We study the classical and quantum theory of spherically symmetric spacetimes with scalar field coupling in general relativity. We utilise the canonical formalism of geometrodynamics adapted to the Painleve-Gullstrand coordinates, and present a new quantisation of the resulting field theory. We give an explicit construction of operators that capture curvature properties of the spacetime and use...

AbstractWe have classified symmetric solutions around the origin to four dimensional degenerate Painleve type equation NYA4 with generic values of parameters. We obtained sixteen meromorphic solutions, which are transformed each other by Backlund transformation. calculated linear monodromy for one them, explicitly.

Using the mathematical aspects of Schwarzschild metric, we present different variables transformation which proves that central singularity hypothesis does not exist. The geometric interpretation black hole from metric is mathematically convincing. approaches taken by many authors were viewed, such as Painleve and its complex variant, to deduce a with throat sphere leads mirror space-time. Subs...