The electromagnetic field is studied in a family of exact solutions of the Einstein equations whose material content is a perfect fluid with stiff equation of state (p = ǫ). The field equations are solved exactly for several members of the family.

We show that almost all metric–affine theories of gravity yield Einstein equations with a non–null cosmological constant Λ. Under certain circumstances and for any dimension, it is also possible to incorporate a Weyl vector field Wμ and therefore the presence of an anisotropy. The viability of these field equations is discussed in view of recent astrophysical observations.

Kossowski and Kriele [1] derived boundary conditions on the metric at a surface of signature change. We point out that their derivation is based not only on certain smoothness assumptions but also on a postulated form of the Einstein field equations. Since there is no canonical form of the field equations at a change of signature, their conclusions are not inescapable. We show here that a weake...

In this paper we study solutions of supergravity equations generated by string-like sources moving with the speed of light. Study of solutions of the Einstein equations for objects moving with the velocity of light has long story. In 1934 Tolman [1] obtained solutions for the gravitational field of beams of light in the linear approximation. The exact solutions of the non-linear Einstein equati...

Einstein field equations with a cosmological constant are linearized assuming a flat background metric. The final result is a set of EinsteinMaxwell-Proca equations for gravity in the weak field approximation. This linearization procedure implements the breaking of gauge symmetry in general relativity. A brief discussion of the physical consequences is proposed in the framework of the gauge the...

A large family of noncommutative Einstein-Maxwell null pp -waves to order one in the noncommutativity parameters is constructed. They are solutions to the Einstein and field equations for general relativity coupled to a Seiberg-Witten electromagnetic field. Noncommutativity enters the spacetime metric through a conformal factor and is responsible for dilating/contracting the separation between ...

We derive an asymptotic solution of the Einstein field equations which describes the propagation of a thin, large amplitude gravitational wave into a curved space-time. The resulting equations have the same form as the colliding plane wave equations without one of the usual constraint equations.

We consider static, spherically symmetric vacuum solutions to the equations of a theory of gravity with the La-grangian f (R) where R is the scalar curvature and f is an arbitrary function. Using a well-known conformal transformation, the equations of f (R) theory are reduced to the " Einstein picture " , i.e., to the equations of general relativity with a source in the form of a scalar field w...

Abstract It is shown that the well-known triviality of the Einstein field equations in two dimensions is not a sufficient condition for the Einstein-Hilbert action to be a total divergence, if the general covariance is to be preserved, that is, a coordinate system is not fixed. Consequently, a Hamiltonian formulation is possible without any modification of the two dimensional Einstein-Hilbert a...

The stability of de Sitter metric in spacetimes where inflaton fields are non-minimally coupled to propagating torsion is investigated. It is shown that the de Sitter background metric is unstable against small perturbations. Axionic torsion is generated by inflaton fluctuations and the analysis of cosmological perturbations in Einstein-Cartan-Klein-Gordon (ECKG) equations is undertaken. Instab...