Why have we Never Observed the Massless Charged Particle?

In this paper we try to explore the possible contact between quantum gravity and the least mass of a charged particle in de Sitter spacetime. The effect of Generalized Uncertainty Principle (GUP) on the thermodynamics of de Sitter spacetime is discussed in a heuristic manner. We find a maximal entropy/probability that corresponds to the absence of charge of a massless particle. Furthermore, the holographic principle provides a possible lower limit to the mass of a charged particle. PACS Numbers: 04.70.Dy, 04.70.-s, 98.80.Es.     

Spinor Field at the Phase Transition Point of Reissner-Nordström de Sitter Space

The radial parts of Dirac equation between the outer black hole horizon and the cosmological horizon are solved in Reissner-Nordström de Sitter (RNdS) space when it is at the phase transition point. We use an accurate polynomial approximation to approximate the modified tortoise coordinate \(\hat{r}_{*}\) in order to get the inverse function \(r=r(\hat{r}_{*})\) and the potential \(V(\hat{r}_{*})\). Then we use a quantum mechanical method to solve the wave equation numerically. We consider two cases, one is when the two horizons are lying close to each other, the other is when the two horizons are widely separated.     

Tunneling from a Quantum Black Hole

A quantum black hole has been presented by Kenmoku et al. (1998), and its surface gravity is divergent. We find that its tunneling probability is essentially different from Boltzmann distribution. It is interesting that two peaks appears in the spectrum when the black hole mass decreases close to Planck mass, which is different from black body radiation. PACS: 04.70.Dy     

The Kantowski-Sachs Space-Time in Loop Quantum Gravity

We extend the ideas introduced in the previous work to a more general space-time. In particular we consider the Kantowski-Sachs space time with space section with topology . In this way we want to study a general space time that we think to be the space time inside the horizon of a black hole. In this case the phase space is four dimensional and we simply apply the quantization procedure suggested by loop quantum gravity and based on an alternative to the Schroedinger representation introduced by H. Halvorson. Through this quantization procedure we show that the inverse of the volume density and the Schwarzschild curvature invariant are upper bounded and so the space time is singularity free. Also in this case we can extend dynamically the space time beyond the classical singularity. PACS number: 04.60.Pp, 04.70.Dy     

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. PACS: 04.70. Dy, 97.60.Lf     

The Scalar Field Equation in Schwarzschild–de Sitter Space

The scalar wave equation between the inner and the outer horizon in the Schwarzschild–de Sitter geometry is solved numerically, and the spatial variations of the field amplitude, as well as of the potential, are shown graphically. By generalizing the "tortoise" coordinate x known from Schwarzschild theory to the SdS system we first transfer the wave equation to a convenient form in which the potential V is written as a function of x. We then show how a useful "tangent" approximation can be introduced which leads to a simple, analytically invertible, relation between x and the radius r. We concentrate on two limiting cases. The first case is when the two horizons are close to each other, the so-called Nariai black hole, and the second case is when the horizons are far apart. Reflection and transmission coefficients are worked out on the basis of a replacement of the real barrier V(x) by a square barrier.     

Correction to Hawking Pure Thermal Spectrum of Stationary Kaluza-Klein Black Hole

Applying Parikh's quantum tunneling method, the tunneling characteristics of stationary Kaluza-Klein black hole is researched. The result shows that the tunneling rate across the event horizon of the black hole is relevant to the change of Bekenstein-Hawking entropy and the derived radiation spectrum deviates from pure thermal when the self-gravitation, energy conservation and angular momentum conservation are taken into consideration. Finally, we use the obtained results to reduce to stationary Kerr black hole and static Swarzschild black hole, and find that only ignoring the spectrum at higher energies the tunneling radiation spectrum is consistent with Hawking pure thermal one. PACS:97.60.Lf,04.70._s     

Hawking Radiation via Tunnelling from Black Holes by Using Eddington–Finkelstein Coordinates

In this paper, by using well-known Eddington–Finkelstein coordinates instead of Painlevè coordinates, we study the tunnelling effect of the black holes once again. As examples of the static and stationary black holes, we calculate the tunnelling rates of Schwarzschild and Kerr black holes. In addition, the result obtained by adopting Eddington–Finkelstein coordinates is in agreement with the Parikh’s and Zhang’s recent work which adopts the Painlevè coordinates. At last, we discuss carefully the condition that the coordinates system in which we study the tunnelling process should satisfy. In our opinion, the terms of the tunnelling effect are not as strict as ones in Parikh’s paper and could be softened properly. PACS: 04.70.Dy     

Effects of k-space orders on the time-intensity curves in dynamic contrast-enhanced magnetic resonance imaging of the breast based on simulation study

PurposeThis study aims to investigate the influence of time-intensity curves (TICs) on the shapes using a dynamic contrast-enhanced magnetic resonance imaging (MRI) study depending on the Cartesian and radial orders for benign and cancerous breast tumors.MethodsBased on kinetic curve parameters, the signal intensities of six concentration gradients comprising two benign and four cancer models were used. The study aimed to construct a dynamic simulated image by creating a digital phantom image according to the following steps: (1) creating a simple numerical phantom, (2) setting the signal intensity in the contrast area, (3) creating the k-space in each time phase, (4) extracting data from k-space in each time phase, (5) filling in the k-space and adding data to the k-space assembly, and (6) creating a magnitude image. The TICs of Cartesian (centric and sequential) and radial (full-length [RFL] and half-length [RHL]) orders were created and sigmoid curve fitting was performed to compare these curves. Maximum slope (MS, s⁻¹), width of the response (WOR, s), and primary signal response (PSR) were then calculated. Phase encode steps were set for 512 and 256.ResultsMS was significantly decreased by radial order in the cancer model. No change was observed in WOR in Cartesian order, whereas RFL and RHL orders increased in the cancer models. PSR increased remarkably in the radial orders of cancer models.The difference in the fill slope in radial orders was remarkable when the TIC was steeper compared with when it was gentle, especially RHL. In WOR, both radial RFL and RHL were well matched except for the one benign model, and the shape of radial TIC was similar to sequential order as compared to centric order in 256 steps.ConclusionThe effects of Cartesian and radial orders on the patterns of TICs in a dynamic contrast-enhanced MRI study of benign and cancerous breast tumors were revealed. Interestingly, the TIC gradient of radial orders became gentler, particularly in the breast cancer MRI.     

Trapping Horizons in Sultana-Dyer Space-Time

The Sultana-Dyer space-time is suggested as a model describing a black hole embedded in an expanding universe. Recently, its global structure is analyzed and the trapping horizons are shown. In the paper, by directly calculating theexpansions of the radial null vector fields normal to the space-like two-spheres foliating the trapping horizons, we find that the trapping horizon outside the event horizon in the Sultana-Dyer space-time is a past trapping horizon. Further, we find that the past trapping horizon is an outer, instantaneously degenerate or inner trapping horizon accordingly when the radial coordinate isless than, equal to or greater than some value.     

Tunneling Radiation of the Charged Particles for Charged Spherical Black Hole in VGM

Applying Parikh’s semi-classical tunneling method, Hawking radiation of charged massive particles via tunneling from charged spherical black hole in vacuum for Vector Graviton Metric theory (VGM) of gravitation is investigated. Because the derivation respects conservation of energy and charge, the tunneling rate of particles is relevant to the change of Bekenstein-Hawking entropy and the exact spectrum is not precisely thermal. The result employs an underlying unitary theory. PACS numbers: 04.70.-s, 97.60. Lf     

Influence of Burner Geometry on Heat Transfer Characteristics of Methane/Air Flame Impinging on Flat Surface

An experimental study has been conducted to find the heat transfer characteristics of methane/air flames impinging normally to a flat surface using different burner geometries. The burners used were of nozzle, tube, and orifice type each with a diameter of 10 mm. Due to different exit velocity profiles, the flame structures were different in each case. Because of nearly flat velocity profile, the flame spread was more in case of orifice and nozzle burners as compared to tube burner. Effects of varying the value of Reynolds number (600–2500), equivalence ratio (0.8–1.5) and dimensionless separation distance (0.7–8) on heat transfer characteristics on the flat plate have been investigated for the tube burner. Different flame shapes were observed for different impingement conditions. It has been observed that the heat transfer characteristics were intimately related to flame shapes. Heat transfer characteristics were discussed for the cases when the flame inner reaction cone was far away, just touched, and was intercepted by the plate. Negative heat fluxes at the stagnation point were observed when the inner reaction cone was intercepted by the plate due to impingement of cool un-burnt mixture directly on the surface. Different heat transfer characteristics were observed for different burner geometries with similar operating conditions. In case of tube burner, the maximum heat flux is around the stagnation point and decay is faster in the radial direction. In case of nozzle and orifice burner, the heat transfer distribution is more uniform over the surface.     

Entropy of Schwarzschild-de Sitter Black Hole with Extra Term Correction

The thermodynamical quantities are usually considered as the independent ones in the case of the existence of multi-horizons. Comparing the first laws for the event horizon and cosmological horizon of Schwarzschild-de Sitter space-time, we find them share the same values of mass, charge and cosmological constant, which might imply that there exists entanglement between the two horizons. Naturally we attempt to add an extra term, which contributed to the total entropy of the black hole. We recalculate the total entropy and the effective specific heat by taking the globally effective first law and find that they will be emanative when the two horizons approach to each other.     

Research on Hawking Radiation as Tunneling from Schwarzshild-anti-de Sitter Black Hole

After taking into account energy conservation and the particle’s self-gravitation interaction, Hawking radiation of the massive particle as tunneling from Schwarzshild-anti-de Sitter black hole is studied by using Parikh-Wilczek’s semi-classical quantum tunneling approach. Meanwhile, Hawking radiation as tunneling from the black hole is reexamined by developing Angheben–Nadalini–Vanzo–Zerbini (ANVZ) covariant method to cover energy conservation and the particle’s self-gravitation interaction. Both the results perfectly generalize those obtained by Parikh and Wilczek, and show that the tunneling rate is related to the change of Bekenstein-Hawking entropy, and the factual emission spectrum is not exactly thermal, but satisfies the underlying unitary theory. PACS: 04.70-s, 9760. Lf.     

Radiation Characteristics of Stationary Axisymmetric Sen Black Hole as Tunneling

Taking energy conservation and angular momentum conservation into account, the tunneling radiation characteristics of stationary axisymmetric Sen black hole is studied in this paper with the quantum tunneling method and the results show that the tunneling rate of particle at the event horizon of the black hole is relevant to Bekenstein–Hawking entropy and that the radiation spectrum is not strictly pure thermal. PACS: 04.70_S, 97.60.Lf     

Tunneling Radiation of a Torus-Like Black Hole in Anti-de Sitter Space-Time

An extension of the Parikh-Wilczek's semi-classical quantum tunneling method, the tunneling radiation of the charged particle from a torus-like black hole is investigated. Difference from the uncharged mass-less particle, the geodesics of the charged massive particle tunneling from the black hole is not light-like, but determined by the phase velocity. The derived result shows that the tunneling rate depends on the emitted particle's energy and electric charge, and takes the same functional form as uncharged particle. It proves also that the exact emission spectrum is not strictly pure thermal, but is consistent with the underlying unitary theory. PACS Numbers: 04.70.Dy, 97.60.Lf, 05.30.Ch.     

On Radial Schrödinger Equations in Curved Spaces and Their Spectra Through Nonlinear Constraints

Abstract

First, we determine the radial Schrödinger equation in D-dimensional curved spaces when central problems are considered. Second, we develop the so-called factorization method on the basis of supersymmetric arguments for solving such radial equations when D = 1, 2, 3-harmonic oscillator and D = 3-hydrogen atom physical interactions are studied in such spherical geometries. Comparisons with conventional methods are pointed out as well as with the corresponding results in flat spaces.     

Homotopic Classification of Yang–Mills Vacua Taking into Account Causality

Existence of θ-vacuum states in Yang–Mills theories defined over asymptotically flat space-times examined taking into account not only the topology but the complicated causal structure of these space-times, too. By a result of Galloway apparently causality makes all vacuum states, seen by a distant observer, homotopically equivalent making the introduction of θ-terms unnecessary. But a more careful analysis shows that certain twisted classical vacuum states survive even in this case eventually leading to the conclusion that the concept of “θ-vacua” is meaningful in the case of general Yang–Mills theories. We give a classification of these vacuum states based on Isham’s results showing that the Yang–Mills vacuum has the same complexity as in the flat Minkowskian case hence the general CP-problem is not more complicated than the well-known flat one. We also construct the θ vacua rigorously via geometric quantization. PACS numbers: 11.15, 11.30.E, 04.20.G, 04.70     

Quantum bound states around black holes

Quantum mechanics in the vicinity of black holes is a fascinating field of theoretical physics. It involves both general relativity and particle physics, opening new eras to establish the principles of unified theories. In this article, we show that quantum bound states with no classical equivalent – as can easily be seen at the dominant monopolar order – should be formed around black holes for massive scalar particles. We qualitatively investigate some important physical consequences, in particular for the Hawking evaporation mechanism and the associated greybody factors. PACS 04.62.+v; 04.70.Dy; 04.70-s     

Remark on state vector construction when flavor mixing exists

In the framework of quantum field theory, we consider the way to construct the one-particle state (with definite 3-momentum) when particle mixing exists, such as in the case of flavor-neutrino mixing. In the preceding report (Prog. Theor. Phys. 112, 901 (2004)), we have examined the structure of expectation values of the flavor neutrino charges (at time t) with respect to a neutrino-source state prepared at time t′ (earlier than t). When there is no mixing, each of various contributions to the expectation value is equal, in its dominant part, to the transition probability corresponding to the respective neutrino-production process. On the basis of the assumption that such an equality holds also in the mixing case, we can find an appropriate form of one-flavor-neutrino state with 3-momentum and helicity. Along the same way, we examine the boson case when flavor mixing exists. We give remarks on the relation and difference between the ordinary and the present approaches to flavor oscillation. The text was submitted by the authors in English.