Self-dual Lorentzian wormholes in n-dimensional Einstein gravity

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 a cosmological constant, we cannot have self-dual Lorentzian wormholes.