We study braneworld scenarios within the framework of five-dimensional general relativity. The braneworld Einstein field equations (BEFE) of Shiromizu, Maeda and Sasaki (SMS) possess two salient features which distinguish them from the analogous Einstein field equations, namely a Weyl term and a term Q quadratic in the braneworld energy-momentum. The former is commonly neglected, while the prec...

We consider asymptotically-flat, static and stationary solutions of the Einstein equations representing Einstein-Maxwell space-times in which the Maxwell field is not constant along the Killing vector defining stationarity, so that the symmetry of the space-time is not inherited by the electromagnetic field. We find that static degenerate black hole solutions are not possible and, subject to st...

The Einstein field equations can be derived in n dimensions (n > 2) by the variations of the Palatini action. The Killing reduction of 5dimensional Palatini action is studied on the assumption that pentads and Lorentz connections are preserved by the Killing vector field. A Palatini formalism of 4-dimensional action for gravity coupled to a vector field and a scalar field is obtained, which giv...

A solution to the Einstein field equations that represents a rigidly rotating dust accompanied by a thin matter shell of the same type is found.

We construct a class of exact solutions of the noncommutative vacuum Einstein field equations, which are noncommutative analogues of the plane-fronted gravitational waves in classical gravity.

We present and analyze exact solutions of the Einstein–Maxwell and Einstein–Maxwell– Dilaton equations that describe static pairs of oppositely charged extremal black holes, i.e., black diholes. The holes are suspended in equilibrium in an external magnetic field. We comment as well on the relation of these solutions to brane–antibrane configurations in string and M-theory.

abstract The Virasoro master equation describes a large set of conformal field theories known as the affine-Virasoro constructions, in the operator algebra (affine Lie algebra) of the WZW model, while the Einstein equations of the general non-linear sigma model describe another large set of conformal field theories. This talk summarizes recent work which unifies these two sets of conformal fiel...

For a contravariant 4-metric which changes signature from Lorentzian to Riemannian across a spatial hypersurface, the mixed Einstein tensor is manifestly nonsingular. In Gaussian normal coordinates, the metric contains a step function and the Einstein tensor contains the Dirac delta function with support at the junction. The coefficient of the Dirac function is a linear combination of the secon...

I review evolutionary aspects of general relativity, in particular those related to the hyperbolic character of the field equations and to the applications or consequences that this property entails. I look at several approaches to obtaining symmetric hyperbolic systems of equations out of Einstein' equations by either removing some gauge freedoms from them, or by considering certain linear com...

Class of axially symmetric solutions of vacuum Einstein field equations including the Papapetrou solution as particular case has been found. It has been shown that the derived solution describes the external axial symmetric gravitational field of the source with nonvanishing mass. The general solution is obtained for this class of functions. As an example of physical application, the spacetime ...