GL(n,R) Wormholes and Waves in Diverse Dimensions

Abstract

We construct the most general Ricci-flat metrics in (D+n) dimensions that preserve the R^{1,n-1}\times SO(D) isometry. The equations of motion are governed by the system of a GL(n,\R)/SO(1,n-1) scalar coset coupled to D-dimensional gravity. Among the solutions, we find a large class of smooth Lorentzian wormholes that connect two asymptotic flat spacetimes. In addition, we obtain new vacuum tachyonic wave solutions in D\ge 4 dimensions, which fit the general definition of pp-waves in that there exists a covariantly constant null vector. The momenta of the tachyon waves are larger than their ADM masses. The world-volume of the tachyon wave is R^{1,2}, instead of R^{1,1} for the usual vacuum pp-wave. We show that the tachyon wave solutions admit no Killing spinors, except in D=4, in which case it preserves half of the supersymmetry. We also obtain a general class of p-brane wormhole and tachyon wave solutions where the R^{1,n-1} part of the spacetime lies in the the world-volume of the p-branes. These include examples of M-branes and D3-brane. Furthermore, we obtain AdS tachyon waves in D\ge 4 dimensions.