investigate the symmetry within black hole event horizons focusing on the spatialtemporal balance surrounding singularities

symmetries black holes event horizon symmetry spacetime hole singularities rotational axisymmetric solutions spherical isotropy space homogeneity time relativity schwarzschild metric kerr solution ernst equation boyerlindquist coordinates asymptotic flatness infalling observer effects frame dragging gravitational redshift light cones cone escape energy conditions penrose diagrams photosphere telescope observations hawking radiation quantum gravity nohair theorems cauchy horizons apparent quasinormal modes bondimetznersachs perturbative analysis