Quantum statistical entropy of Schwarzchild-de Sitter spacetime

Using the quantum statistical method, we calculate quantum statistical entropy between the black hole horizon and the cosmological horizon in Schwarzchild spacetime and derive the expression of quantum statistical entropy in de Sitter spacetime. Under the Unruh-Verlinde temperature of Schwarzchild-de Sitter spacetime in the entropic force views, we obtain the expression of quantum statistical entropy in de Sitter spacetime. It is shown that in de Sitter spacetime quantum statistical entropy is the sum of thermodynamic entropy corresponding black hole horizon and the one corresponding cosmological horizon. And the correction term of de Sitter spacetime entropy is obtained. Therefore, it is confirmed that the black hole entropy is the entropy of quantum field outside the black hole horizon. The entropy of de Sitter spacetime is the entropy of quantum field between the black hole horizon and the cosmological horizon.     

Nernst theorem and Hawking radiation from a Reissner-Nordstrom black hole

The thermal character of inner horizon in a Reissner-Nordstrom black hole is studied via Hamilton-Jacobi method. There is “Hawking absorption” as a quantum effect near the inner horizon, and a negative temperature of the inner horizon was attained by choosing an observer outside the black hole. Using a redefined entropy of the black hole, we give a new expression of Bekenstein-Smarr formula. The redefined entropy satisfies Nernst Theorem, so it can be regarded as Planck absolute entropy of the Reissner-Nordstrom black hole.     

Plenty of nothing: Black hole entropy in induced gravity

We demonstrate how Sakharov's idea of induced gravity allows one to explain the statistical-mechanical origin of the entropy of a black hole. According to this idea, gravity becomes dynamical as the result of quantum effects in the system of heavy constituents of the underlying theory.The black hole entropy is related to the properties of the vacuum in the induced gravity in the presence of the horizon. We obtain the Bekenstein-Hawking entropy by direct counting the states of the constituents.     

Spacetime dimensionality and logarithmic prefactor in the black hole entropy relation

We study the relation between the existence of the logarithmic prefactor and spacetime dimensionality in black hole entropy relation by a detailed study of a TeV-scale black hole entropy. In a model universe with large extra dimensions and within the Generalized Uncertainty Principle (GUP) framework, we show that probability of black hole production in the Large Hadronic Collider (LHC) decreases for sufficiently large values of the GUP parameter. In this regard, even observation of micro-black holes may be suppressed at TeV energy scale. We determine also the GUP parameter in an extra dimensional scenario by comparing black hole entropy calculated within the GUP and loop quantum gravity frameworks.     

Thermodynamics of the five-dimensional Schwarzschild-de Sitter black hole

Considering the fact that there is a correlation between the black hole horizon and cosmological horizon, we discuss the thermodynamic properties of de Sitter spacetime. The equivalent temperature and energy of de Sitter spacetime are obtained. It is shown that the upper limit energy of de Sitter spacetime is equal to the energy of a pure de Sitter spacetime. The thermodynamic entropy of de Sitter spacetime is the sum of the black hole horizon thermodynamic entropy and the one of cosmological horizon.     

Back reaction and quantum gravity corrections of Hawking radiation from Schwarzschild-de Sitter black hole

Following the Parikh and Wilczek semiclassical tunneling method of massless particle, hawking radiation of Schwarzschild-de Sitter (SdS) black hole have been computed using null geodesic method. Purely thermal and quantum gravity corrections have been made and have shown that both the corrections give the same results and all the tunneling rates are related to change of Bekenstein-Hawking entropy of SdS black hole. The results obtained for SdS black hole are also in accordance with Parikh and Wilczek’s opinion and gives a correction to the Hawking radiation of SdS black hole.     

Hawking radiation and entropy of Kerr-Newman black hole

The entropy correction of Kerr-Newman black hole is investigated using the Hamilton-Jacobi method beyond semiclassical approximation. To get entropy correction, the inverse of the sum of square of event horizon (r ₊) and the square of rotational parameter a of the black hole is taken as the proportionality parameter for quantum corrections of the action I _i to the semiclassical action I ₀. It has been shown that as quantum effects are taken into account the corrections to the Bekenstein-Hawking entropy of the stationary black hole include a logarithmic term and an inverse area term beyond the semiclassical approximation.     

Quantum gravity effects on the radiation of a stimulated emission from quantum black holes

In the recent interest to the quantum black hole spectroscopy, we calculate the quantum gravity effects to Hawking radiation. In the view of our calculation, the quantum black hole radiation is a stimulated emission.     

Thermodynamics of 4-dimensional charged black holes in Brans-Dicke-Born-Infeld gravity theory

In this work, the charged black hole solution to the Brans-Dicke gravity theory in the presence of the nonlinear electrodynamics has been investigated. To simplify the field equations, a suitable conformal transformation has been used which transforms the Brans-Dicke-Born-Infeld Lagrangian to that of Einstein-dilaton theory with new nonlinear electrodynamics field. A new class of 4-dimensional black hole solution has been constructed out as the exact solution to the Brans-Dicke theory in the presence of the Born-Infeld nonlinear electrodynamics. The physical properties of the solutions have been studied. The black hole charge and temperature have been calculated making use of the Gauss’s law and the concept of surface gravity, respectively. Also, the black hole mass and entropy have been obtained from geometrical methods. Through a Smarr-type mass formula as a function of the black hole charge and entropy the black hole temperature and electric potential, as the intensive parameters conjugate to the black hole entropy and charge, have been calculated.     

Model dependence of the multi-transonic behaviour,stability properties and the corresponding acoustic geometry for accretion onto rotating black holes

Stationary, multi-transonic, integral solutions of hydrodynamic axisymmetric accretion onto a rotating black hole have been compared for different geometrical configurations of the associated accretion disc structures described using the polytropic as well as the isothermal equations of state. Such analysis is performed for accretion under the influence of generalised post Newtonian pseudo Kerr black hole potential. The variations of the stationary shock characteristics with black hole spin have been studied in details for all the disc models and are compared for the flow characterised by the two aforementioned equations of state. Using a novel linear perturbation technique it has been demonstrated that the aforementioned stationary solutions are stable, at least upto an astrophysically relevant time scale. It has been demonstrated that the emergence of the horizon related gravity like phenomena (the analogue gravity effects) is a natural consequence of such stability analysis, and the corresponding acoustic geometry embedded within the transonic accretion can be constructed for the propagation of the linear acoustic perturbation of the mass accretion rate. The analytical expression for the associated sonic surface gravity κ has been obtained self consistently. The variations of κ with the black hole spin parameter for all different geometric configurations of matter and for various thermodynamic equations of state have been demonstrated.     

The generalized uncertainty principle and the quantum entropy due to spin fields on the Reissner-Nordström black hole background

By using the null tetrad and the ’t Hooft brick-wall model, the quantum entropies of a Reissner-Nordström black hole due to the Weyl neutrino, electromagnetic, massless Rarita-Schwinger and gravitational fields for the source-free case are investigated from a generalized uncertainty principle. The divergence structure for the entropy is demonstrated. In addition to the usual linearly and logarithmically divergent terms, additional quadratic, cubic, biquadratic and other higher order divergences exist near the event horizon in the entropy, which not only depend on the black hole characteristics but also on the spin fields and the gravitational interactions. The terms describe the contribution of the quantum fields to the entropy and the effects of the generalized uncertainty principle on it. If the smallest length scale is taken into account, the contribution of the gravitational interactions to the entropy is found to be a part of the dominant term and very important, and therefore it can not be neglected.     

Extremal black hole entropy satisfying the Nernst theorem

Quantum entropy of extremal black holes has been discussed by many authors. However the contribution of inner event horizon has not been considered. In this paper, we consider the Reissner-Nordström-anti-de Sitter black hole, and show that the contributions lead extremal black hole entropy to obey the Nernst theorem, naturally. Therefore the contributions are important and cannot be neglected in near-extremal and extremal black hole cases.     

Fading Hawking radiation

In this study, we explore a particular type Hawking radiation which ends with zero temperature and entropy. The appropriate black holes for this purpose are the linear dilaton black holes. In addition to the black hole choice, a recent formalism in which the Parikh-Wilczek’s tunneling formalism amalgamated with quantum corrections to all orders in ? is considered. The adjustment of the coefficients of the quantum corrections plays a crucial role on this particular Hawking radiation. The obtained tunneling rate indicates that the radiation is not pure thermal anymore, and hence correlations of outgoing quanta are capable of carrying away information encoded within them. Finally, we show in detail that when the linear dilaton black hole completely evaporates through such a particular radiation, entropy of the radiation becomes identical with the entropy of the black hole, which corresponds to “no information loss”.     

自引力辐射体系的熵与引力坍缩

本文利用李立新和刘辽导出的黑洞视界附近的辐射态方程，计算了约束在一个球形盒子中的目引力辐射体系的墙（不含中心黑洞和含有中心黑洞两种情况）．与Sorkin等人的计算比较，本文的结果不会出现发散困难，而且体系的总摘（包括中心黑洞的墙）的上阳正好等于坍缩后形成的同质量的黑洞嫡．作者认为，自引力辐射体系坍绩的合理模式是先形成中心黑洞，然后中心黑洞逐渐长大直至整个体系全部坍缩为黑洞．在坍缩过程中，任一中间态的媳总是比末态的黑洞墙小，到坍缩过程结束总熵才等于对应的黑洞摘．这一结果为黑洞滴的起源提供了一个合理的解释．     

Hawking radiation and entropy in de Sitter spacetime

Using the analytic extension method, we study Hawking radiation of an (n+4)-dimensional Schwarzschild-de Sitter black hole. Under the condition that the total energy is conserved, taking the reaction of the radiation of particles to the spacetime into consideration and considering the relation between the black hole event horizon and cosmological horizon, we obtain the radiation spectrum of de Sitter spacetime. This radiation spectrum is no longer a strictly pure thermal spectrum. It is related to the change of the Bekenstein-Hawking (B-H) entropy corresponding the black hole event horizon and cosmological horizon. The result satisfies the unitary principle. At the same time, we also testify that the entropy of de Sitter spacetime is the sum of the entropy of black hole event horizon and the one of cosmological horizon.     

Thermodynamics of Vaidya-Bonner-de Sitter space time based on the generalized space-time uncertainty

In each static or stationary space time k is just surface gravity of the horizon, but in the of Vaidya-Bonner-de Sitter space time, it is no longer the surface gravity of the event horizon. This property makes the Vaidya-Bonner as an important horizon. In this paper, the entropy of Vaidya-Bonner-de Sitter space time is calculated. In continue, employing the generalized uncertainty principle, quantum gravitational corrections to the entropy of Vaidya-Bonner space time is studied.     

Hawking Radiation of Mass Generating Particles from Dyonic Reissner–Nordström Black Hole

The Hawking radiation is considered as a quantum tunneling process, which can be studied in the framework of the Hamilton–Jacobi method. In this study, we present the wave equation for a mass generating massive and charged scalar particle (boson). In sequel, we analyse the quantum tunneling of these bosons from a generic 4-dimensional spherically symmetric black hole. We apply the Hamilton–Jacobi formalism to derive the radial integral solution for the classically forbidden action which leads to the tunneling probability. To support our arguments, we take the dyonic Reissner–Nordström black hole as a test background. Comparing the tunneling probability obtained with the Boltzmann formula, we succeed in reading the standard Hawking temperature of the dyonic Reissner–Nordström black hole.     

Evaporating quantum Lukewarm black holes final state from back-reaction corrections of quantum scalar fields

We obtain renormalized stress tensor of a mass-less, charge-less dynamical quantum scalar field, minimally coupled with a spherically symmetric static Lukewarm black hole. In two dimensional analog the minimal coupling reduces to the conformal coupling and the stress tensor is found to be determined by the nonlocal contribution of the anomalous trace and some additional parameters in close relation to the work presented by Christensen and Fulling. Lukewarm black holes are a special class of Reissner-Nordström-de Sitter space times where its electric charge is equal to its mass. Having the obtained renormalized stress tensor we attempt to obtain a time-independent solution of the well known metric back reaction equation. Mathematical derivations predict that the final state of an evaporating quantum Lukewarm black hole reduces to a remnant stable mini black hole with moved locations of the horizons. Namely the perturbed black hole (cosmological) horizon is compressed (extended) to scales which is smaller (larger) than the corresponding classical radius of the event horizons. Hence there is not obtained an deviation on the cosmic sensor-ship hypothesis.     

Change in entropy of non-spinning black holes w.r.t. the radius of event horizon in XRBs

The present research paper discusses the derivation for the change in entropy of Non- spinning black holes with respect to the change in the radius of event horizon applying the first law of black hole mechanics ( $\delta M = \frac{\kappa}{8\pi} \delta A + \varOmega\delta J - \upsilon\delta Q$ ) with the relation for the change in entropy δS=8πMδM. When the work is further extended with proper operation, the entropy of black hole is obtained almost the same as the Bekenstein-Hawking entropy of black hole. This is the entirely new method to obtain the change in entropy of Non-spinning black holes w.r.t. the radius of event horizon and Hawking entropy of black hole. We have also calculated their values for different types of test non-spinning black holes having masses 5–20M _⊙ found in X-ray binaries (Narayan, gr-qc/0506078v1, 2005).     

Basic thermodynamic parameters of a black hole resulting from a Yukawa type of correction to the metric

There has been a renewed interest in the recent years in the possibility of deviations from the predictions of Newton’s “inverse-square law” of universal gravitation. One of the reasons for renewing this interest lies in various theoretical attempts to construct a unified elementary particle theory, in which there is a natural prediction of new forces over macroscopic distances. Therefore the existence of such a force would only coexist with gravity, and in principle could only be detected as a deviation from the inverse square law, or in the “universality of free fall” experiments. New experimental techniques such that of Sagnac interferometry can help explore the range of the Yukawa correction λ≥10¹⁴ m where such forces might be present. It may be, that future space missions might be operating in this range which has been unexplored for very long time. In this paper we derive the basic thermodynamic parameters of such a Yukawa stationary spherically symmetric black hole. First, the expression for the event horizon of such a black hole is derived, with the help of which the temperature, entropy and heat capacity of this particular black hole are obtained. We have also obtained analytical expressions for the change of mass of such black hole, and also its corresponding evaporation time.