Schwarzschild spacetime without coordinates (Q547851)

The main goal of the paper is to derive the extended Kruskal-Szekeres space-time. Instead of studying the geometry of the Schwarzschild space-time \(N\) directly, the author works in the bundle \(\mathcal{F} (N)\) of orthonormal Lorentz frame. By using the Einstein equations the full space-time is constructed. The Cartan structure equation for the bundle of orthogonal frames of a semi-Riemannian manifold is discussed and the case of fiber bundle manifolds is also studied.