Entropic force, holography and thermodynamics for static space-times

Recently Verlinde has suggested a new approach to gravity which interprets gravitational interaction as a kind of entropic force. The new approach uses the holographic principle by stating that the information is kept on the holographic screens which coincide with equipotential surfaces. Motivated by this new interpretation of gravity (but not being limited by it) we study equipotential surfaces, the Unruh–Verlinde temperature, energy and acceleration for various static space-times: generic spherically symmetric solutions, axially symmetric black holes immersed in a magnetic field, traversable spherically symmetric wormholes of an arbitrary shape function, system of two and more extremely charged black holes in equilibrium. In particular, we have shown that the Unruh–Verlinde temperature of the holographic screen reaches absolute zero on the wormhole throat independently of the particular form of the wormhole solution.     

Black holes in general relativity

It is assumed that the singularities which occur in gravitational collapse are not visible from outside but are hidden behind an event horizon. This means that one can still predict the future outside the event horizon. A black hole on a spacelike surface is defined to be a connected component of the region of the surface bounded by the event horizon. As time increase, black holes may merge together but can never bifurcate. A black hole would be expected to settle down to a stationary state. It is shown that a stationary black hole must have topologically spherical boundary and must be axisymmetric if it is rotating. These results together with those of Israel and Carter go most of the way towards establishing the conjecture that any stationary black hole is a Kerr solution. Using this conjecture and the result that the surface area of black holes can never decrease, one can place certain limits on the amount of energy that can be extracted from black holes.     

Debye Entropic Force and Modified Newtonian Dynamics

Verlinde has suggested that the gravity has an entropic origin, and agravitational system could be regarded as a thermodynamical system. It is well-known that the equipartition law of energy is invalid at very low temperature. Therefore, entropic force should be modified while the temperature of the holographic screen is very low. It is shown that the modified entropic force is proportional to the square of the acceleration, while the temperature of the holographic screen is much lower than the Debye temperature T_D. The modified entropic force returns to the Newton's law of gravitation while the temperature of the holographic screen is much higher than the Debye temperature. The modified entropic force is connected with modified Newtonian dynamics (MOND). The constant a₀ involved in MOND is linear in the Debye frequency ω_D, which can be regarded as the largest frequency of the bits in screen.We find that there do have a strong connection between MOND and cosmology in the framework of Verlinde's entropic force, if the holographic screen is takento be bound of the Universe. The Debye frequency is linear in the Hubble constant H₀.     

Impact of Thermal Fluctuations on Logarithmic Corrected Massive Gravity Charged Black Hole

We investigate the influence of the first-order correction of entropy caused by thermal quantum fluctuations on the thermodynamics of a logarithmic corrected charged black hole in massive gravity. For this black hole, we explore the thermodynamic quantities, such as entropy, Helmholtz free energy, internal energy, enthalpy, Gibbs free energy and specific heat. We discuss the influence of the topology of the event horizon, dimensions and nonlinearity parameter on the local and global stability of the black hole. As a result, it is found that the holographic dual parameter vanishes. This means that the thermal corrections have no significant role to disturb the holographic duality of the logarithmic charged black hole in massive gravity, although the thermal corrections have a substantial impact on the thermodynamic quantities in the high-energy limit and the stability conditions of black holes.     

Conformally invariant thermodynamics of a Maxwell-Dilaton black hole

The thermodynamics of Maxwell-Dilaton black holes has been extensively studied. It has served as a fertile ground to test ideas about temperature through various definitions of surface gravity. In this paper, we make an independent analysis of this black hole solution in both, Einstein and Jordan, frames. We explore a set of definitions for the surface gravity and observe the different predictions they make for the near extremal configuration of this black hole. Finally, motivated by the singularity structure in the interior of the event horizon, we use a holographic argument to remove the micro-states from the disconnected region of this solution. In this manner, we construct a frame independent entropy from which we obtain a temperature which agrees with the standard results in the non-extremal regime, and has a desirable behaviour around the extremal configurations according to the third law of black hole mechanics.     

Entropic force between two horizons of dilaton black holes with a power-Maxwell field

In this paper,we consider(n+1)-dimensional topological dilaton de Sitter black holes with a powerMaxwell field as thermodynamic systems.The thermodynamic quantities corresponding to the black hole horizon and the cosmological horizon are interrelated.Therefore,the total entropy of the space-time should be the sum of the entropies of the black hole horizon and the cosmological horizon plus a correction term which is produced by the association of the two horizons.We analyze the entropic force produced by the correction term at given temperatures,which is affected by the parameters and dimensions of the space-time.It is shown that the change of entropic force with the position ratio of the two horizons in some regions is similar to that of the variation of the Lennard-Jones force with the position of particles.If the effect of entropic force is similar to that of the Lennard-Jones force,and other forces are absent,the motion of the cosmological horizon relative to the black hole horizon should have an oscillating process.The entropic force between the two horizons is probably one of the participants in driving the evolution of the universe.     

Modified Friedmann Equations on the Brane from Entropic Force

The well-known area relation of the black hole entropy can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity. Applying this modified entropy-area relation to brane cosmology, we derive the modified cosmological equations governing the evolution of the universe on the brane. We adopt the viewpoint that interprets gravity as an entropic force caused by the changes in the information when a material body moves away from the holographic screen.     

Dilatonic Entropic Force

We show in detail that the entropic force of the static spherically symmetric spacetimes with unusual asymptotics can be calculated through the Verlinde’s arguments. We introduce three different holographic screen candidates, which are first employed thoroughly by Myung and Kim [Phys. Rev. D 81, 105012 (2010)] for Schwarzschild black hole solutions, in order to identify the entropic force arising between a charged dilaton black hole and a test particle. The significance of the dilaton parameter on the entropic force is highlighted, and shown graphically.     

Unruh–Verlinde Temperature and Energy of Charged Black Hole via Entropic Force

Verlinde’s recent work, which showed that gravity may be explained as entropic force caused by the changes of information associated with the positions of material bodies, is extended to study the Unruh–Verlinde temperature and energy of a static spherically symmetric charged black hole. The results indicate that the Unruh–Verlinde temperature is equal to the Hawking temperature at the outer and inner horizons. The energy is dependent on the radius of the screen, which is also a consequence of the Gauss’ laws of gravity and electrostatics.     

Particle acceleration in Horava–Lifshitz black holes

In this paper we calculate the center-of-mass energy of two colliding test particles near the rotating and non-rotating Horava–Lifshitz black hole. For the case of a slowly rotating KS solution of Horava–Lifshitz black hole we compare our results with the case of Kerr black holes. We confirm the limited value of the center-of-mass energy for static black holes and unlimited value of the center-of-mass energy for rotating black holes. Numerically, we discuss temperature dependence of the center-of-mass energy on the black hole horizon. We obtain the critical angular momentum of particles. In this limit the center-of-mass energy of two colliding particles in the neighborhood of the rotating Horava–Lifshitz black hole could be arbitrarily high. We found appropriate conditions where the critical angular momentum could have an orbit outside the horizon. Finally, we obtain the center-of-mass energy corresponding to this circle orbit.     

Remarks on the Equipartition Rule and Thermodynamics of Reissner-Nordstrom Black Holes

In Verlinde’s work, gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. In this paper, we investigate the thermodynamic property of Reissner-Nordstrom black holes from the equipartition rule and holographic scenario. As a result, the first law of thermodynamics of the black holes is recovered.     

Thermodynamic surface system of static black holes and area law

We propose a new picture of black holes through a special holographic screen. This holographic screen contains all the degrees of freedom of a black hole. We find that this holographic screen is similar to the ordinary thermodynamic surface system. Meanwhile, through the "white-wall box" and the formula of sound velocity, we find some similarities between gravitons and photons. We further assume that such a holographic screen is a kind of Bose-Einstein condensate of gravitons. Through this assumption and those similarities, we finally get the area law of static black holes.     

Holographic superconductor in the analytic hairy black hole

We study the charged black hole of hyperbolic horizon with scalar hair (charged Martinez-Troncoso-Zanelli: CMTZ black hole) as a model of analytic hairy black hole for holographic superconductor. For this purpose, we investigate the second order phase transition between CMTZ and hyperbolic Reissner-Nordström-AdS (HRNAdS) black holes. However, this transition unlikely occurs. As an analytic treatment for holographic superconductor, we develop superconductor in the bulk and superfluidity on the boundary using the CMTZ black hole below the critical temperature. The presence of charge destroys the condensates around the zero temperature, which is in accord with the thermodynamic analysis of the CMTZ black hole.     

Modified Friedmann equations from Debye entropic gravity

A remarkable new idea on the origin of gravity was recently proposed by Verlinde who claimed that the laws of gravitation are no longer fundamental, but rather emerge naturally as an entropic force. In Verlinde derivation, the equipartition law of energy on the holographic screen plays a crucial role. However, the equipartition law of energy fails at the very low temperature. Therefore, the formalism of the entropic force should be modified while the temperature of the holographic screen is very low. Considering the Debye entropic gravity and following the strategy of Verlinde, we derive the modified Newton’s law of gravitation and the corresponding Friedmann equations which are valid in all range of temperature. In the limit of strong gravitational field, i.e. high temperature compared to Debye temperature, T » T _D , one recovers the standard Newton’s law and Friedmann equations. We also generalize our study to the entropy corrected area law and derive the dynamical cosmological equations for all range of temperature. Some limits of the obtained results are also studied.     

Nernst Theorem and Entropy of the Axisymmetric Einstein–Maxwell–Dilaton-Axion Black Hole

The free energy and the entropy of scalar field are calculated by brick-wall in the axisymmetric Einstein–Maxwell–Dilaton-axion black hole. It is shown that when the black hole has inner and outer horizons, the entropy is not only related to the area of an outer horizon but also is the function of the area of an inner horizon. When the area of an inner horizon approaches zero, we can obtain the known conclusion. The entropy expressed by location parameter of outer horizon and inner horizons approaches absolute zero. It obeys Nernst theorem. It can be taken as Planck absolute entropy of a black hole.     

Entropy bound of horizons for accelerating,rotating and charged Plebanski–Demianski black hole

We first review the accelerating, rotating and charged Plebanski–Demianski (PD) black hole, which includes the Kerr–Newman rotating black hole and the Taub-NUT spacetime. The main feature of this black hole is that it has 4 horizons like event horizon, Cauchy horizon and two accelerating horizons. In the non-extremal case, the surface area, entropy, surface gravity, temperature, angular velocity, Komar energy and irreducible mass on the event horizon and Cauchy horizon are presented for PD black hole. The entropy product, temperature product, Komar energy product and irreducible mass product have been found for event horizon and Cauchy horizon. Also their sums are found for both horizons. All these relations are dependent on the mass of the PD black hole and other parameters. So all the products are not universal for PD black hole. The entropy and area bounds for two horizons have been investigated. Also we found the Christodoulou–Ruffini mass for extremal PD black hole. Finally, using first law of thermodynamics, we also found the Smarr relation for PD black hole.     

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.     

直线加速运动动态黑洞的熵

选取超前爱丁顿坐标,采用薄膜brickwall模型,计算Kinnersley度规表述的直线加速运动动态黑洞的熵.通过此方法,可以给出视界面上每一点的温度和熵密度.这一结果表明,熵与视界面积成正比的结论,不仅适用于整个视界,也适用于视界面上的局部;不仅适用于稳态黑洞,也适用于动态黑洞.在薄膜趋于视界面时,其厚度也趋于零,薄膜本身成为视界面,黑洞熵就是视界面上量子态的熵 关键词： 熵 加速黑洞 薄膜brickwall模型     

Entropy of Kerr-Newman Black Hole to All Orders in the Planck Length

Using the quantum statistical method, the difficulty of solving the wave equation on the background of the black hole is avoided. We directly solve the partition functions of Bose and Fermi field on the background of an axisymmetric Kerr-Newman black hole using the new equation of state density motivated by the generalized uncertainty principle in the quantum gravity. Then near the black hole horizon, we calculate entropies of Bose and Fermi field between the black hole horizon surface and the hypersurface with the same inherent radiation temperature measured by an observer at an infinite distance. In our results there are not cutoffs and little mass approximation introduced in the conventional brick-wall method. The series expansion of the black hole entropy is obtained. And this series is convergent. It provides a way for studying the quantum statistical entropy of a black hole in a non-spherical symmetric spacetime.     

Spectrum of a quantized black hole,correspondence principle,and holographic bound

An equidistant spectrum of the horizon area of a quantized black hole does not follow from the correspondence principle or from general statistical arguments. On the other hand, such a spectrum obtained in loop quantum gravity (LQG) either does not comply with the holographic bound or requires a special choice of the Barbero-Immirzi parameter for the horizon surface, distinct from its value for other quantized surfaces. The problem of distinguishability of the edges in LQG is discussed, with the following conclusion: Only under the assumption of partial distinguishability of the edges can the microcanonical entropy of a black hole be made both proportional to the horizon area and satisfying the holographic bound.