International Journal of Modern Physics D

We take Mach's principle to mean that the local properties of a test particle should depend on the global properties of the geometry. Using a complex wave-like metric and an appropriate redefinition of the energy-momentum tensor, we show this to be possible in principle within the context of general relativity. We outline implications for higher-dimensional theories of gravity.

We consider a version of Kaluza–Klein theory where the cylinder condition is not imposed. The metric is allowed to have explicit dependence on the "extra" coordinate(s). This is the usual scenario in brane-world and space-time-matter theories. We extend the usual discussion by considering five-dimensional metrics with off-diagonal terms. We replace the condition of cylindricity by the requirement that physics in four-dimensional space-time should remain invariant under changes of coordinates in the five-dimensional bulk. This invariance does not eliminate physical effects from the extra dimension but separates them from spurious geometrical ones. We use the appropriate splitting technique to construct the most general induced energy-momentum tensor, compatible with the required invariance. It generalizes all previous results in the literature. In addition, we find two four-vectors, and , induced by off-diagonal metrics, that separately satisfy the usual equation of continuity in 4D. These vectors appear as source-terms in equations that closely resemble the ones of electromagnetism. These are Maxwell-like equations for an antisymmetric tensor that generalizes the usual electromagnetic one. This generalization is not an assumption, but follows naturally from the dimensional reduction. Thus, if could be identified with the electromagnetic tensor, then the theory would predict the existence of classical magnetic charge and current. The splitting formalism used allows us to construct 4D physical quantities from five-dimensional ones, in a way that is independent from how we choose our space-time coordinates from those of the bulk.

Using the method of quantum statistics, we directly derive the partition functions of bosonic and fermionic field in Kerr black hole with axial symmetry. Then via the improved brick-wall method for membrane model, we show that the entropy of the bosonic and fermionic field in the black hole is proportional to the area of the horizon. In our result, the stripped term and the divergent logarithmic term no longer exist. Hence the problem that the state density is divergent around the horizon doesn't exist. We also give the influence of the spining degeneracy of particles on the entropy of black hole. We offer a new simple and direct way of calculating the entropy of different complicated black holes.

A cosmological model with perfect fluid and self-interacting quintessence field is considered in the framework of the spatially flat Friedmann–Robertson–Walker (FRW) geometry. By assuming that all physical quantities depend on the volume scale factor of the Universe, the general solution of the gravitational field equations can be expressed in an exact parametric form, with the volume taken as the parameter, and with the quintessence field as a free parameter. With an appropriate choice of the scalar field a class of exact parametric solutions is obtained, with an exponential type scalar field potential fixed via the gravitational field equations. The general physical behavior of the model is consistent with the recent cosmological scenario favored by supernova type Ia observations, indicating an accelerated expansion of the Universe.

We consider dilatonic brane-world models with a non-minimal coupling between dilaton and usual matter on the brane. We demonstrate that the variation of fundamental constants on the brane due to such interaction can lead to strong restrictions on model parameters. In particular, the experimental bounds on the variation of the fine structure constant rule out non-minimal dilatonic models with a Liouville-type coupling potential f(φ) = exp(bφ) where .

The supersymmetry transformations under which the four-dimensional massless Dirac equation for a two-component, spin-1/2 fermion field ψ (the Weyl equation) remains invariant were obtained by Volkov and Akulov, who used the result to construct the action S = a^-1 ∫ |W| d⁴x in terms of the energy-momentum tensor , where W_ij = δ_ij + aT_ij and a is a constant. Here, we show, in the approximation , that the terms linear, quadratic and quartic in T_ij are contained in the bosonic sector of the dimensionally reduced, heterotic superstring action, including higher-derivative gravitational terms up to order ℛ⁴. By comparison of coefficients, we derive the value B_r ≈ 3.5 for the radius squared of the internal space in units of the Regge slope parameter α′, slightly greater than the Hagedorn radius squared . The cubic terms are also discussed.

We utilise a form for the Hubble parameter to generate a number of solutions to the Einstein field equations with variable cosmological constant and variable gravitational constant in the presence of a bulk viscous fluid. The Hubble law utilised yields a constant value for the deceleration parameter. A new class of solutions is presented in the Robertson–Walker spacetimes. The coefficient of bulk viscosity is assumed to be a power function of the mass density. For a class of solutions, the deceleration parameter is negative which is consistent with the supernovae Ia observations.

Primordial black hole formation has been studied using an inflaton field with a variable cosmological term as the potential.

The transformation laws for the electric and magnetic parts of the electromagnetic 2-form and the Weyl tensor under a boost are studied using the complex vector approach, which shows the close analogy between the two cases. For a nonnull electromagnetic field, one can always find an observer who sees parallel electric and magnetic fields (vanishing Poynting vector) and also sees a minimum electromagnetic energy density (and minimum electric and magnetic field magnitudes) compared to other observers. For Weyl fields of all Petrov types except III, and boosts along certain directions of the Weyl principal tetrad, the more complicated Weyl transformation closely mimics the electromagnetic boost transformation, allowing one to extend the electromagnetic results directly to the families of boosts along those directions. In particular for black hole spacetimes, the alignment of the electric and magnetic parts of the Weyl tensor (vanishing super-Poynting vector) leads to minimal gravitational super-energy as seen by the Carter observer within the family of all circularly rotating observers at each spacetime point outside the horizon.

A non-perturbative canonical quantization of the Gowdy T³ polarized models is considered here. This approach profits from the equivalence between the symmetry reduced model and 2 + 1 gravity coupled to a massless real scalar field. The system is partially gauge fixed and a choice of internal time is made, for which the true degrees of freedom of the model reduce to a massless free scalar field propagating on a two-dimensional expanding torus. It is shown that the symplectic transformation that determines the classical dynamics cannot be unitarily implemented on the corresponding Hilbert space of quantum states. The implications of this result for both the quantization of fields on curved manifolds and other physically relevant questions regarding the initial singularity are discussed.

We find analytical solutions describing the collapse of an infinitely long cylindrical shell of counter-rotating dust. We show that — for the classes of solutions discussed herein — from regular initial data a curvature singularity inevitably develops, and no apparent horizons form, thus in accord with the spirit of the hoop conjecture.

A regularization procedure, that allows one to relate singularities of curvature to those of the Einstein tensor without some of the shortcomings of previous approaches, is proposed. This regularization is obtained by requiring that (i) the density , associated to the Einstein tensor of the regularized metric, rather than the Einstein tensor itself, be a distribution and (ii) the regularized metric be a continuous metric with a discontinuous extrinsic curvature across a non-null hypersurface of codimension one. In this paper, the curvature and Einstein tensors of the geometries associated to point sources in the (2 + 1)-dimensional gravity and the Schwarzschild spacetime are considered. In both examples the regularized metrics are continuous regular metrics, as defined by Geroch and Traschen, with well defined distributional curvature tensors at all the intermediate steps of the calculation. The limit in which the support of these curvature tensors tends to the singular region of the original spacetime is studied and the results are contrasted with the ones obtained in previous works.

Exact solutions are obtained for an inhomogeneous cosmological model in normal gauge for Lyra's geometry. Some properties of the model have also been discussed.

We study the effect of the inclusion of muons and the muon neutrinos on the phase transition from nuclear to quark matter in a magnetized proto-neutron star and compare our results with those obtained by us without the muons. We find that the inclusion of muons changes slightly the nuclear density at which transition occurs. However the dependence of this transition density on various chemical potentials, temperature and the magnetic field remains quantitatively the same.