Brick-wall Model Research Articles

Entropy of the scalar field in general accelerating non-stationary black holes with electric charge and magnetic charge

Using tortoise coordinate transformation, Klein-Gordon field equation is simplified and thermal radiation temperature near the event horizon is obtained. Meanwhile, adopting thin film brick-wall model and regulating the cut-off parameter and the thin film's thickness properly, the entropy of thin film near the event horizon is acquired. The results show that the entropy of the black hole is proportional to the area of the event horizon.

WKB APPROXIMATION AND EFFECT OF SPIN ON THE BLACK HOLE ENTROPY

The black hole entropy due to spin fields are calculated by using brick-wall model. The appearance of the logarithmic terms is demonstrated and we specially deal with the subleading logarithmic term which exists for any spin fields. It is shown that the subleading logarithmic term is related to the use of WKB approximation but it usually includes not only a quadratic term and a linear term of the spin but also a zero-power term of the spin.

Entropy of a charged black hole in two dimensions without cutoff

By introducing the generalized uncertainty principle (GUP) on quantum density states, we obtain a consistent entropy of a scalar field on the $(1+1)$-dimensional Maxwell-dilaton background without an artificial cutoff in contrast to the results of the brick wall model, which depends on the choice of the Hawking temperature for the extremal case.

Approximation in Thin Film Brick-Wall Model

The thin film brick-wall model is an important method on calculating the entropy of the non-static black hole. But we can see in this paper that the approximation used in the thin film brick-wall model is a rate of two infinitesimal parameters in fact. in this paper, we make an exact calculation of the approximation term and give the solution in the Schwarzschild black hole space-time.

Entropy of BTZ black strings in the brick-wall approach

During the last few years, exact solutions describing black holes bound to a 2-brane in a four-dimensional anti-de Sitter bulk have been constructed. In situations where there is a negative cosmological constant on the brane for large masses, these solutions are exactly the rotating Banados–Teitleboim–Zanelli (BTZ) black holes on the brane and, in fact, describe rotating BTZ black strings in the bulk. We evaluate the canonical entropy of a free and massless scalar field (at the Hawking temperature) around the rotating BTZ black string using the brick-wall model. We explicitly show that the Bekenstein–Hawking ‘area’ law is satisfied both on the brane and in the bulk.

Fermion entropy of non-uniformly rectilinearly accelerating black hole with electric and magnetic charges

Using the thin film brick-wall model, we calculate the fermion entropy on event horizon and the surface density of the entropy on the Rindler Horizon to a rectilinearly accelerating non-stationary black hole with electric and magnetic charges. The conclusion that black hole entropy is proportional to its area can still be applied by regulating the cut-off factor ɛ and the film's thickness δ , which are time dependent.

The generalized uncertainty relation and Dirac field entropy of black hole with an internal global monopole

The generalized uncertainty relation is considered in the new equation of state density. Using the WKB approximation, Dirac field entropy of the horizon of the black hole with an internal global monopole is calculated directly. The result shows that the black hole entropy is proportional to the horizon area, which brings to light the relationship between the black hole entropy and the entropy of quantum state near the event horizon. The difference from the brick-wall model is that the present result is convergent without any cutoff. It is indicated that this method can be used to calculate the entropy of the scale field of black hole, and it can be extended to calculate the entropy of Dirac field.

Entropy of Dirac field in a rectilinearly nonuniformly accelerating Kinnersley black hole

Using the Tortoise coordinate transformation and the Dirac field equation near the event horizon, the Hawking temperature of Kinnersley black hole is obtained. Meanwhile, adopting thin film brick-wall model, the entropy of Kinnersley black hole is calculated. The entropy near the event horizon is shown to be the entropy of black hole by regulating the cut-off parameter and the thin film's thickness properly. The results show that the entropy of the black hole is proportional to the area of the event horizon.

Generalized model for IGC growth in aluminum alloys

A generalized brick wall model is developed to describe intergranular corrosion in Equi-axed AA7178-T6 and Wingskin AA7178-T6 aluminum alloys. The intergranular corrosion rate is highly related to grain size and shape. High strength aluminum alloys are often elongated and anisotropic, with the fastest nominal IGC growth rate in the longitudinal direction (L) or long transverse direction (T) and the slowest in the short transverse direction (S). We propose a three-way intersection model and use it to simulate the corrosion kinetics for each direction. With a proper combination of model parameters, the generalized IGC model provides a good fit to experimental data developed by the foil penetration technique.

Logarithmic terms in brick wall model

Abstract We clarify the relation between black hole entropy and quantum field spin. Starting from the Newman–Penrose formalism, we derive the Teukolsky-type master equation governing massless fields of arbitrary spin s ⩽ 2 in the Kerr–Newman–de Sitter spacetime. Then using the 't Hooft's brick wall model, we calculate the entropy of the black hole due to the quantum fields by the WKB approximation on the Teukolsky-type master equation. In particular, we carefully deal with the logarithmic term contribution to the entropy. It is shown that the term not only depends on the characteristics of the metric and the quadratic term of quantum field spin but also on the linear term of quantum field spin. This is very different from the result obtained earlier. All results of the present work are valid for the Schwarzschild, Reissner–Nordstrom, Kerr, Kerr–Newman, and de Sitter spacetime background, or any combination of these.

Quantum entropy of Dirac fields in black holes

We use the brick-wall model to study the quantum entropy of the Dirac field in a static black hole with a global monopole or a cosmic string. We show that the entropy of the Dirac field contains a quadratically divergent term and two logarithmically divergent ones and it is not proportional to the entropy of the scalar field. The contribution of the logarithmic term to the entropy depends on the black-hole characteristics and is always negative.

The Free Energy and Entropy of Schwarzschild Black Hole Due to Scalar Field

Using the thin film brick-wall model,taking into account the effect of the generalized uncertainty principle on the equation of the density of the states, we calculate the free energy and entropy of schwarzschild black hole due to scalar field, we obtain the entropy proportional to the event horizon area without cutoff. This implies that quantum theory of gravity can remove the divergence of the state density on the event horizon and avoid the cutoff in the original brick-wall model, these results also mean that the thin film brick-wall model is universal.

Quantum Entropy of Spin Fields in the Schwarzschild-Anti-de Sitter Black Hole with a Global Monopole

The quantum entropies of gravitational, electromagnetic, neutrino and scalar fields in the static Schwarzschild-anti-de Sitter black hole with a global monopole are investigated by using the brick-wall model. The quantum entropy contain two parts: One is quadratically divergent term which takes a geometric character; the other is spin-dependent, logarithmically divergent terms. The whole expression of the entropy of a spin field does not take the form of the scalar field.

Brick Wall Model and the Spectrum of a Schwarzschild BlackHole

The quantum entropy of a scalar field near a Schwarzschild black hole isinvestigated by employing the brick-wall model in the grand canonicalensemble. A positive chemical potential is introduced if the cutoff isset to be of order of the Planck length. We also discuss the relationbetween the chemical potential and the mass quantum of the black hole.

Erratum: Entropy of a Kerr-de Sitter black hole due to arbitrary spin fields [Phys. Rev. D69, 044019 (2004)

The Newman-Penrose formalism is used to derive the Teukolsky master equations controlling massless scalar, neutrino, electromagnetic, gravitino, and gravitational field perturbations of the Kerr-de Sitter spacetime. Then the quantum entropy of a non-extreme Kerr-de Sitter black hole due to arbitrary spin fields is calculated by the improved thin-layer brick wall model. It is shown that the subleading order contribution to the entropy is dependent on the square of the spins of particles and that of the specific angular momentum of black holes as well as the cosmological constant. The logarithmic correction of the spins of particles to the entropy relies on the rotation of the black hole and the effect of the cosmological constant.

Quantum entropy of Dirac field in toroidal black hole

The quantum entropy of Dirac field in toroidal black hole is considered and the effects of the spins of the Dirac particles on the entropy are investigated using brick-wall model. It is shown that the quantum entropy has both linearly and logarithmically divergent terms and it has the different structure from that of the black hole. It is also shown that the contribution of the subleading logarithmic term which relates to the spins of the Dirac particles are always positive.

Entanglement entropy of the Gibbons-Maeda dilaton black hole

By using the entanglement entropy method, in the Gibbons-Maeda(G-M) dilaton space-time, the statistical entropy of the quantum field in a thin film is calculated and the Bekenstein-Hawking entropy of the G-M dilaton black hole is obtained.Here, the quantum field is entangled with the quantum states in the black hole and the thin film sticks to the event horizon from outskirt of the black hole.Taking into account the effect of the generalized uncertainty principle on the quantum state density, the difficulty of the divergence of the state density near the event horizon in the brick-wall model is removed.Calculating the statistical entropy of the degrees of freedom entangling to the quantum states in the black hole in the quantum field outside the brick-wall and comparing the result to the entropy from the degrees of freedom inside brick-wall, we see that the two results are consistent but the latter may embody preferably the essence of black hole entropy.Using the residue theorem, the integration difficulty in he calculation is overcome and the result of the paper is founded quantitatively. These calculation and discussion imply that the high density quantum states near the event horizon are strongly correlated with the quantum states in black hole and the ultraviolet cut-off in the brick-wall model is not reasonable. The quantization of gravity field should be considered in the high energy quantum field near the event horizon and the ultraviolet cut-off is not necessary. In the quantum field inside and outside the brick-wall, the degrees of freedom contributing to the black hole entropy are just those correlating with the degrees of freedom in the black hole.

Quantum entropy of cylindrical black hole in Anti-de Sitter space-time

By using the brick-wall model, the quantum entropy of a cylindrical black hole in Anti-de Sitter space-time arising from the massless Dirac field is discussed. It is shown that the quantum entropy has both linear and logarithmical divergences if the usual contribution from the vacuum surrounding the system is ignored, and the whole expression does not take the form of the scalar one. Both the whole logarithmic term and the subleading logarithmic term which relates to the spins of the Dirac particles are always positive.

Grain boundary effects on dielectric, infrared and Raman response of SrTiO 3 nanograin ceramics

Dielectric, infrared reflectivity and Raman measurements were carried out on dense undoped SrTiO 3 ceramic with the average grain size of 150 nm processed by spark-plasma sintering. The results were compared with our earlier data on conventional ceramics (grain size 1500 nm), see Petzelt et al., Phys. Rev. B 2001, 64, 184111, and on single crystals. Permittivity is dramatically reduced at low temperatures, the soft mode correspondingly stiffened and in Raman spectra the forbidden infrared modes are more pronounced compared to conventional ceramics. All the effects can be accounted for by the existence of polar dead layers with smaller permittivity at grain boundaries. Two models are suggested to explain the data quantitatively. The first model assumes that the dead layer is caused by grain-boundary dipole moment, which penetrates into the grain bulk with the polarization correlation length. Its estimate, using the soft-phonon branch curvature from inelastic neutron data and Landau theory, yields 1.2 nm at 120 K and 5.6 nm at 5 K. Fitting the data with brick-wall model to this dead-layer thickness required also temperature dependence of its permittivity ( ɛ ∼12 at 120 K and ∼56 at 5 K). Comparably good fit of both ceramics can be obtained with temperature-independent dead-layer parameters. The latter model is supported by strongly reduced local refractive index at room temperature in the grain-boundary region (von Benthem et al., Phys. Rev. Lett. 2004, 93, 227201).

Entropy of Dirac Field in Non-stationary and Slowly ChangingReissner–Nordström Black Hole**The project supported by NationalNatural Science Foundation of China under Grant No. 10347008

Using the thin film brick-wall model and WKBapproximation, the entropy of the Dirac field in the non-stationary andslowly changing Reissner-Nordström (R-N) black hole is calculated. Theresult shows that the entropy of the R-N black hole is still proportional toits surface area if we choose proper cut-off.