Self--dual Lorentzian wormholes in n--dimensional Einstein gravity

TL;DR

This paper constructs a family of self--dual Lorentzian wormholes in n--dimensional Einstein gravity, analyzing their geometric properties and parameter domains, and finds such wormholes cannot exist in lower dimensions without a cosmological constant.

Contribution

It introduces a new class of self--dual Lorentzian wormhole solutions in n--dimensional Einstein gravity and explores their geometric structure and parameter conditions.

Findings

Includes n-dimensional Schwarzschild black holes and traversable wormholes.

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

Shows no self--dual Lorentzian wormholes exist in lower dimensions without cosmological constant.

Abstract

A family of spherically symmetric, static and self--dual Lorentzian wormholes is obtained in n--dimensional Einstein gravity. This class of solutions includes the n--dimensional versions of the Schwarzschild black hole and the spatial--Schwarzschild traversable wormhole. Using isotropic coordinates we study the geometrical structure of the solution, and delineate the domains of the free parameters for which wormhole, naked singular geometries and the Schwarzschild black hole are obtained. It is shown that, in the lower dimensional Einstein gravity without cosmological constant, we can not have self--dual Lorentzian wormholes.