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Collision of plane waves in dilaton gravity theories and low energy limit of string theory is considered. The formulation of the the problem and some exact solutions are presented., Comment: 23 pages, Latex, to appear in Phys. Rev.D

We find constant scalar curvature Type-N and Type-D solutions in all higher curvature gravity theories with actions of the form $f({R}_{\ensuremath{\mu}\ensuremath{\nu}})$ that are built on the Ricci tensor, but not on its derivatives. In our construction, these higher derivative theories inherit some of the previously studied solutions of the cosmological topologically massive gravity and the new massive gravity field equations, once the parameters of the theories are adjusted. Besides the generic higher curvature theory, we have considered in some detail the examples of the quadratic curvature theory, the cubic curvature theory, and the Born-Infeld extension of the new massive gravity.

The effect of string theory on the four-dimensional classical Einstein equations is investigated. It is shown that the throats of nonrotating charged black holes are exact solutions of the gravitational field equations with string correction terms.

The stationary axially symmetric (AS) Einstein-Maxwell equations are shown to be a special case of the static AS self-dual SU(3) Yang-Mills equations; they can become identical by imposing certain functional relations on the Yang-Mills fields. Certain techniques developed for the Einstein-Maxwell equations are translated into the SU(3) Yang-Mills equations, and a linear eigenvalue problem for the stationary AS Einstein-Maxwell equations is formulated.

It is shown that a restricted class of static, axially symmetric self-dual $\mathrm{SU}(n+1)$ Yang-Mills field equations are equivalent to the stationary, axially symmetric Einstein-($n\ensuremath{-}1$)-Maxwell field equations.

x 5(x' —z'{s))5(x' —z'(s }) is the mass density which is infinite on the world line z =z (s) of the singularity and zero elsewhere. Because of the scalar density character of the 6 function the left-hand side of Eq. (2} is a tensor density. From Eq. (1) follows the conservation law The string equation of motion was further studied by many authors' ' in connection with duality. The purpose of this note is to show that the worldsheet equation (8) can be derived in general relativity following Einstein's method for the geodesic world line.

We propose an ansatz for the strong-gravity $f$ field which is motivated by the quark-confinement problem and construct exact solutions of the vacuum $f\ensuremath{-}g$ field equations.

It is shown that there are only two distinct conformally flat solutions of the coupled Einstein scalar field equations. One of them has recently been given by Penney.