Spontaneous creation of massive spin half particles by a rotating block hole

The techniques of second quantization in Kerr metric for the scalar and neutrino (massless) fields are extended to the massive spin half case. The normal modes of Dirac field in Kerr metric are obtained in Chandrasekhar’s representation and the field is quantized as usual by imposing equal-time anti-commutation relations. The vacuum expectation value of energy-momentum tensor is evaluated asymptotically, leading to the result that a Kerr black hole spontaneously creates, in addition to scalar and neutrino quanta, massive Dirac particles in the classical superradiant modes.     

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.     

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”     

New Tortoise Coordinate and Hawking Radiation of Dirac Particles in a Non-stationary Kerr-Newman Black Hole

The Hawking effect of Dirac particles in a non-stationary Kerr-Newman black hole is investigated using an improved Damour-Ruffini method with a new tortoise coordinate transformation. In contrast with the old tortoise coordinate, the new one satisfies the dimensional requirement. It is interesting to note that the Hawking emission spectrum remains a blackbody one with a correction term ξ existing in the Hawking temperature. Compared with the old tortoise coordinate transformation, our results appears more accurate and reliable.     

General radiation via tunneling in Kerr and Kerr-Newman black holes

Hawking radiation can be viewed as a process of quantum tunneling near the black hole horizon. When a particle with angular momentum L ≠ ωa tunnels across the event horizon of Kerr or Kerr-Newman black hole, the angular momentum per unit mass a should be changed. The emission rate of the massless particles under this general case is calculated, and the result is consistent with an underlying unitary theory. Supported by the National Natural Science Foundation of China (Grant No. 10773002) and the National Basic Research Program of China (Grant No. 2003CB716302)     

Tunneling effect of Dirac particles from the non-extremal black hole in <Emphasis Type="Italic">D</Emphasis> = 5, <Emphasis Type="Italic">SO</Emphasis>(6) gauged supergravity

Recent research shows that Hawking radiation from black hole horizon can be treated as a quantum tunneling process, and fermions tunneling method can successfully recover Hawking temperature. In this tunneling framework, choosing a set of appropriate matrices γ ^μ is an important technique for fermions tunneling method. In this paper, motivated by Kerner and Man’s fermions tunneling method of 4 dimension black holes, we further improve the analysis to investigate Hawking tunneling radiation from the non-extremal black hole in D = 5, SO(6) gauged supergravity by constructing a set of appropriate matrices γ ^μ for general covariant Dirac equation. Finally, the expected Hawking temperature of the black hole is correctly recovered, which takes the same form as that obtained by other methods.     

Dynamical behavior and nonminimal derivative coupling scalar field of Reissner-Nordstr?m black hole with a global monopole

In this paper, we research the dynamical evolution and quasinormal modes of nonminimal derivative coupling scalar field in Reissner-Nordstr?m spacetime with a global monopole. We also find that Hawking radiation behavior near the event horizon is similar to the scalar field case. In the whole spacetime, the conclusions show that weak coupling field will affect the dynamical behavior delicately, but the strong coupling constant η results in the deformation of dynamical evolution curve. When η > η _c , the black hole system will not be stable. The break from the global monopole also intensely affect the dynamical behavior of this black hole spacetime. Furthermore, the break will promote the instability of the coupling field.     

Quantum Tunneling of Dirac Particles from?the?Generalized Spherical Symmetric Evaporating Charged Black Hole

Kerner and Mann’s recent research shows that, for an uncharged and non-rotating black hole, its Hawking temperature and tunneling rate can be exactly obtained by the fermion tunneling method from its event horizon. In this paper, considering the tunneling charged particles with spin 1/2, we extend Kerner and Mann’s method to the generalized spherical symmetric evaporating charged black hole which is non-stationary. In order to investigate the fermion tunneling through the event horizon, we choose a set of appropriate matrices γ ^μ . As a result, the tunneling probability and truly effective temperature are well recovered by charged fermions tunneling from the black hole.     

Stochastic equations in black hole backgrounds and non-equilibrium fluctuation theorems

We apply the non-equilibrium fluctuation theorems developed in the statistical physics to the thermodynamics of black hole horizons. In particular, we consider a scalar field in a black hole background. The system of the scalar field behaves stochastically due to the absorption of energy into the black hole and emission of the Hawking radiation from the black hole horizon. We derive the stochastic equations, i.e. Langevin and Fokker-Planck equations for a scalar field in a black hole background in the ?→0 limit with the Hawking temperature ?κ/2π fixed. We consider two cases, one confined in a box with a black hole at the center and the other in contact with a heat bath with temperature different from the Hawking temperature. In the first case, the system eventually becomes equilibrium with the Hawking temperature while in the second case there is an energy flow between the black hole and the heat bath. Applying the fluctuation theorems to these cases, we derive the generalized second law of black hole thermodynamics. In the present paper, we treat the black hole as a constant background geometry.Since the paper is also aimed to connect two different areas of physics, non-equilibrium physics and black holes physics, we include pedagogical reviews on the stochastic approaches to the non-equilibrium fluctuation theorems and some basics of black holes physics.     

Anti-de Sitter时空中黑洞量子熵的发散结构

用“brick- wall”模型研究了Anti-de Sitter时空中起源于电磁和引力场的黑洞量子熵的发散结构, 结果表明量子熵由线性发散项和对数发散项构成. 如果平衡温度选为Hawking温度，固有截断替代坐标截断，则线性发散项可化为正比于事件视界面积的形式；而对数发散项不仅依赖于黑洞的特征，也依赖于场的自旋，由于此项的存在，自旋场的贡献不再与标量场的贡献成正比. 关键词： 发散结构 黑洞熵 AdS时空 电磁和引力场     

Entropy correction to stationary black hole via fermions tunneling beyond semiclassical approximation

Recently, fermions tunneling beyond semiclassical approximation from an uncharged static black hole was investigated by Majhi, which was based on the work of Banerjee and Majhi, it was found that the black hole entropy correction can be produced as the quantum effect of a particle is taken into account. In this paper, we further extend this idea to the stationary Kerr black hole to discuss its entropy correction. To get the corrections correctly, the proportionality parameters of quantum corrections of action I _i to the semiclassical action I ₀ in this case are regarded as the inverse of the product of Planck Length and Planck Mass. The result shows that entropy corrections to the stationary black hole also include the logarithmic term and inverse area term in Bekenstein–Hawking entropy beyond semiclassical approximation.     

Entropy in Kerr–de Sitter Black Holes with Spin Fields

Generalized master equations due to spin fields are given. We obtain the entropy of electromagnetic, gravitational, Dirac, and scalar fields in a unified form by using the improved brick-wall method—membrane model. The results show that, as the cutoff is properly chosen, the entropy in the black hole satisfies the Bekenstein–Hawking area formula.     

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.     

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.     

Hidden conformal symmetry of self-dual warped AdS<Subscript>3</Subscript> black holes in topological massive gravity

We extend the recently proposal of hidden conformal symmetry to the self-dual warped AdS₃ black holes in topological massive gravity. It is shown that the wave equation of massive scalar field with sufficient small angular momentum can be reproduced by the SL(2, R) Casimir quadratic operator. Due to the periodic identification in the φ direction, it is found that only the left section of hidden conformal symmetry is broken to U(1), while the right section is unbroken, which only gives the left temperature of dual CFT. As a check of the dual CFT conjecture of self-warped AdS₃ black hole, we further compute the Bekenstein–Hawking entropy and absorption cross section and quasinormal modes of scalar field perturbation and show these are just of the forms predicted by the dual CFT.     

Comparing decay rates for black holes and D-branes

We compute the leading order (in coupling) rate of emission of low energy quanta from a slightly non-extremal system of 1-D- and 5-D-branes. We also compute the classical cross-section, and hence the Hawking emission rate, for low energy scalar quanta for the black hole geometry that corresponds to these branes (at sufficiently strong coupling). These rates are found to agree with each other.     

Dilaton driven Hawking radiation in AdS2 black hole

A recent study shows that Hawking radiation of a massless scalar field does not appear on the two-dimensional AdS₂ black hole background. We shall study this issue by calculating absorption and reflection coefficients under dilaton coupling with the matter field. If the scalar field does not couple to the dilaton, then it is fully absorbed into the black hole without any outgoing mode. On the other hand, once it couples to the dilaton field, the outgoing mode of the massless scalar field exists, and the nontrivial Hawking radiation appears. Finally, we comment on this dilaton dependence of Hawking radiation in connection with a three-dimensional black hole.     

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.     

Orbital resonances in discs around braneworld Kerr black holes

Rotating black holes in the brany universe of the Randall–Sundrum type with infinite additional dimension are described by the Kerr geometry with a tidal charge b representing the interaction of the brany black hole and the bulk spacetime. For b < 0 rotating black holes with dimensionless spin a > 1 are allowed. We investigate the role of the tidal charge in the orbital resonance model of quasiperiodic oscillations (QPOs) in black hole systems. The orbital Keplerian frequency v _K and the radial and vertical epicyclic frequencies v _r, v _θ of the equatorial, quasicircular geodetical motion are given. Their radial profiles related to Keplerian accretion discs are discussed, assuming the inner edge of the disc located at the innermost stable circular geodesic. For completeness, naked singularity spacetimes are considered too. The resonant conditions are given in three astrophysically relevant situations: for direct (parametric) resonances of the oscillations with the radial and vertical epicyclic frequencies, for the relativistic precession model, and for some trapped oscillations of the warped discs, with resonant combinational frequencies involving the Keplerian and radial epicyclic frequencies. It is shown, how the tidal charge could influence matching of the observational data indicating the 3 : 2 frequency ratio observed in GRS 1915 + 105 microquasar with prediction of the orbital resonance model; limits on allowed range of the black hole parameters a and b are established. The “magic” dimensionless black hole spin enabling presence of strong resonant phenomena at the radius, where v _K: v _θ : v _r = 3 : 2 : 1, is determined in dependence on the tidal charge. Such strong resonances could be relevant even in sources with highly scattered resonant frequencies, as those expected in Sgr A*. The specific values of the spin and tidal charge are given also for existence of specific radius where v _K : v _θ : v _r = s : t : u with 5≥s >t >u being small natural numbers. It is shown that for some ratios such situation is impossible in the field of black holes. We can conclude that analysing the microquasars high-frequency QPOs in the framework of orbital resonance models, we can put relevant limits on the tidal charge of brany Kerr black holes.     

Hawking radiation of black holes in non-minimal <Emphasis Type="Italic">R</Emphasis><Superscript><Emphasis Type="Italic">β</Emphasis></Superscript><Emphasis Type="Italic">F</Emphasis><Superscript>2</Superscript>-type coupled Einstein–Maxwell theory

We investigate the Hawking radiation and greybody factor for a scalar field on the background of the black holes in the theory of the non-minimal R ^β F ²-coupled electromagnetic fields to gravity. For different asymptotic structures caused by the real power number β, we find that the influences of the real power number on the Hawking radiation and greybody factor are different. We also show that the different coupling constant also affects the Hawking radiation and greybody factor.