized the Hawking temperature and entropy of Schwarzschild black hole from quantization of surface gravity. We also have shown that the change of entropy reduces to zero when the boundary shrinks to very small size.     

Entropy corrections for Schwarzschild black holes

Recently it is shown that the Bekenstein–Hawking entropy for black holes receives logarithmic corrections due to thermodynamic fluctuations. Schwarzschild black hole which possesses a negative specific heat is thermodynamically unstable, so the entropy corrections cannot be obtained directly. In this Letter, Schwarzschild black hole will be put in the center of a spherical cavity of finite radius to achieve equilibrium with surroundings, so that a thermodynamically stable solution is obtained based on a uniformly spaced area spectrum approach. Our conclusion show that there are two correction terms for Schwarzschild black holes. The sign of the second correction term depends on the size of the cavity.     

Correction to Hawking Radiation Characteristics of Stationary Demianski-Newman Black Hole

The pure thermal spectrum in dragging coordinate system and the tunneling radiation characteristics across the event horizon for stationary Demianski-Newman black hole are researched. The result shows that the tunneling rate of the particle is relevant to Bekenstein-Hawking entropy, and the derived radiate spectrum is not strictly pure thermal, but is consistent with underlying unitary theory. Finally, we use the obtained results to reduce to stationary Kerr black hole and static Schwarzschild black hole, and find that only when ignoring the spectrum at higher energies is the tunneling radiation spectrum consistent with Hawking pure thermal one.     

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.     

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.