R=0 spacetimes and self-dual Lorentzian wormholes

TL;DR

This paper introduces a family of self-dual, R=0 Lorentzian spacetimes, including wormholes, black holes, and naked singularities, characterized by specific stress-energy conditions and analyzed for traversability.

Contribution

It derives a new class of spherically symmetric, static Lorentzian wormholes as solutions to the self-duality condition, expanding the understanding of exotic spacetimes with R=0.

Findings

Identifies parameter ranges for wormholes, black holes, and naked singularities.

Provides a model for exotic stress-energy needed for wormholes.

Examines conditions for traversability of the wormholes.

Abstract

A two-parameter family of spherically symmetric, static Lorentzian wormholes is obtained as the general solution of the equation $\rho=\rho_t=0$, where $\rho = T_{ij} u^iu^j$, $\rho_t = (T_{ij} - {1\over2} T g_{ij}) u^iu^j$, and $u^i u_i =- 1$. This equation characterizes a class of spacetimes which are ``self dual'' (in the sense of electrogravity duality). The class includes the Schwarzschild black hole, a family of naked singularities, and a disjoint family of Lorentzian wormholes, all of which have vanishing scalar curvature (R=0). Properties of these spacetimes are discussed. Using isotropic coordinates we delineate clearly the domains of parameter space for which wormholes, nakedly singular spacetimes and the Schwarzschild black hole can be obtained. A model for the required ``exotic'' stress-energy is discussed, and the notion of traversability for the wormholes is also examined.