BRAJERČÍK JánGeometry of Schwarzschild spacetimesIn a broader sense, a Schwarzschild spacetime is a smooth manifold, endowed with an action of the special orthogonal group SO(3) and a Schwarzschild metric, an SO(3)-invariant metric field, satisfying the Einstein equations. Explicit formulas of all Schwarzschild metrics on 4-dimensional manifold R x (R3{(0,0,0)}) are introduced, using spherical charts. Existence of a Schwarzschild metric on different manifolds is also disscused. |