General Relativity: An Introduction for Physicists · Problem 11.17

Schwarzschild black holes — Hobson, Efstathiou & Lasenby

Physics · einstein-rosen-wormhole-embedding

Problem

Perform an embedding into three-dimensional Euclidean space of the 2-space with line element

d\sigma^2 = dr^2 + (r^2 + a^2)\,d\phi^2,

and hence show that the resulting 2-surface has a geometry reminiscent of a wormhole.