Variational Methods in General Relativity - Lagrangian Methods

Lagrangian Methods

The equations of motion in physical theories can often be derived from an object called the Lagrangian. In classical mechanics, this object is usually of the form, 'kinetic energy − potential energy'. For more general theories, the Lagrangian is some functional, such that the formation of the Euler–Lagrange equations from it recovers the required equations.

David Hilbert gave an early and classic formulation of the equations in Einstein's general relativity. This used the functional now called the Einstein-Hilbert action.