Global properties of warped solutions in General Relativity

TL;DR

This paper classifies and explicitly constructs all global vacuum solutions in four-dimensional General Relativity with a warped product structure, revealing new solutions with diverse physical interpretations such as wormholes and cosmic strings.

Contribution

It provides a comprehensive classification and explicit construction of all global vacuum solutions with warped product structure in four-dimensional GR, including many previously unstudied solutions.

Findings

Includes known solutions like Schwarzschild and (anti-)de Sitter

Identifies new solutions with wormholes and cosmic strings

Analyzes global properties of these solutions

Abstract

Assuming the four-dimensional space-time to be a general warped product of two surfaces we reduce the four-dimensional Einstein equations to a two-dimensional problem which can be solved. All global vacuum solutions are explicitly constructed and analysed. The classification of the solutions includes the Schwarzschild, the (anti-)de Sitter, and other well-known solutions but also many exact ones whose detailed global properties to our knowledge have not been discussed before. They have a natural physical interpretation describing single or several wormholes, domain walls of curvature singularities, cosmic strings, cosmic strings surrounded by domain walls, solutions with closed timelike curves, etc.