The gyraton solutions on generalized Melvin universe with cosmological constant

TL;DR

This paper introduces new exact gyraton solutions on a generalized Melvin universe with a cosmological constant, expanding the understanding of such solutions in Einstein's theory of gravity.

Contribution

It presents the first known gyraton solutions on a generalized Melvin universe with non-zero cosmological constant, unifying previous solutions on Melvin and direct product spacetimes.

Findings

Solutions are of algebraic type II and belong to the Kundt family.

The Einstein equations simplify to equations on a 2D transverse space.

Scalar invariants are generally non-constant, but constant for specific subcases.

Abstract

We present and analyze new exact gyraton solutions of algebraic type II on generalized Melvin universe of type D which admit non-vanishing cosmological constant $\Lambda$. We show that it generalizes both, gyraton solutions on Melvin and on direct product spacetimes. When we set $\Lambda = 0$ we get solutions on Melvin spacetime and for $\Sigma = 1$ we obtain solutions on direct product spacetimes. We demonstrate that the solutions are member of the Kundt family of spacetimes as its subcases. We show that the Einstein equations reduce to a set of equations on the transverse 2-space. We also discuss the polynomial scalar invariants which are non-constant in general but constant for sub-solutions on direct product spacetimes.