Siklos waves in Poincar\'e gauge theory

TL;DR

This paper extends Siklos waves, known solutions in general relativity, to include torsion within Poincaré gauge theory, providing explicit examples of new vacuum solutions with potential implications for gravitational theories.

Contribution

It introduces a new class of Siklos waves with torsion in Poincaré gauge theory and constructs three explicit vacuum solutions, expanding the understanding of exact solutions in this framework.

Findings

Constructed three explicit vacuum solutions: generalized Kaigorodov, homogeneous, exponential.

Extended Siklos waves to include torsion in Poincaré gauge theory.

Demonstrated the existence of exact vacuum solutions with torsion.

Abstract

A class of Siklos waves, representing exact vacuum solutions of general relativity with a cosmological constant, is extended to a new class of Siklos waves with torsion, defined in the framework of the Poincar\'e gauge theory. Three particular exact vacuum solutions of this type, the generalized Kaigorodov, the homogeneous and the exponential solution, are explicitly constructed.