International Journal of Modern Physics D

Analytic spherically symmetric solutions of the Einstein field equations coupled with a perfect fluid and with self-similarities of the zeroth, first and second kinds, found recently by Benoit and Coley [Class. Quantum Grav.15, 2397 (1998)], are studied, and found that some of them represent gravitational collapse. When the solutions have self-similarity of the first (homothetic) kind, some of the solutions may represent critical collapse but in the sense that now the "critical" solution separates the collapse that forms black holes from the collapse that forms naked singularities. The formation of such black holes always starts with a mass gap, although the "critical" solution has homothetic self-similarity. The solutions with self-similarity of the zeroth and second kinds seem irrelevant to critical collapse. Yet, it is also found that the de Sitter solution is a particular case of the solutions with self-similarity of the zeroth kind, and that the Schwarzschild solution is a particular case of the solutions with self-similarity of the second kind with the index α=3/2.

A vector–tensor theory of gravity that was introduced in an earlier publication is analyzed in detail and its consequences for early universe cosmology are examined. The multiple light cone structure of the theory generates different speeds of gravitational and matter wave fronts, and the contraction of these light cones produces acausal, superluminary inflation that can resolve the initial value problems of cosmology.

We present a class of exact solutions of the Einstein gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solution is represented in a closed integral form. The energy density and both radial and tangential pressure are finite and positive inside the anisotropic star. The energy density, radial pressure, pressure-density ratio and the adiabatic speed of sound are monotonically decreasing functions. Several stellar models with the anisotropy coefficient proportional to r² are discussed, the values of the basic physical parameters of the star (radius, mass and red shift) and bound on anisotropy parameter is obtained.

The Petrov classification is studied with the language of spacetime splitting with respect to a generic timelike unit vector field. Canonical forms of the Weyl tensor for each Petrov type are introduced in terms of preferred reference frames. As an application, the canonical forms of the Bel–Robinson superenergy density and flux are constructed and applications to Bel's definition of gravitational radiation are considered.

We analyze here the spherically symmetric collapse of a charged null fluid in a higher dimensional spacetime. Both naked singularities and black holes are shown to be developing as final outcome of the collapse. A relationship between weak energy condition and occurrence of strong curvature singularity is pointed out.

Increasing numbers of active galaxies with significant alignments of quasars are being observed. It is the purpose of this paper to explore ejection dynamics of these quasars using the variable mass hypothesis (VMH) originally discussed by Narlikar and Das in 1980. According to the VMH quasars are ejected from parent galaxies initially with zero rest mass which grows through a Machian interaction. The intrinsic redshift of the quasar steadily decreases as its mass grows, but always remains in excess of the redshift of the galaxy. The ultimate aim of this hypothesis is to quantitatively relate the observed ordering of redshifts of ejected quasars, with separation from the galaxy, their intrinsic redshifts and the age of the evolutionary stage of the ejecta.

The important studies of Peebles, and Bond and Efstathiou have led to the formula C_ℓ=const./[ℓ(ℓ+1)] aimed at describing the lower order multipoles of the CMBR temperature variations caused by density perturbations with the flat spectrum. Clearly, this formula requires amendments, as it predicts an infinitely large monopole C₀, and a dipole moment C₁ only 6/2 times larger than the quadrupole C₂, both predictions in conflict with observations. We restore the terms omitted in the course of the derivation of this formula, and arrive at a new expression. According to the corrected formula, the monopole moment is finite and small, while the dipole moment is sensitive to short-wavelength perturbations, and numerically much larger than the quadrupole, as one would expect on physical grounds. At the same time, the function ℓ(ℓ+1)C_ℓ deviates from a horizontal line and grows with ℓ, for ℓ≥2. We show that the inclusion of the modulating (transfer) function terminates the growth and forms the first peak, recently observed. We fit the theoretical curves to the position and height of the first peak, as well as to the observed dipole, varying three parameters: red-shift at decoupling, red-shift at matter-radiation equality, and slope of the primordial spectrum. It appears that there is always a deficit, as compared with the COBE observations, at small multipoles, ℓ~10. We demonstrate that a reasonable and theoretically expected amount of gravitational waves bridges this gap at small multipoles, leaving the other fits as good as before. We show that the observationally acceptable models permit somewhat "blue" primordial spectra. This allows one to avoid the infrared divergence of cosmological perturbations, which is otherwise present.