The Analytical Solution of Charged Black Hole and Calculation of Quantities (<Emphasis Type="Italic">T</Emphasis>,<Emphasis Type="Italic">s</Emphasis>,<Emphasis Type="Italic">f</Emphasis>)

One of the most remarkable features of black hole is the connection between properties of the classical solutions and thermodynamics. We include the electric and magnetic charges and this lead us to resolve Einstein equations. We obtain thermodynamic properties, such as temperature, entropy density and speed of sound with analytical solution. In that case we characterize equation of state in to V(φ) language.     

Lovelock tensor as generalized Einstein tensor

We show that the splitting feature of the Einstein tensor, as the first term of the Lovelock tensor, into two parts, namely the Ricci tensor and the term proportional to the curvature scalar, with the trace relation between them is a common feature of any other homogeneous terms in the Lovelock tensor. Motivated by the principle of general invariance, we find that this property can be generalized, with the aid of a generalized trace operator which we define, for any inhomogeneous Euler–Lagrange expression that can be spanned linearly in terms of homogeneous tensors. Then, through an application of this generalized trace operator, we demonstrate that the Lovelock tensor analogizes the mathematical form of the Einstein tensor, hence, it represents a generalized Einstein tensor. Finally, we apply this technique to the scalar Gauss–Bonnet gravity as an another version of string–inspired gravity. This work was partially supported by a grant from the MSRT/Iran.     

Einstein's First Steps Toward General Relativity: Gedanken Experiments and Axiomatics

Jahrbuch paper is an extraordinary document because it contains his first steps toward generalizing the 1905 relativity theory to include gravitation. Ignoring the apparent experimental disconfirmation of the 1905 relativity theory and his unsuccessful attempts to generalize the mass-energy equivalence, Einstein boldly raises the mass-energy equivalence to an axiom, invokes equality between gravitational and inertial masses, and then postulates the equivalence between a uniform gravitational field and an oppositely directed constant acceleration, the equivalence principle. How did this come about? What is at issue is scientific creativity. This necessitates broadening historical analysis to include aspects of cognitive science such as the role of visual imagery in Einstein's thinking, and the relation between conscious and unconscious modes of thought in problem solving. This method reveals the catalysts that sparked a Gedanken experiment that occurred to Einstein while working on the Jahrbuch paper. A mental model is presented to further explore Einstein's profound scientific discovery.     

Theoretical Analysis of the Einstein Relation in n-Channel Inversion Layers on A3IIB2V Semiconductors under Magnetic Quantization

We have investigated the Einstein relation in n-channel inversion layers on A₃^IIB₂^V semiconductors at low temperatures on the basis of a newly derived dispersion relation of the carriers under arbitrary magnetic quantization for the general case which occurs from the consideration of the anisotropies of the band parameters within the frame work of k · p formalism. It is found by incorporating both the effects of electron spin and broadening of Landau levels, using n-Cd₃As₂ as an example, that the theoretical formulation is in qualitative agreement with the suggested experimental method of determining the Einstein relation in degenerate semiconductors having arbitrary dispersion law. In addition, the corresponding well-known results for bulk specimens of two band Kane model both in the presence and absence of magnetic quantization, are also obtained from the generalized expressions as special cases.     

Ultrarelativistic Bose–Einstein gas on Lorentz symmetry violation

In this paper, we study the effects of Lorentz Symmetry Breaking on the thermodynamic properties of ideal gases. Inspired by the dispersion relation coming from the Carroll–Field–Jackiw model for Electrodynamics with Lorentz and CPT violation term, we compute the thermodynamics quantities for a Boltzmann, Fermi–Dirac and Bose–Einstein distributions. Two regimes are analyzed: the large and the small Lorentz violation. In the first case, we show that the topological mass induced by the Chern–Simons term behaves as a chemical potential. For Bose–Einstein gases, a condensation in both regimes can be found.     

Thermal Equilibrium Between Radiation and Matter

In 1916, Einstein rederived the blackbody radiation law of Planck that originated the idea of quantized energy one hundred years ago. For this purpose, Einstein introduced the concept of transition probability, which had a profound influence on the development of quantum theory. In this article, we adopt Einstein's assumptions with two exceptions and seek the statistical condition for the thermal equilibrium of matter without referring to the inner details of either statistical thermodynamics or quantum theory. It is shown that the conditions of thermodynamic equilibrium of electromagnetic radiation and the energy balance of thermal radiation by the matter, between any of its two energy-states, not only result in Planck's radiation law and the Bohr frequency condition, but they remarkably yield the law of the statistical thermal equilibrium of matter: the Maxwell–Boltzmann distribution. Since the transition probabilities of the modern quantum theory of radiation coincide with their definition in Einstein's theory of blackbody radiation, the presented deduction of the Maxwell–Boltzmann distribution is equally valid within the bounds of modern quantum theory. Consequently, within the framework of the fundamental assumptions, the Maxwell–Boltzmann distribution of energy-states is not only a sufficient, but a necessary condition for thermal equilibrium between the matter and radiation.     

Singularities in general relativity

The problem of singularities is examined from the stand-point of a local observer. A singularity is defined as a state with an infinite proper rest mass density. The approach consists of three steps: (i) The complete system of equations describing a non-symmetric motion of a perfect fluid under assumption of adiabatic thermodynamic processes and of no release of nuclear energy is reduced to six Einstein field equations and their four first integrals for six remaining unknown componentsgik. (ii) A differential relation for the behavior of the rest mass density is deduced. It shows that any inhomogeneity and anisotropy in the distribution and motion of a non-rotating ideal fluid accelerates collapse to a singularity which will be reached in a finite proper time. Collapse is also inevitable in a rotating fluid in the case of extremely high pressure when the relativistic limit of the equation of state must be applied. In the case of a lower or zero pressure the relation does not give an unambiguous answer if the matter is rotating. (iii) The influence of rotation on the motion of an incoherent matter is investigated. Some qualitative arguments are given for a possible existence of a narrow class of singularity-free solutions of Einstein equations. Assuming rotational symmetry the Einstein partial differential equations together with their first integrals are reduced to a system of simultaneous ordinary differential equations suitable for numerical integration. Without integrating this system the existence of the class of singularity-free solutions is confirmed and exactly delimited. These solutions, representing a new general relativistic effect, are, however, of no importance for the application in cosmology or astrophysics. It is proved that in all the other cases interesting from the point of view of application the occurrence of a point singularity in incoherent matter with a rotational symmetry is inevitable even if the rotation is present.Read on 15 May 1970 at the Gwatt Seminar on the Bearings of Topology upon General Relativity     

Gravitation,thermodynamics, and the bound on viscosity

The anti-de Sitter/conformal field theory (AdS/CFT) correspondence implies that small perturbations of a black hole correspond to small deviations from thermodynamic equilibrium in a dual field theory. For gauge theories with an Einstein gravity dual, the AdS/CFT correspondence predicts a universal value for the ratio of the shear viscosity to the entropy density, η/s = 1/4π. It was conjectured recently that all fluids conform to the lower bound η/s ≥ 1/4π. This conjectured bound has been the focus of much recent attention. However, despite the flurry of research in this field we still lack a proof for the general validity of the bound. In this essay we show that this mysterious bound is actually a direct outcome of the interplay between gravity, quantum theory, and thermodynamics.     

Normal Transport Properties in a Metastable Stationary State for a Classical Particle Coupled to a Non-Ohmic Bath

We study the Hamiltonian motion of an ensemble of unconfined classical particles driven by an external field F through a translationally-invariant, thermal array of monochromatic Einstein oscillators. The system does not sustain a stationary state, because the oscillators cannot effectively absorb the energy of high speed particles. We nonetheless show that the system has at all positive temperatures a well-defined low-field mobility μ over macroscopic time scales of order exp (c/F), during which it finds itself in a metastable stationary state. The mobility is independent of F at low fields, and related to the zero-field diffusion constant D through the Einstein relation. The system therefore exhibits normal transport even though the bath obviously has a discrete frequency spectrum (it is simply monochromatic) and is therefore highly non-Ohmic. Such features are usually associated with anomalous transport properties.     

On the diffusivity-mobility ratio of the carriers in n-channel inversion layers on ternaryChalcopyrite semiconductors

An attempt is made to study the Einstein relations for the diffusivity-mobility ratios of the carriers in n-channel inversion layers on ternary chalcopyrite semiconductors under both weak and strong electric field limits, taking n-channel inversion layers on CdGeAs₂ as an example. It is found, on the basis of newly derived 2D E-k_s dispersion relations of the conduction electrons for both the limits by considering the various types of anisotropies in the energy band, that the ratios increase with increasing surface electric fields for both the limits and the theoretical results are in qualitative agreement with the suggested experimental method of determining the Einstein relation in degenerate semiconductors having arbitrary dispersion law. The corresponding well-known results for isotropic twoband Kane model are also obtained from the expressions derived.     

On the Einstein Relation in Ternary Semiconductors in the Presence of Crossed Electric and Magnetic Fields

We investigate theoretically the Einstein relation for the diffusivity-mobility ratio of the electrons in ternary semiconductors at low temperatures in the presence of crossed electric and quantizing magnetic fields on the basis of threeband Kane model. It is found, taking n-Hg_1-xCd_xTe as an example, that DMR shows an oscillatory magnetic field dependence. Besides, the DMR increase both with increasing electron concentration and decreasing alloy composition respectively.     

Plane symmetric self-gravitating fluids with pressure equal to energy density

Solutions of the Cauchy problem associated with the Einstein field equations which satisfy general initial conditions are obtained under the assumptions that (1) the source of the gravitational field is a perfect fluid with pressure,p, equal to energy density,w, and (2) the space-time admits the three parameter group of motions of the Euclidean plane, that is, the space-time is plane symmetric. The results apply to the situation where the source of the gravitational field is a massless scalar field since such a source has the same stress-energy tensor as an irrotational fluid withp=w. The relation between characteristic coordinates and comoving ones is discussed and used to interpret a number of special solutions. A solution involving a shock wave is discussed.     

Thermodynamic consistency for nuclear matter calculations

We investigate the relation between the binding energy and the Fermi energy and between different expressions for the pressure in cold nuclear matter. For a self-consistent calculation based on a Φ derivable T-matrix approximation with off-shell propagators, the thermodynamic relations are well satisfied unlike for a G-matrix or a T-matrix approach using quasi-particle propagators in the ladder diagrams. Received: 8 February 2001 / Accepted: 11 June 2001     

Models of the universe

In this paper a theory of models of the universe is proposed. We refer to such models ascosmological models, where a cosmological model is defined as an Einstein-inextendible Einstein spacetime. A cosmological model isabsolute if it is a Lorentz-inextendible Einstein spacetime,predictive if it is globally hyperbolic, andnon-predictive if it is nonglobally-hyperbolic. We discuss several features of these models in the study of cosmology. As an example, any compact Einstein spacetime is always a non-predictive absolute cosmological model, whereas a noncompact complete Einstein spacetime is an absolute cosmological model which may be either predictive or non-predictive. We discuss the important role played by maximal Einstein spacetimes. In particular, we examine the possible proper Lorentz-extensions of such spacetimes, and show that a spatially compact maximal Einstein spacetime is exclusively either a predictive cosmological model or a proper sub-spacetime of a non-predictive cosmological model. Provided that the Strong Cosmic Censorship conjecture is true, a generic spatially compact maximal Einstein spacetime must be a predictive cosmological model. It isconjectured that the Strong Cosmic Censorship conjecture isnot true, and converting a vice to a virtue it is argued that the failure of the Strong Cosmic Censorship conjecture would point to what may be general relativity's greatest prediction of all, namely,that general relativity predicts that general relativity cannot predict the entire history of the universe.     

Gradient conformal killing vectors and exact solutions

We establish a connection between conformally related Einstein spaces and conformai killing vectors (CKV). We begin with the conformal map and prove that (a) under the conformal mapping¯g _ik=^–2g_ik, the necessary and sufficient condition for the tracefree part of the Ricci tensor (S _ik=R_ik–(R/4)g _ik) to remain invariant is that _i is a CKV ofg _ik, and (b) the most general form for for conformally flat Einstein space, which is the de Sitter space, is composed of three terms each of which alone represents a flat space. The existence of gradient CKV (GCKV) is examined in relation to vacuum and perfect fluid spacetimes.     

Neighbours of Einstein's equations: Connections and curvatures

Once the action for Einstein's equations is rewritten as a functional of anSO(3, ) connection and a conformal factor of the metric, it admits a family of neighbours having the same number of degrees of freedom and a precisely defined metric tensor. This paper analyzes the relation between the Riemann tensor of that metric and the curvature tensor of theSO(3) connection. The relation is very complicated in general. The Einstein case is distinguished by the fact that two naturalSO(3) metrics on theGL(3) fibres coincide. In the general case the theory is bimetric on the fibres.     

A Dicke Type Model for Equilibrium BEC Superradiance

We study the effect of electromagnetic radiation on the condensate of a Bose gas. In an earlier paper we considered the problem for two simple models showing the cooperative effect between Bose–Einstein condensation and superradiance. In this paper we formalize the model suggested by Ketterle et al. in which the Bose condensate particles have a two level structure. We present a soluble microscopic Dicke type model describing a thermodynamically stable system. We find the equilibrium states of the system and compute the thermodynamic functions giving explicit formulæ expressing the cooperative effect between Bose–Einstein condensation and superradiance.     

Relativistic Point Dynamics and Einstein Formula as a Property of Localized Solutions of a Nonlinear Klein-Gordon Equation

Einstein’s relation E = Mc ² between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems which do not accelerate. By contrast, the Newtonian approach to the mass is based on an accelerated motion. We study here a particular neoclassical field model of a particle governed by a nonlinear Klein-Gordon (KG) field equation. We prove that if a solution to the nonlinear KG equation and its energy density concentrate at a trajectory, then this trajectory and the energy must satisfy the relativistic version of Newton’s law with the mass satisfying Einstein’s relation. Therefore the internal energy of a localized wave affects its acceleration in an external field as the inertial mass does in Newtonian mechanics. We demonstrate that the “concentration” assumptions hold for a wide class of rectilinear accelerating motions.     

125m Te (109.3 keV) stimulated emission and gamma lasers

Summary Proceeding from the drastic discrepancy between experimental data and theory, we show (contrary to other authors) that the relations between the Einstein's coefficients are true for transitions from any of the excited levels and theground state of the quantum system only. The relations connecting those coefficients are derived for transitions betweenany two states; the corresponding cross-sections are calculated and it is shown (contrary to other authors) that the stimulated emission cross-section may be large enough for the creation of gamma lasers. The new relation for Einstein's coefficients (and the corresponding cross-sections) are fundamentally different from those known so far (74 years after Einstein). The results are compared with experiment and the coincidence is very good. These investigations can lead to progress in the study of physical processes in star atmospheres. The author of this paper has agreed to not receive the proofs for correction.     

Diffusion and Einstein relation for a massive particle in a one-dimensional free fas: Numerical evidence

A computer simulation is used to investigate the motion of a marked particle of massM in a free gas of particles with massm=1, for large times. Previous results seem to indicate a non-Wiener behavior for the rescaled trajectory whenMm. The results reported here, with better statistics, are compatible with the Wiener hypothesis. The Einstein relation between mobility and diffusion coefficient is also investigated. The results indicate that it holds both forM=m and forMm.