Schwarzschild and de Sitter solutions from the argument by Lenz and Sommerfeld

TL;DR

This paper demonstrates how the Lenz-Sommerfeld argument can be used to derive both Schwarzschild and de Sitter solutions in general relativity, providing a simple and elegant approach to these fundamental spacetime metrics.

Contribution

It extends the Lenz-Sommerfeld derivation method to include the de Sitter solution, offering a unified and simplified approach to key solutions in general relativity.

Findings

Derivation of Schwarzschild solution using Lenz-Sommerfeld argument

Construction of de Sitter line element with the same reasoning

Simplified approach to fundamental spacetime metrics in GR

Abstract

The Lenz-Sommerfeld argument allows an ingenious and simple derivation of the Schwarzschild solution of Einstein equations of general relativity. In this paper, we use the same reasoning to construct the de Sitter line element.