We describe the departure from equilibrium of matter distributions representing sources for a class of Weyl metric. It is shown that, for extremely high gravitational fields, slight deviations from spherical symmetry may enhance the stability of the system weakening thereby its tendency to a catastrophic collapse. For critical values of surface gravitational potential, in contrast with the exac...

We consider the semiclassical dynamics of CGHS black holes with a Weyl-invariant effective action for conformal matter. The trace anomaly of Polyakov effective action is converted into the Virasoro anomaly thus leading to the same flux of Hawking radiation. The covariance of semiclassical equations can be restored through a non-local redefinition of the metric-dilaton fields. The resulting theo...

We present the explicit metric forms for higher dimensional vanishing scalar invariant (V SI) Lorentzian spacetimes. We note that all of the V SI spacetimes belong to the higher dimensional Kundt class. We determine all of the V SI spacetimes which admit a covariantly constant null vector, and we note that in general in higher dimensions these spacetimes are of Ricci type III and Weyl type III....

A study covering some aspects of the Einstein–Rosen metric is presented. The electric and magnetic parts of the Weyl tensor are calculated. It is shown that there are no purely magnetic E–R spacetimes, and also that a purely electric E–R spacetime is necessarily static. The geodesics equations are found and circular ones are analyzed in detail. The super–Poynting and the “Lagrangian” Poynting e...

We are answering the question why 4-dimensional space has the metric 1+ 3 by making a general argument from a certain type of equations of motion linear in momentum for any spin (except spin zero) in any even dimension d. All known free equations for non-zero spin for massless fields belong to this type of equations. Requiring Hermiticity1 of the equations of motion operator ∗NBI-HE-00-26 1This...

We derive differential equations for the flow of entanglement entropy as a function of the metric and the couplings of the theory. The variation of the universal part of entanglement entropy under a local Weyl transformation is related to the variation under a local change in the couplings. We show that this relation is in fact equivalent to the trace Ward identity. As a concrete application of...

The converse was proved by A. Horn [5], so that all points in this convex hull occur as diagonals of some matrix A with the given eigenvalues. Kostant [7] generalized these results to any compact Lie group G in the following manner. We consider the adjoint action of G on its Lie algebra L(G). If T is a maximal torus of G and W its Weyl group, then it is well known that W-orbits in L(T) correspo...

of the Dissertation Self-Dual Metrics on 4-Manifolds by Mustafa Kalafat Doctor of Philosophy in Mathematics Stony Brook University 2007 Under a vanishing hypothesis, Donaldson and Friedman proved that the connected sum of two self-dual Riemannian 4-Manifolds is again self-dual. Here we prove that the same result can be extended over to the positive scalar curvature case. Secondly we give an exa...

We explore the possible physical consequences derived from the fact that the only static and asymptotically-flat vacuum space-time possessing a regular horizon is the Schwarzschild solution (Israel theorem). If small deviations from the Schwarzschild metric are described by means of exact solutions to Einstein equations (as it should be), then for very compact configurations, at the time scale ...

Using the Chern-Simon formulation of (2+1) gravity, we derive, for the general asymptotic metrics given by the Fefferman-Graham-Lee theorems, the emergence of the Liouville mode associated to the boundary degrees of freedom of (2+1) dimensional anti de Sitter geometries. Special attention is paid to holonomies, which are shown to relate the non-connected components of spatial infinity and are e...