Spacetime Splitting, Admissible Coordinates and Causality

To confront relativity theory with observation, it is necessary to split spacetime into its temporal and spatial components. The (1+3) timelike threading approach involves restrictions on the gravitational potentials $(g_{\mu \nu})$, while the (3+1) spacelike slicing approach involves restrictions on $(g^{\mu \nu})$. These latter coordinate conditions protect chronology within any such coordinate patch. While the threading coordinate conditions can be naturally integrated into the structure of Lorentzian geometry and constitute the standard coordinate conditions in general relativity, this circumstance does not extend to the slicing coordinate conditions. We explore the influence of chronology violation on wave motion. In particular, we consider the propagation of radiation parallel to the rotation axis of stationary G\"odel-type universes characterized by parameters $\eta > 0$ and $\lambda > 0$ such that for $\eta 1$) chronology is protected (violated). We show that in the WKB approximation such waves can freely propagate only when chronology is protected.Comment: 25 pages, 3 figures; v2: minor typos corrected, accepted for publication in Phys. Rev.

Exact Solution of Photon Equation in Stationary G\"{o}del-type and G\"{o}del Space-Times

In this work the photon equation (massless Duffin-Kemmer-Petiau equation) is written expilicitly for general type of stationary G\"{o}del space-times and is solved exactly for G\"{o}del-type and G\"{o}del space-times. Harmonic oscillator behaviour of the solutions is discussed and energy spectrum of photon is obtained.Comment: 9 pages,RevTeX, no figure, revised for publicatio

Anisotropic cosmological models in terms of Raychaudhuri and Wheeler-DeWitt equations

Classical anisotropic cosmological models are described in terms of the Raychaudhuri equation for a perfect fluid. Quantum ones are considered using the Wheeler-DeWitt equation. The Universe birth probability has been calculated for a flat model with dust and de Sitter vacuum. © 2009 Pleiades Publishing, Ltd

Anisotropic cosmological models in terms of Raychaudhuri and Wheeler-DeWitt equations

Classical anisotropic cosmological models are described in terms of the Raychaudhuri equation for a perfect fluid. Quantum ones are considered using the Wheeler-DeWitt equation. The Universe birth probability has been calculated for a flat model with dust and de Sitter vacuum. © 2009 Pleiades Publishing, Ltd