International Journal of Modern Physics D

The problem of topology change description in gravitation theory is analyzed in details. It is pointed out that in standard four-dimensional theories the topology of space may be considered as a particular case of the boundary conditions (or constraints). Therefore to describe the changes of space or spacetime topology the number of the coordinate maps, the order of their junction and the junction conditions must be converted from the class of constraints or boundary data into the class of dynamical variables. In the framework of four-dimensional theory this problem cannot be solved in its general formulation, while it is possible to describe the changes of three-space topology on the given four-manifold. In the framework of multidimensional theories the space (and spacetime) may be considered as the embedded manifolds. It gives the real possibilities both for the dynamical description of the topology of space or spacetime and for the description of the topology changes of general kind.

We report new calculations of the physical properties of a quark–diquark plasma. A vacuum contribution is taken into account and is responsible for the appearance of a stable state at zero pressure and at a baryon density of about 2.2 times the nuclear matter density in this model. The resulting equation of state was used to integrate numerically the Tolman–Oppenheimer–Volkoff equations. The mass-radius relationship has been derived from a series of equilibrium configurations constituted by a mixture of quarks and diquarks. These stellar models, which are representative of a whole class, may be helpful to understand the possible compactness of the X-ray source Her X-1 and related objects.

We study the general properties of compact objects made up of strange matter in the framework of a new equation of state in which the quark masses are parametrized as functions of the baryon density, so that they are heavy (light) at low (high) densities. This has been called the "quark mass-density-dependent model." In this approximation, the strange matter equation of state is rather similar to the corresponding to the MIT Bag Model, but it is significantly stiffer at low densities. Such a property modifies the structure of strange stars in a sizeable way.

In this framework, we calculate the structure of strange stars (mass, radius, central density, gravitational redshift, moment of inertia, and total baryon number) finding that the resulting structures are rather similar to those obtained in the MIT Bag model, although some important differences appear. Comparing to the standard bagged case (with a bag constant in the range of B = 60 - 80 MeV fm^-3), we find that these objects may be more massive and may show gravitational redshifts larger (up to ≈ 10%) than in the bag case. The moment of inertia and total baryon number may be larger than in the bagged case up to a factor of three.

We also calculate the first three radial pulsation modes of these objects, finding that the relation of period vs. gravitational redshift is rather similar to the bag case. Also, we present an analytical treatment for such modes in the low-mass strange stars regime, which is in reasonable agreement with the numerical results.

Eigenfrequencies of radial pulsations of "slowly" rotating neutron stars are calculated in a general relativistic formalism given by Chandrasekhar & Friedman. It is found that the square of the frequencies are always a decreasing function of the central density of the neutron star. The decrease of the squared frequency is sensitive to the equation of state of neutron star matter, and is illustrated using realistic models.

In Rindler space, we determine in terms of special functions the expression of the static, massive scalar or vector field generated by a point source. We find also an explicit integral expression of the induced electrostatic potential resulting from the vacuum polarization due to an electric charge at rest in the Rindler coordinates. For a weak acceleration, we give then an approximate expression in the Fermi coordinates associated with the uniformly accelerated observer.

The effective four-dimensional action for string theory contains non-minimal couplings of the dilaton and the moduli arising from the compactification of higher dimensions. We show that the resulting field equations admit multi-black hole solutions. The Euclidean continuation of these solutions can be interpreted as an instanton mediating the splitting and recombination of the throat of extremal magnetically charged black holes.

Thick domain walls with nonvanishing stress component in the direction perpendicular to the plain of the wall are considered. Their exact solutions are obtained in the background of a five-dimensional spacetime. There may be both expanding and collapsing walls. The energy density decreases on both sides of the walls and the spacetime in all cases is found to be reflection symmetric with respect to the walls.

The effects of limited sky coverage in large-angle cosmic microwave background anisotropy experiments are investigated by computing the variance of the angular two-point correlation function with an incomplete sphere. We find that, assuming a power spectrum of density fluctuations with spectral index n = 1, the Galactic cut of half-width 20° (40°) about the Equator made by the COBE DMR experiment would induce a sample variance on the rms temperature fluctuation [(ΔT/T)_rms]² (or equivalently, the correlation function at zero lag), which is 12% (38%) greater than the cosmic variance with a whole sky coverage. This result is about two times smaller than the naive expectation that the cosmic variance is enhanced by a factor of , where A is the solid angle sampled by the experiment. We also find that the sample variance of the correlation function at nonzero lag can approach the cosmic variance limit. Our approach provides an analytic way of finding a theoretical error to the theoretical prediction for a particular experiment (either large- or small-scale), without having recourse to computationally intensive Monte Carlo or maximum likelihood methods.

We point out several features of the quantum Hamiltonian constraints recently introduced by Thiemann for Euclidean gravity. In particular we discuss the issue of the constraint algebra and of the quantum realization of the object q^abV_b, which is classically the Poisson Bracket of two Hamiltonians.

We discuss the Hawking theory of quantum cosmology with regard to approximation at the lowest order of the Planck constant. At this level, the quantum scenario will be reduced to its classical evolutions in real and imaginary times. We restrict our attention to the so-called real tunneling case. It can be shown that, even at this level, there still exist some quantum effects, the classical field equation may not hold at the transition surface. One can introduce the concept of constrained gravitational instanton. It may play some important role in the scenario of black hole creation in the inflationary background at the Planckian era of the universe. From the constrained gravitational instanton, the real tunneling can occur through different ways. Consequently, it will lead to the creation of different parts of the black hole spacetime in the de Sitter background. The global aspects of the black hole creation are discussed.

Continuing the investigation of the simplest cosmological model with the massive real scalar noninteracting inflaton field minimally coupled to gravity, we study an influence of the cosmological constant on the behavior of trajectories in closed minisuperspace Friedmann–Robertson–Walker model. Combining numerical calculations with qualitative analysis both in configuration and phase space we present a convenient classification of trajectories.