International Journal of Modern Physics D

By reconciling the wave equation for the Weyl tensor with the corresponding wave equation for the Weyl spinor, we establish a new tensor identity—involving the sum of terms each consisting of a product of the Weyl and Ricci tensors—valid in four (and only four) dimensions. This enables us to give, for the first time, the correct and simplest form of the wave equation for the Weyl tensor in four-dimensional nonvacuum spacetimes. The wave equation for the Weyl tensor in n(> 4) dimensional nonvacuum spaces is also presented for the first time; we show that there does not exist an analogous n-dimensional tensor identity matching the four-dimensional one, and so it follows that there does not exist an analogous simplification of the Weyl wave equation in the n-dimensional case. It is also shown how our new identity, and some other recently discovered identities, relate to a large class of dimensionally dependent identities found some time ago by Lovelock.

We quantize by the Dirac-Wheeler-DeWitt method the canonical formulation of the Schwarzschild black hole developed in a previous paper. We investigate the properties of the operators that generate rigid symmetries of the Hamiltonian, establish the form of the invariant measure under the rigid transformations, and determine the gauge fixed Hilbert space of states. We also prove that the reduced quantization method leads to the same Hilbert space for a suitable gauge fixing.

It is known that certain properties of charged dilaton black holes depend on a free parameter β which controls the strength of the coupling of the dilaton to the Maxwell field. We obtain the energy associated with static spherically symmetric charged dilaton black holes for arbitrary value of the coupling parameter and find that the energy distribution depends on the value of β. With increasing radial distance, the energy in a sphere increases for β=0 as well as for β<1, decreases for β>1, and remains constant for β=1. However, the total energy turns out to be the same for all values of β.

The gravitational instability of free and dilute Newtonian boson clouds has been examined. For collisionless Newtonian boson clouds with a uniform unperturbated Bose gas density, it is deduced that the gravitational instability will never give rise to the formation of boson stars, but only black holes; however if the unperturbated density, in the neighbourhood of the perturbation, has a scale length equal to or smaller than the perturbation wavelength, the formation of free Newtonian boson stars could also be possible. For dilute Newtonian boson clouds it is shown that the gravitational instability can lead the cloud to condense into boson stars of different masses but identical radii, in agreement with studies about equilibrium configurations of dilute Newtonian boson stars. The galactic distribution of these Newtonian boson stars, and hence, the average distance among them is also discussed.

We propose that the Universe was created from “Nothing” with a relatively small number of particles and it very quick relaxed to a quasi-equilibrium state at the Planck parameters. The classic cosmological solution for this Universe, with the calculation of its ability to undergo the second order relativistic phase transition (RPT), has two branches divided by a gap. On one of these branches near to the “Nothing” state the second order RPT is not possible at the GUT scale. The other branch is thermodynamically unstable. The quantum process of tunneling between the cosmological solution branches and the kinetics of the second order RPT are investigated by numerical methods. Another quantum geometrodynamics process (bounce from singularity) is also taken into consideration. It is shown that the discussed phenomenon with the calculation of all RPTs from the GUT scale (10¹⁶ Gev) to the Salam-Weinberg scale (10² Gev) gives the new cosmological scenarios of the macroscopic Universe origin with the observable number of particles.

We propose a scale-dependent cosmology with the stress-energy tensor of viscous fluid, in which the Robertson-Walker metric and the Einstein equation are generalized in such a way that Ω₀, H₀ and the age of the Universe all become scale-dependent. Its implications on the observational cosmology and possible modifications of the standard Friedmann cosmology are discussed. For example, since the age of the Universe in this model depends on the local values of Ω₀ and the Hubble parameter, the age of the locally open Universe even with the high value of hubble parameter can be long enough to accommodate the measured ages of the oldest stars and globular clusters.

We investigate cosmological models with a free scalar field and a viscous fluid. We find exact solutions for a linear and nonlinear viscosity pressure. Both yield singular and bouncing solutions. In the first regime, a de Sitter stage is asymptotically stable, while in the second case we find power-law evolutions for a vanishing cosmological constant.