Interpolating the Schwarzschild and de Sitter metrics

Abstract

The binary potential technique of interpolation (by [M. Riesz, Acta Math. 81 (1949) 1]) is applied to some well-known metrics of general relativity. These include Schwarzschild, de Sitter and 2+1-dimensional BTZ spacetimes. In particular, the Schwarzschild de Sitter solution is analyzed in some detail with a finite range parameter. Reasoning by the high level of nonlinearity and absence of a superposition law necessitates searching for alternative approaches. We propose the method of interpolation between different spacetimes as one such possibility paving the way toward controling the two-metric system by a common parameter.