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.     

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.     

Quantum corrections for ABGB black hole

In this paper, we study quantum corrections to the temperature and entropy of a regular Ayón-Beato-García-Bronnikov black hole solution by using tunneling approach beyond semiclassical approximation. We use the first law of black hole thermodynamics as a differential of entropy with two parameters, mass and charge. It is found that the leading order correction to the entropy is of logarithmic form. In the absence of the charge, i.e., e=0, these corrections approximate the corresponding corrections for the Schwarzschild 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.     

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”.     

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.     

Planck absolute entropy of a rotating BTZ black hole

In this paper, the Planck absolute entropy and the Bekenstein–Smarr formula of the rotating Banados–Teitelboim–Zanelli (BTZ) black hole are presented via a complex thermodynamical system contributed by its inner and outer horizons. The redefined entropy approaches zero as the temperature of the rotating BTZ black hole tends to absolute zero, satisfying the Nernst formulation of a black hole. Hence, it can be regarded as the Planck absolute entropy of the rotating BTZ black hole.     

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.     

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.     

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.     

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．     

Entanglement entropy of a black hole and isolated horizon

Using Unruh-Verlinde temperature obtained by entropic force, we directly calculate partition functions of quantum field in Schwarzschild spacetime via quantum statistical method and derive the expression of the black hole statistical entropy. In our calculation the lower limit of integral is the location of isolated horizon introduced in loop quantum gravity and the upper limit of integral is infinity. So the obtained entropy is the statistical entropy from isolated horizon to the infinite. In our calculation there are not the cutoff and approximation. The results showed that, as long as proper Immirzi parameters are selected, the entropy obtained by loop quantum gravity is consistent with the quantum statistical entropy outside the black hole horizon. Therefore the black hole entropy is a quantum entanglement entropy outside the isolated horizon.     

Asymptotic formulas for the magnification of a gravitational lens system near a fold caustic

An approximate formula for the magnification of a point source near a fold caustic obtained in the first linear caustic approximation is widely used in the theory of gravitational lens systems. Here, this formula is refined to include the post-linear terms that have been found both for a point source and for an extended Gaussian source in the absence of continuous matter on the line of sight. The formulas are reduced to a form containing three additional parameters; the derivation of nontrivial corrections requires including the expansion terms in the lens equation up to the fourth order. The modified formula for an extended source is used to analyze strong microlensing events in the gravitational lens system Q2237+0305 (the Einstein Cross). For such an event on the light curve of image C (1999, OGLE data), the corrections found are statistically significant.     

Gravitational collapse in generalized Vaidya space-time for Lovelock gravity theory

In this work, we have assumed the generalized Vaidya solution in Lovelock theory of gravity in (n+2)-dimensions. It has been shown that Gauss-Bonnet gravity, dimensionally continued Lovelock gravity and pure Lovelock gravity can be constructed by suitable choice of parameters. We have investigated the occurrence of singularities formed by the gravitational collapse in above three particular forms of Lovelock theory of gravity. The dependence of the nature of singularity on the existence of radial null geodesic for Vaidya space-time has been specially considered. In all the three models, we have shown that the nature of singularities (naked singularity or black hole) completely depend on the parameters. Choices of various parameters are shown in tabular form. In Gauss-Bonnet gravity theory, it can be concluded that the possibility of naked singularity increases with increase in dimensions. In dimensionally continued Lovelock gravity, the naked singularity is possible for odd dimensions for several values of parameters. In pure Lovelock gravity, only black hole forms due to the gravitational collapse for any values of parameters. It has been shown that when accretion is taking place on a collapsing object, it is highly unlikely to get a black hole. Finally on considering the phantom era in the expanding universe it is observed that there is no possibility of formation of a black hole if we are in the Gauss-Bonnet gravity considering the accreting procedure upon a collapsing object.     

非理想流体自引力坍缩体系的熵变

本文利用共动度规讨论了非理想流体开放体系在自引力作用下的坍缩过程之熵变,结果表明,形成视界之前,体系的总熵不增,这说明黑洞的高熵产生于突变之中。     

缘于任意自旋场的Vaidya黑洞的熵(英文)

用在brick模型基础上发展起来的membrane模型 ,计算了缘于任意自旋场的非静态黑洞———Vaidya黑洞的自由能和熵。结果表明 ,玻色子场 (自旋s =1,2 )和费米子场 (自旋s =1/2 )的熵都恰好与黑洞的视界面积成正比 ,这与静态和稳态的情况相同。而且 ,玻色子和费米子场的熵具有相同的形式 ,二者相差一个系数     

The fundamental cosmic distance scale: state of the art and the Gaia perspective

In recent papers we had developed a unified picture of black hole entropy and curvature which was shown to lead to Hawking radiation. It was shown that for any black hole mass, holography implies a phase space of just one quantum associated with the interior of the black hole. Here we study extremal rotating and charged black holes and obtain unique values for ratios of angular momentum to entropy, charge to entropy, etc. It turns out that these ratios can be expressed in terms of fundamental constants in nature, having analogies with other physical systems, like in condensed matter physics.     

Three classical tests of Hořava-Lifshitz gravity theory

Recently, a renormalizable gravity theory has been proposed by Hořava, and it might be an ultraviolet completion of general relativity or its infrared modification. Particular limit of the theory allows for the Minkowski vacuum. A spherical asymptotically flat black hole solution that represents the analogy of Schwarzschild solution of general relativity has been obtained. It will be very interesting to find the difference between traditional general relativity and Hořava-Lifshitz gravity theory. The three classical tests of general relativity including gravitational red-shift, perihelion precession of the planet Mercury, and light deflection in gravitational field in the spherical asymptotically flat black hole solution of infrared modified Hořava-Lifshitz gravity are investigated. The first order corrections from the standard general relativity is obtained. The result can be used to limit the parameters in Hořava-Lifshitz gravity and to show the viability of the theory.     

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.     

Entropic gravity resulting from a Yukawa type of correction to the metric for a solar mass black hole

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. In this paper we study the entropic gravity correction to the gravitational force on the horizon of a black hole whose metric has been modified by a Yukawa term. We find that the gravitational radius of such a black hole is given in-terms of the Lambert function, and the entropic force introduces a extra term that depends on the square of the coupling constant α of the Yukawa potential. In the case alpha equals zero we recover the Newtonian gravitational force on the horizon. In a first effort to obtain a relation between geometry and information, we calculate the Ricci scalar and through entropy we establish a relation to the number of information N where this is given in nats. Finally, we calculate a critical entropy value as well as a critical information number N _c for which the curvature becomes identically zero which implies that the space becomes flat.