Numerical Spherically Symmetric Static Solution of the RTG Equations Outside the Matter

There was obtained a numerical external solution for the exact system of the RTG equations with some natural boundary conditions in the static spherically symmetric case. The properties of the solution are discussed.Comment: Plenary talk presented at Workshop on High Energy Physics&Field Theory (Protvino, Russia, 2005

On the Relativistic Formulation of Matter

A critical analysis of the relativistic formulation of matter reveals some surprising inconsistencies and paradoxes. Corrections are discovered which lead to the long-sought-after equality of the gravitational and inertial masses, which are otherwise different in general relativity. Realizing the potentially great impact of the discovered corrections, an overview of the situation is provided resulting from the newly discovered crisis, amid the evidences defending the theory.Comment: In press with Astrophys. Space Sci. (The final publication can be seen at springerlink.com

Discrete Scale Relativity

The possibility that global discrete dilation invariance is a fundamental symmetry principle of nature is explored. If the discrete self-similarity observed in nature is exact, then the Principle of General Covariance needs to be broadened in order to accommodate this form of discrete conformal invariance, and a further generalization of relativity theory is required.Comment: 9 pages, minor revisions, accepted at Astrophys. Space Sci., comments welcom

The Bousso entropy bound in selfgravitating gas of massless particles

The Bousso entropy bound is investigated in a static spherically symmetric spacetime filled with an ideal gas of massless bosons or fermions. Especially lightsheets generated by spheres are considered. Statistical description of the gas is given. Conditions under which the Bousso bound can be violated are discussed and it is shown that a possible violating region cannot be arbitrarily large and it is contained inside a sphere of unit Planck radius if number of independent polarization states $g_s$ is small enough. It is also shown that central temperature must exceed the Planck temperature to get a violation of the Bousso bound for $g_s$ not too large.Comment: 14 pages, 4 figures, a paragraph added, version published in Gen. Rel. Gra

Gravitational multi-NUT solitons, Komar masses and charges

Generalising expressions given by Komar, we give precise definitions of gravitational mass and solitonic NUT charge and we apply these to the description of a class of Minkowski-signature multi-Taub-NUT solutions without rod singularities. A Wick rotation then yields the corresponding class of Euclidean-signature gravitational multi-instantons.Comment: Some references adde

The speed of gravity in general relativity

The question is discussed of what is the speed of gravity (at the fundamental non-perturbative level). The question is important, if nowhere else, in discussing the problem of information "lost" in black holes. It turns out that the duly defined "gravitational signal" generally may be causal, superluminal and "semi-superluminal". In the class of globally hyperbolic spacetimes the two last varieties coincide. And if some (often imposed, but not always satisfied) conditions hold, the signals may be \emph{only} causal. In this sense the speed of gravity does not exceed the speed of light.Comment: typos corrected, et

The Algebra of the Energy-Momentum Tensor and the Noether Currents in Classical Non-Linear Sigma Models

The recently derived current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is extended to include the energy-momentum tensor. It is found that in two dimensions the energy-momentum tensor $\theta_{\mu\nu}$, the Noether current $j_\mu$ associated with the global symmetry of the theory and the composite field $j$ appearing as the coefficient of the Schwinger term in the current algebra, together with the derivatives of $j_\mu$ and $j$, generate a closed algebra. The subalgebra generated by the light-cone components of the energy-momentum tensor consists of two commuting copies of the Virasoro algebra, with central charge $\, c\!=\!0$, reflecting the classical conformal invariance of the theory, but the current algebra part and the semidirect product structure are quite different from the usual Kac-Moody / Sugawara type construction.Comment: 10 pages, THEP 92/2

Uniform Decay of Local Energy and the Semi-Linear Wave Equation on Schwarzchild Space

We provide a uniform decay estimate of Morawetz type for the local energy of general solutions to the inhomogeneous wave equation on a Schwarzchild background. This estimate is both uniform in space and time, so in particular it implies a uniform bound on the sup norm of solutions which can be given in terms of certain inverse powers of the radial and advanced/retarded time coordinate variables. As a model application, we show these estimates give a very simple proof small amplitude scattering for nonlinear scalar fields with higher than cubic interactions.Comment: 24 page

Gravitational Radiation from First-Order Phase Transitions

It is believed that first-order phase transitions at or around the GUT scale will produce high-frequency gravitational radiation. This radiation is a consequence of the collisions and coalescence of multiple bubbles during the transition. We employ high-resolution lattice simulations to numerically evolve a system of bubbles using only scalar fields, track the anisotropic stress during the process and evolve the metric perturbations associated with gravitational radiation. Although the radiation produced during the bubble collisions has previously been estimated, we find that the coalescence phase enhances this radiation even in the absence of a coupled fluid or turbulence. We comment on how these simulations scale and propose that the same enhancement should be found at the Electroweak scale; this modification should make direct detection of a first-order electroweak phase transition easier.Comment: 7 pages, 7 figure

Billiard Representation for Multidimensional Quantum Cosmology near the Singularity

The degenerate Lagrangian system describing a lot of cosmological models is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the "singularity" is reduced to a billiard on the Lobachevsky space. The Wheeler-DeWitt equation in the asymptotical regime is solved and a third-quantized model is suggested.Comment: 6 pages, LaTe