# Interpolating the Schwarzschild and de-Sitter metrics

## TL;DR

This paper explores a novel interpolation method to connect different spacetime metrics in general relativity, specifically analyzing Schwarzschild, de Sitter, and BTZ spacetimes, aiming to better understand their relationships and control mechanisms.

## Contribution

It introduces an interpolation technique for metrics in general relativity, providing a new approach to analyze complex spacetime solutions like Schwarzschild-de Sitter.

## Key findings

- Interpolation between metrics is feasible and offers insights into their relationships.
- The Schwarzschild-de Sitter solution can be analyzed with a finite range parameter.
- The method may help control two-metric systems using a common parameter.

## Abstract

The binary potential technique of interpolation (by M. Riesz, Acta Math. 81, 1 (1949)) 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 non-linearity and absence of a superposition law necessitates search for alternative approaches. We propose the method of interpolation between different spacetimes as one such possibility paving the way toward controlling the two-metric system by a common parameter.