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.     

Fifth force from Kaluza-Klein unification

We discuss the possible modification of Einstein's theory of gravitation due to the fifth force generated by the Kaluza-Klein dilaton. In particular we discuss the gravitational redshift, the deflection of light, the precession of perihelia, and the time-delay of radar echo around a spherically symmetric black hole in a 7-dimensional Kaluza-Klein unification which hasE ₂ as the internal isometry. It is shown that the long-range effect of the higher-dimensional fifth force is characterized by the dilatonic charge carried by the black hole even when it is neutral.     

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.     

The AdS5 Black Hole Space-time with the Perturbed?Dilaton Field Background

The AdS ₅ black hole space-time with perturbed dilaton field background considered. We use the holographic AdS/QCD soft-wall model to investigate the wave functions and the effective potential. In this model, glueballs are described by a massless scalar field in an AdS ₅ black hole with a dilaton soft-wall background. For the first time we use modified dilaton field and discuss the consequence of the perturbation. In order to obtain the effective potential we rewrite the equation of motion in the Schr?dinger like equation, then try to find corresponding solution.     

Dilaton gravity approach to three-dimensional Lifshitz black hole

The z=3 Lifshitz black hole is an exact black hole solution to the new massive gravity in three dimensions. In order to understand this black hole clearly, we perform a dimensional reduction to two-dimensional dilaton gravity by utilizing the circular symmetry. Considering the linear dilaton, we find the same Lifshitz black hole in two dimensions. This implies that all thermodynamic quantities of the z=3 Lifshitz black hole could be obtained from its corresponding black hole in two dimensions. As a result, we derive the temperature, mass, heat capacity, Bekenstein–Hawking entropy, and free energy.     

Curvature-corrected dilatonic black holes and black hole—string transition

We investigate extremal charged black hole solutions in the four-dimensional string frame Gauss-Bonnet gravity with the Maxwell field and the dilaton. Without curvature corrections, the extremal electrically charged dilatonic black holes have singular horizon and zero Bekenstein entropy. When the Gauss-Bonnet term is switched on, the horizon radius expands to a finite value provided curvature corrections are strong enough. Below a certain threshold value of the Gauss-Bonnet coupling the extremal black hole solutions cease to exist. Since decreasing Gauss-Bonnet coupling corresponds to decreasing string coupling g _s , the situation can tentatively be interpreted as classical indication on the black hole—string transition. Previously the extremal dilaton black holes were studied in the Einstein-frame version of the Gauss-Bonnet gravity. Here we work in the string frame version of the theory with the S-duality symmetric dilaton function as required by the heterotic string theory. The article is published in the original.     

Letter: Quasinormal Modes of the Electrically Charged Dilaton Black Hole

We sketch the results of calculations of the quasinormal frequencies of the electrically charged dilaton black hole. At the earlier phase of evaporation (Q is less than 0.7–0.8M), the dilaton black hole rings with the complex frequencies which differ negligibly from those of the Reissner-Nordström black hole. The spectrum of the frequencies weakly depends upon the dilaton coupling.     

Higher dimensional charged rotating dilaton black holes

In this paper, we present the metric for the n-dimensional charged slowly rotating dilaton black hole with N = [(n −1)/2] independent rotation parameters, associated with N orthogonal planes of rotation in the background of asymptotically flat and asymptotically (anti)-de Sitter spacetime. The mass, angular momentum and the gyromagnetic ratio of such a black hole are determined for the arbitrary values of the dilaton coupling constant. We find that the gyromagnetic ratio crucially depends on the dilaton coupling constant, α, and decreases with increasing α in any dimension.     

Temperature and Energy of 4-Dimensional Axisymmetric Black Holes from Entropic Force

We investigate the temperature and energy on holographic screens for 4-dimensional axisymmetric black holes with the entropic force idea proposed by Verlinde. According to the principle of thermal equilibrium, the location of holographic screen outside the axisymmetric black hole horizon is not a equivalent radius surface. The location of isothermal holographic screen outside the axisymmetric black hole horizon is obtained. Using the equipartition rule, we derive the correction expression of energy of isothermal holographic screen. When holographic screens are far away the black hole horizon, the entropic force of charged rotating particles can be expressed as Newton’s law of gravity. When the screen crosses the event horizon, the temperature of the screen agrees with the Hawking temperature and the entropic force gives rise to the surface gravity for both of the black holes.     

非对易时空下Gibbons-Maeda dilaton黑洞和Garfinkle-Horowitz-Strominger dilaton黑洞的热力学性质

以Gibbons-Maeda dilaton黑洞和Garfinkle-Horowitz-Strominger dilaton黑洞为例，研究空间的非对易性对黑洞热力学性质的影响.通过对比对易时空中Gibbons-Maeda dilaton黑洞和非对易时空中Garfinkle-Horowitz-Strominger dilaton黑洞的温度，得出如下结论：从对黑洞热力学性质产生影响这一角度来说，时空的非对易性和黑洞的荷(电荷或磁荷)有相似的作用.     

Effect of the Born–Infeld parameter in higher dimensional Hawking radiation

We show in detail that the Hawking temperature calculated from the surface gravity is in agreement with the result of exact semi-classical radiation spectrum for higher dimensional linear dilaton black holes in various theories. We extend the method derived first by Clément–Fabris–Marques for 4-dimensional linear dilaton black hole solutions to the higher dimensions in theories such as Einstein–Maxwell dilaton, Einstein–Yang–Mills dilaton and Einstein–Yang–Mills–Born–Infeld dilaton. Similar to the Clément–Fabris–Marques results, it is proved that whenever an analytic solution is available to the massless scalar wave equation in the background of higher dimensional massive linear dilaton black holes, an exact computation of the radiation spectrum leads to the Hawking temperature TH$T_H$ in the high frequency regime. The significance of the dimensionality on the value of TH$T_H$ is shown, explicitly. For a chosen dimension, we demonstrate how higher dimensional linear dilaton black holes interpolate between the black hole solutions with Yang–Mills and electromagnetic fields by altering the Born–Infeld parameter in aspect of measurable quantity TH$T_H$. Finally, we explain the reason of, why massless higher dimensional linear dilaton black holes cannot radiate.     

Critical behavior and phase transition of dilaton black holes with nonlinear electrodynamics

In this paper, we take into account the dilaton black hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. First of all, we consider the cosmological constant and nonlinear parameter as thermodynamic quantities which can vary. We obtain thermodynamic quantities of the system such as pressure, temperature and Gibbs free energy in an extended phase space. We complete the analogy of the nonlinear dilaton black holes with the Van der Waals liquid–gas system. We work in the canonical ensemble and hence we treat the charge of the black hole as an external fixed parameter. Moreover, we calculate the critical values of temperature, volume and pressure and show that they depend on the dilaton coupling constant as well as on the nonlinear parameter. We also investigate the critical exponents and find that they are universal and independent of the dilaton and nonlinear parameters, which is an expected result. Finally, we explore the phase transition of nonlinear dilaton black holes by studying the Gibbs free energy of the system. We find that in the case of \(T>T_c\), we have no phase transition. When \(T=T_c\), the system admits a second-order phase transition, while for \(T=T_\mathrm{f}<T_c\) the system experiences a first-order transition. Interestingly, for \(T_\mathrm{f}<T<T_c\) we observe a zeroth-order phase transition in the presence of a dilaton field. This novel zeroth-order phase transition occurs due to a finite jump in the Gibbs free energy which is generated by the dilaton–electromagnetic coupling constant, \(\alpha \), for a certain range of pressure.     

Phantom Accretion onto the Schwarzschild AdS Black Hole with Topological Defect

In this paper, we have studied phantom energy accretion of prefect fluid onto the Schwarzschild AdS black hole with topological defect. We have obtained critical point during the accretion of fluid on the black hole where the speed of flow is equal speed of sound (Sharif and Abbas in Phantom accretion onto the Schwarzschild de-Sitter black hole, 2011, [gr-qc]). The critical velocities have been computed so that the speed of fluid into the black hole is less than speed of sound. Finally, we have found that the critical point is near the black hole horizon.     

Entropies of Static Dilaton Black Holes from the Cardy Formula

A standard Virasoro subalgebra for a static dilaton black hole obtained in the low-energy effective field theory describing heterotic string is constructed at a Killing horizon. The statistical entropies of the Garfinkle–Horowitz–Strominger dilaton black hole and the Gibbons–Maeda dilaton black hole obtained by standard Cardy formula agree with their Bekenstein–Hawking entropies only if we take period T of function as the periodicity of the Euclidean black hole. We also consider first-order quantum correction to the entropy and find that the correction is described by a logarithmic term with a factor of , which is different from Kaul and Majumdar's factor of .     

黑洞背景下费米物质能量密度涨落的计算

应用泛函积分方法推导了量子Thirring模型中的传播子和有效势,计算了二维点物质黑洞和dilaton黑洞模型中费米物质的能量密度涨落,在相同的物理条件下,发现dilaton黑洞外费米物质的能量密度涨较大.     

Scaling Laws at the Extremal Limit of Dilaton Black Holes

The thermodynamics of an arbitrary dimensional charged dilaton black hole is investigated. We find that the extremal limit of the black hole is a critical point and the entropy of the black hole is a homogeneous function. Thus the scaling laws hold at the critical point and a phase transition is expected to appear from the extremal to nonextremal dilaton black holes. Some relevant critical exponents are given and they depend manifestly on the content of the theory.     

Thermodynamics and spectroscopy of charged dilaton black holes

The Bohr–Sommerfeld quantization rule is useful to study the area spectrum of black holes by employing adiabatic invariants. This method is extended to charged dilaton black holes in 2 $+$ + 1 dimensions. We put the background space-time into the Kruskal-like coordinate to find the period with respect to Euclidian time. Also assuming that the adiabatic invariant obeys Bohr–Sommerfeld quantization rule, detailed study of area and entropy spectrum has been done. It is dependent on the charge and is equally spaced as well. We also investigate the thermodynamics of the charged dilaton black hole.     

Schwarzschild and Synge once again

We complete the historical overview about the geometry of a Schwarzschild black hole at its horizon by emphasizing the contribution made by Synge in [6] to its clarification.     

Virtual black holes in generalized dilaton theories

The virtual black hole phenomenon, which has been observed previously in specific models, is established for generic 2D dilaton gravity theories with scalar matter. The ensuing effective line element can become asymptotically flat only for two classes of models; among them spherically reduced theories and the string inspired dilaton black hole. We present simple expressions for the lowest order scalar field vertices of the effective theory which one obtains after integrating out geometry exactly. Treating the boundary in a natural and simple way, asymptotic states, tree-level vertices and the tree-level S-matrix are conformally invariant. Examples are provided pinpointing the physical consequences of virtual black holes on the (CPT-invariant) S-matrix for gravitational scattering of scalar particles. For minimally coupled scalars the evaluation of the S-matrix in closed form is straightforward. For a class of theories including the string inspired dilation black hole all tree-graph vertices vanish, which explains the particular simplicity of that model and at the same time shows yet another essential difference to the Schwarzschild case.Received: 7 August 2002, Revised: 2 June 2003, Published online: 11 July 2003D.V. Vassilevich: On leave from V. Fock Institute of Physics, St. Petersburg University, 198904 St. Petersburg, Russia     

Topological Born–Infeld-dilaton black holes

We construct a new analytic solution of Einstein–Born–Infeld-dilaton theory in the presence of Liouville-type potentials for the dilaton field. These solutions describe dilaton black holes with nontrivial topology and nonlinear electrodynamics. Black hole horizons and cosmological horizons in these spacetimes, can be a two-dimensional positive, zero or negative constant curvature surface. The asymptotic behavior of these solutions are neither flat nor (A)dS. We calculate the conserved and thermodynamic quantities of these solutions and verify that these quantities satisfy the first law of black hole thermodynamics.