Genesis of general relativity - a concise exposition

TL;DR

This paper provides a concise historical overview of the conceptual and mathematical developments leading to Einstein's formulation of general relativity, highlighting key experiments, theories, and mathematical tools used in its creation.

Contribution

It offers a summarized account of the chronological scientific and mathematical progress that culminated in Einstein's general relativity, emphasizing less-explored historical details.

Findings

Historical sequence of key discoveries and experiments

Development of tensor analysis and differential geometry

Formulation of Einstein's field equations

Abstract

This short exposition starts with a brief discussion of situation before the completion of special relativity (Le Verrier's discovery of the Mercury perihelion advance anomaly, Michelson-Morley experiment, E\"otv\"os experiment, Newcomb's improved observation of Mercury perihelion advance, the proposals of various new gravity theories and the development of tensor analysis and differential geometry) and accounts for the main conceptual developments leading to the completion of the general relativity: gravity has finite velocity of propagation; energy also gravitates; Einstein proposed his equivalence principle and deduced the gravitational redshift; Minkowski formulated the special relativity in 4-dimensional spacetime and derived the 4-dimensional electromagnetic stress-energy tensor; Einstein derived the gravitational deflection from his equivalence principle; Laue extended the Minkowski's method of constructing electromagnetic stress-energy tensor to stressed bodies, dust and relativistic fluids; Abraham, Einstein, and Nordstr\"om proposed their versions of scalar theories of gravity in 1911-13; Einstein and Grossmann first used metric as the basic gravitational entity and proposed a "tensor" theory of gravity (the "Entwurf" theory, 1913); Einstein proposed a theory of gravity with Ricci tensor proportional to stress-energy tensor (1915); Einstein, based on 1913 Besso-Einstein collaboration, correctly derived the relativistic perihelion advance formula of his new theory which agreed with observation (1915); Hilbert discovered the Lagrangian for electromagnetic stress-energy tensor and the Lagrangian for the gravitational field (1915), and stated the Hilbert variational principle; Einstein equation of general relativity was proposed (1915); Einstein published his foundation paper (1916).