A comprehensive survey of Schwarzschild's original papers: Schwarzschild's trick and Einstein's s(h)tick

TL;DR

This paper reviews Schwarzschild's original contributions to general relativity, emphasizing his methods and solutions, and explores the historical interaction between Schwarzschild and Einstein, revealing insights into Einstein's preferences for approximate solutions in 1916.

Contribution

It provides a detailed analysis of Schwarzschild's original papers and clarifies misconceptions about Einstein's choice of solutions in 1916, highlighting historical and methodological nuances.

Findings

Schwarzschild's exact solutions were significant in early general relativity.

Einstein's 1916 preference for approximate solutions was not due to singularity issues.

The divergence in solution preferences evolved with Einstein's later focus on unified field theory.

Abstract

This paper examines Schwarzschild's key contributions to general relativity through his two papers. It focuses on his method for developing exterior and interior solutions. The study emphasizes Schwarzschild's ingenious methods and the implications of his solutions. The paper delves into the exchange of letters between Schwarzschild and Einstein, highlighting the collaborative nature of their scientific interaction. Interestingly, despite presenting Schwarzschild's exact solutions to the Prussian Academy, Einstein exhibited a preference for his approximate methods in his 1916 review paper "The Foundation of the General Theory of Relativity." Contrary to common belief, the paper reveals that in 1916, Einstein's preference for approximate solutions over Schwarzschild's exact exterior solution was not due to a singularity concern. This finding dissociates Einstein's 1916 methodology from his later preoccupation with singularities, which became prominent only during his subsequent focus on unified field theory. Thus, the research posits that factors other than singularities influenced Einstein's decision to stick with approximate methods in 1916.