Brick-wall Method Research Articles

Noncommutative Correction to the Entropy of Charged BTZ Black Hole

Noncommutative geometry is an established potential candidate for including quantum phenomena in gravitation. We outlined the formalism of Hopf algebras and its connection to the algebra of infinitesimal diffeomorphisms. Using a Drinfeld twist, we deformed spacetime symmetries, algebra of vector fields and differential forms, leading to a formulation of noncommutative Einstein equations. We studied a concrete example of charged BTZ spacetime and deformations steaming from the so-called angular twist. The entropy of the noncommutative charged BTZ black hole was obtained using the brick-wall method. We used a charged scalar field as a probe and obtained its spectrum and density of states via WKB approximation. We provide the method used to calculate corrections to the Bekenstein–Hawking entropy in higher orders in WKB, but we present the final result in the lowest WKB order. The result is that, even in the lowest order in WKB, the entropy, in general, contains higher powers in ℏ, and it has logarithmic corrections and polynomials of logarithms of the black hole area.

Quantum gravity effect on the entropy of a novel four-dimensional Gauss-Bonnet black hole

Taking the generalized uncertainty principle into account, we apply the corrected state density and brick-wall method to calculate the entropy of a novel four-dimensional Gauss-Bonnet black hole surrounded by an arbitrary field with spin . It is shown that the leading and logarithmic terms of the entropy are respectively modified by the quantum gravity effect and spin of the field. Meanwhile, the correction coming from gravitational interaction has the same form as the leading term, that is, they all are proportional to the horizon area and inversely proportional to the gravity correction factor. The ratio of the correction term to the leading one is respectively −5/7 and −1395/1764 for Bose and Fermi cases, where negative sign means that the effect of quantum gravity decreases the entropy. It is very interesting that these proportion values are independent of the black hole characteristics.

Statistical entropy of a class of regular black holes by brick Wall Model Journal of Physics: Conference Series

In the paper we study the entropy of the scalar field in the background of regular black holes (Heyward and nonsingular)by using the brick-wall method suggested by the’t Hooft. We show the leading term of entropy follows the Bekenstein-Hawking area law and the brickwall method predicts the corrections to the entropy of the regular black hole. The general structure of the coefficient of logarithmic sub-leading corrections for the both black holes are same. The coefficients of the logarithmic corrections are-1/180 for both regular black holes which differ from the Schwarzschild black hole.

Late-time tails, entropy aspects, and stability of black holes with anisotropic fluids

In this work we consider black holes surrounded by anisotropic fluids in four dimensions. We first study the causal structure of these solutions showing some similarities and differences with Reissner–Nordström–de Sitter black holes. In addition, we consider scalar perturbations on this background geometry and compute the corresponding quasinormal modes. Moreover, we discuss the late-time behavior of the perturbations finding an interesting new feature, i.e., the presence of a subdominant power-law tail term. Likewise, we compute the Bekenstein entropy bound and the first semiclassical correction to the black hole entropy using the brick wall method, showing their universality. Finally, we also discuss the thermodynamical stability of the model.

Numerical calculation of the entanglement entropy for scalar field in dilaton spacetimes

Using coupled harmonic oscillators model, we numerical analyze the entanglement entropy of massless scalar field in Gafinkle–Horowitz–Strominger (GHS) dilaton spacetime and Gibbons–Maeda (GM) dilaton spacetime. By numerical fitting, we find that the entanglement entropy of the dilaton black holes receive contribution from dilaton charge and is proportional to the area of the event horizon. It is interesting to note that the results of numerical fitting are coincide with ones obtained by using brick wall method and Euclidean path integral approach.

Entropy of Schwarzschild-de Sitter Black Hole with Generalized Uncertainty Principle Revisited**Supported by National Natural Science Foundation of China under Grant Nos. 11275099, 11435006, 11405130, and the Double First-Class University Construction Project of Northwest University

We study the entropy of Schwarzschild-de Sitter black holes based on generalized uncertainty principle with brick-wall method by counting degrees of freedom near the horizons and obtain the entropy proportional to the surface area at the horizons without cut-off. And reveal the possible value of the minimum length.

Entanglement entropy renormalization for the noncommutative scalar field coupled to classical BTZ geometry

In this work, we consider a noncommutative (NC) massless scalar field coupled to the classical nonrotational BTZ geometry. In a manner of the theories where the gravity emerges from the underlying scalar field theory, we study the effective action and the entropy derived from this noncommutative model. In particular, the entropy is calculated by making use of the two different approaches, the brick wall method and the heat kernel method designed for spaces with conical singularity. We show that the UV divergent structures of the entropy, obtained through these two different methods, agree with each other. It is also shown that the same renormalization condition that removes the infinities from the effective action can also be used to renormalize the entanglement entropy for the same system. Besides, the interesting feature of the NC model considered here is that it allows an interpretation in terms of an equivalent system comprising of a commutative massive scalar field, but in a modified geometry; that of the rotational BTZ black hole, the result that hints at a duality between the commutative and noncommutative systems in the background of a BTZ black hole.

Revision of the brick wall method for calculating the black hole thermodynamic quantities

Within the framework of the "brick wall model", a novel method is developed to compute the contributions of a scalar field to the thermodynamic quantities of black holes. The relations between (transverse) momenta and frequencies in Rindler space are determined numerically with high accuracy and analytically with an accuracy of better than 10 % and are compared with the corresponding quantities in Minkowski space. In conflict with earlier results, the thermodynamic properties of black holes turn out to be those of a low temperature system. The resulting discrepancy for partition function and entropy by two orders of magnitude is analyzed in detail. In the final part we carry out the analogous studies for scalar fields in de Sitter space and thereby confirm that our method applies also to the important case of spherically symmetric spaces.

Perbandingan Metode Konstruksi Dinding Bata Merah dengan Dinding Bata Ringan

The development of technology and the demands on the speed of the construction project cause the material manufacturers compete to create a new material that can accelerate the process to build a building. Wall is one of the non-structural elements on a building. Both low-rise building and high-rise building are no doubts using this material. Wall works can use two different types of material, such as brick wall made of red clay and light brick wall made of cement, silica sand, and limestone. In the construction process wall is needed in a large amount of area, so the difference of the price should be examined in choosing the type of the material to gain efficient cost. The purpose of this study is to determine which method of wall construction is more efficient in terms of cost and time, the use of red brick wall or brick wall light. The study was conducted using survey, comparative, literature study method. Results indicate that both methods have advantages and disadvantages. Red brick wall method is cheaper in the cost of the process, while the lighter brick wall method much faster in the process.

Effects of Noncommutativity on the Black Hole Entropy

The BTZ black hole geometry is probed with a noncommutative scalar field which obeys theκ-Minkowski algebra. The entropy of the BTZ black hole is calculated using the brick wall method. The contribution of the noncommutativity to the black hole entropy is explicitly evaluated up to the first order in the deformation parameter. We also argue that such a correction to the black hole entropy can be interpreted as arising from the renormalization of the Newton’s constant due to the effects of the noncommutativity.

Superradiance and statistical entropy of a hairy black hole in three dimensions

We calculate the statistical entropy of a rotating hairy black hole by taking into account superradiant modes in the brick wall method. The UV cutoff is independent of the gravitational hair, which gives the well-defined area law of the entropy. It can be shown that the angular momentum and the energy of matter field depend on the gravitational hair. For the vanishing gravitational hair, it turns out that the energy for matter is related to both the black hole mass and the black hole angular momentum whereas the angular momentum for matter field is directly proportional to the angular momentum of the black hole.

Entropy and temperatures of Nariai black hole

The statistical entropy of the Nariai black hole in a thermal equilibrium is calculated by using the brick-wall method. Even if the temperature depends on the choice of the timelike Killing vector, the entropy can be written by the ordinary area law which agrees with the Wald entropy. We discuss some physical consequences of this result and the properties of the temperatures.

Area law of the entropy in the critical gravity

The entropy of the Schwarzschild-anti de Sitter black hole in the recently proposed four-dimensional critical gravity is trivial in the Euclidean action formulation, while it can be expressed by the area law in terms of the brick wall method given by ʼt Hooft. To resolve this discrepancy, we relate the Euclidean action formulation to the brick wall method semiclassically, and show that the entropy of the black hole can be expressed by the area law even at the critical point.

Black Hole Entropy of IR Modified Hořava-Lifshitz Gravity in Quantum Statistics Perspective

In this paper we investigate quantum statistical entropy for the Kehagias-Sfetsos black hole in IR modified Hořava-Lifshitz gravity by using t’ Hooft’s brick-wall method and generalized uncertainty principle method. By carefully calculating, we obtain the brick-wall entropy SBWM=A/4 and the generalized uncertainty principle entropy SGUP=A/96πγ. It is found if we view from quantum statistics, the brick-wall entropy and generalized uncertainty principle entropy may possibly is proportional to the event horizon area. This type area entropy is also justified by Wang et al. (Phys. Rev. D 81:083006, 2010). The study of the quantum statistical entropy may shed light on the understand of Hořava-Lifshitz gravity.

ENTROPY OF COSMOLOGICAL BLACK HOLES AND THE GENERALIZED SECOND LAW IN THE PHANTOM-ENERGY-DOMINATED UNIVERSE

Adopting the thin layer improved brick wall method, we investigate the thermodynamics of a black hole embedded in a spatially flat Friedmann–Robertson–Walker universe. We calculate the temperature and the entropy at every apparent horizon for arbitrary solution of the scale factor. We show that the temperature and entropy display a nontrivial behavior as functions of time. In the case of black holes immersed in a universe driven by phantom energy, we show that for specific ranges of the equation-of-state parameter and apparent horizons the entropy is compatible with the D-bound conjecture, and even the null, dominant and strong energy conditions are violated. In the case of accretion of phantom energy onto a black hole with small Hawking–Hayward quasi-local mass, we obtain an equation-of-state parameter in the range w ≤ -5/3, guaranteeing the validity of the generalized second law.

Lifshitz scalar, brick wall method, and generalized uncertainty principle in Hořava-Lifshitz gravity

Using the brick-wall method, we study statistical entropy for spherically symmetric black holes in Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity. In particular, a Lifshitz scalar field is considered in order to incorporate foliation-preserving diffeomorphism, which eventually gives a modified dispersion relation. Finally, we obtain the area law without the UV cutoff for $z>3$ and discuss some of the consequences in connection with the generalized uncertainty principle.

BOUND OF NONCOMMUTATIVITY PARAMETER BASED ON BLACK HOLE ENTROPY

We study the bound of the noncommutativity parameter in the noncommutative Schwarzschild black hole which is a solution of the noncommutative ISO(3, 1) Poincaré gauge group. The statistical entropy satisfying the area law in the brick wall method yields a cutoff relation which depends on the noncommutativity parameter. Requiring both the cutoff parameter and the noncommutativity parameter to be real, the noncommutativity parameter can be shown to be bounded as Θ > 8.4 × 10-2lp.

Entropy of Sonic Black Hole in the Brick Wall Approach

We calculate the free energy and the entropy of a massive scalar field in a sonic black hole by using the brick wall method. The leading order entropy turns out to be precisely in agreement with the entropy-area law.

ENTROPY OF THE FRW UNIVERSE BASED ON THE GENERALIZED UNCERTAINTY PRINCIPLE

The statistical entropy of the FRW universe described by time-dependent metric is newly calculated using the brick wall method based on the general uncertainty principle with the minimal length. We can determine the minimal length with the Planck scale to obtain the entropy proportional to the area of the cosmological apparent horizon.

State equations for massless spin fields in static spherical spacetime filled with quintessence

The entropy density, energy density, pressure and equation of state for the gases of massless particles with spin s ≤ 2 around the static spherical black hole with quintessence are investigated by using the brick-wall method. It is shown that the state equations for spin fields in curved spacetime do not take the same forms as that in flat spacetime and contain additional terms with spin dependence. Then the character of the terms and the effect of quintessence and spin on them are discussed.