Gravitation as a Quantum Diffusion

Inhomogeneous Nelson's diffusion in flat spacetime with a tensor of diffusion can be described as a homogeneous one in a Riemannian manifold with this tensor of diffusion as a metric tensor. The influence of matter to the energy density of the stochastic background (vacuum) is considered. It is shown that gravitation can be represented as inhomogeneity of the quantum diffusion, the Einstein equations for the metrics can be derived as the equations for the corresponding tensor of diffusion.Comment: Published in: "Z.Zakir (2003) Structure of Space-Time and Matter, CTPA, Tashkent.

General Relativity Constraints the Proper Times and Predicts the Frozen Stars Instead of the Black Holes

In a static gravitational field an intersection of a worldline by a global hypersurface of simultaneity t=const gives an invariant constraint relating the proper time of this event by t. Since at any finite t the such constrained proper time intervals are less than reqiured for crossing a horizon, general relativity predicts the gravitational freezing of proper times in stars with time-like or null geodesics everywhere. The time dilation stabilizes contracting massive stars by freezing, which is maximal but finite at the centre, and the surface is frozen near the gravitational radius. The frozen stars (frozars) slowly defrost due to emissions and external interactions, the internal phase transitions can initiate refreezing with bursts and explosions.Comment: 10 pages. Submitted to Phys. Lett. B. Reviesed versio

New Equations for Gravitation with Riemann Tensor and 4-Index Energy-Momentum Tensors for Gravitation and Matter

A generalized version of the Einstein equations in the 4-index form, containing the Riemann tensor linearly, is derived. It is shown, that the gravitational energy-momentum density tensor outside a source is represented across the Weyl tensor vanishing at the 2-index contraction. The 4-index energy-momentum density tensor for matter also is constructed.Comment: Published in: "Z.Zakir (2003) Structure of Space-Time and Matter. CTPA, Tashkent