We give all exact solutions of the Einstein-Gauss-Bonnet Field Equations coupled with a scalar field in four dimensions under certain assumptions. The main assumption we make in this work is to take the second covariant derivative of the coupling function proportional to the spacetime metric tensor. Although this assumption simplifies the field equations considerably, to obtain exact solutions ...

Hence .0V is a quantity which can only increase with the time and may be regarded as the entropy of the universe. This quantity proves to be equivalent to the expression that Lenz took for the entropy of the Einstein universe, but, in general, the expression for the entropy of a system in a gravitational field does not reduce to so simple a form. 1 Tolman, R. C., these PROCzSDINGs, 14, No. 3, 2...

The Vlasov-Einstein equations are a closed self-consistent collision-less system of kinetic equations. They were introduced to model the dynamics of self gravitating multi-particles system. The particles could be a neutral gas, plasma, interstellar dust, stars, galaxies or even clusters of galaxies. In 1990 Rendall and Rein initiated the mathematical study of the Einstein-Vlasov system. Since t...

A model is proposed to describe a transition from a charged black hole of mass M and charge Q to one of mass M and charge Q. The basic equations are derived from the non-vacuum Einstein field equations sourced by the Coulomb field and by a null scalar field with a nonvanishing trace anomaly. It is shown that the nonvanishing trace of the energy-momentum tensor prevents the formation of a naked ...

We provide a geometric framework for the construction of non-vacuum black holes whose metrics are stationary and axisymmetric. Under suitable assumptions we show that Einstein equations reduce to an Einstein-harmonic map type system analyze compatibility resulting equations. This will be fundamental our forthcoming metric-stationary axisymmetric bifurcations Kerr solving Einstein--Klein--Gord...

Riemannian and teleparallel geometrical approaches to the investigation of Maxwell electrodynamics shown that a unified field theory of gravitation and electromagnetism a la Einstein can be obtained from a stationary metric. This idea contrasts with the recently proposed premetric electrodynamics by Hehl and Obukhov. In the teleparallel case the definition of the electric field is obtained stra...

The positive energy theorem precludes the possibility of Minkowski flat space decaying by any mechanism. In certain circumstances, however, large quantum fluctuations of the gravitational field could arise—not only at the Planck scale, but also at larger scales. This is because there exists a set of localised weak field configurations which satisfy the condition ∫ dx √ gR = 0 and thus give a nu...

We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational field with an eigenspinor of the Dirac operator via the energymomentum tensor. For this purpose we introduce a new field equation generalizing the notion of Killing spinors. The solutions of this spinor field equation are called weak Killing spinors (WK-spinors). They are special solutions of the Einste...