International Journal of Modern Physics D

In this paper we develop the theory of clusterization of peaks in a Gaussian random field. We have obtained new mathematical results from this theory and the theory of percolation and have proposed a topological method of analysis of sky maps based on these results. We have simulated 10°×10° sky maps of the cosmic microwave background anisotropy expected from different cosmological models with 0.5°–1° resolution in order to demonstrate how this method can be used for detection of non-Gaussian noise in the maps and detection of the Doppler-peak in the spectrum of perturbation of ΔT/T.

We study the phenomenological consequences of the recently proposed idea of a running gravitational coupling on macroscopic scales. When applied to the rotation curves of galaxies, we find that their flatness requires the presence of baryonic dark matter. Bounds on the variation of the gravitational coupling from primordial nucleosynthesis and the change of the period of binary pulsars are analysed. We also study constraints on the variations of G with scale from gravitational lensing and the cosmic virial theorem, as well as briefly discuss the implications of such a scenario for structure formation.

The Brill-Hartle gravitational geon construct as a spherical shell of small amplitude, high frequency gravitational waves is reviewed and critically analyzed. The Regge-Wheeler formalism is used to represent the most general gravitational wave perturbations of the spherical background as a superposition of tensor spherical harmonics and an attempt is made to build a nonsingular solution to meet the requirements of a gravitational geon. The attempted constructs of gravitational and electromagnetic geons are contrasted. High-frequency waves are seen to be a necessary condition for the geon and the field equations are decomposed accordingly. It is shown that this leads to the impossibility of forming a spherical gravitational geon. The attempted constructs of gravitational and electromagnetic geons are constructed. The spherical shell in the proposed BrillHartle geon does not meet the regularity conditions required for a nonsingular source and hence cannot be regarded as an adequate geon construct. Since it is the high frequency attribute which is the essential cause of the geon nonviability, it is argued that a geon with less symmetry is an unlikely prospect. The broader implications of the result are discussed with particular reference to the problem of gravitational energy.

As is well-known, when searching for Petrov type I vacuum solutions the imposition of tetrad conditions leads to integrability conditions on the Bianchi identities. Such post-Bianchi equations are simplest in GHP. They are exhibited explicitly for both a “canonical” frame and an “aligned” frame. Choosing a particular gauge, however, complicates the situation considerably; many more conditions are obtained. When this is done for the “canonical” case the resulting equations, when translated to NP, are the Brans-Edgar equations. How all such equations can be checked is reviewed in some detail.

We study a mechanism of increasing Hawking radiation from a black hole by using the example of twisted topologically inequivalent configurations (TICs) of a complex scalar field on the Schwarzschild black hole. Physically this increase is tied with the natural presence of Dirac monopoles on black holes. We satisfy both analytical and numerical considerations and find that twisted TICs give the contribution of order 17% to the total luminosity (summed up over all the TICs) of a black hole.

A simple quantum mechanical model of a closed interacting system is studied following the intrinsic time formalism developed recently, on the basis of the modified Born-Oppenheimer approximation. Apart from shedding further insights into the recent results on a possible nongravitating vacuum energy in the universe, the study also offers potentially interesting possibilities even in atomic/molecular physics.