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

TL;DR

This paper constructs general Ricci-flat solutions in higher dimensions, including wormholes and tachyonic waves, revealing new geometries and supersymmetry properties, with implications for string theory and higher-dimensional gravity.

Contribution

It introduces the most general Ricci-flat metrics with specific symmetries, discovering new wormhole and tachyon wave solutions, and explores their supersymmetry and brane configurations.

Findings

Found smooth Lorentzian wormholes connecting asymptotically flat spacetimes.

Discovered vacuum tachyonic wave solutions with larger momenta than ADM masses.

Identified supersymmetry preservation in D=4 tachyon wave solutions.

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.