In physics, the Lemaître–Tolman metric, also known as the Lemaître–Tolman–Bondi metric or the Tolman metric, is a Lorentzian metric based on an exact solution of Einstein's field equations ; it describes an isotropic and expanding (or contracting) universe which is not homogeneous, and is thus used in cosmology as an alternative to the standard Friedmann–Lemaître–Robertson–Walker metric to model the expansion of the universe. It has also been used to model a universe which has a fractal distribution of matter to explain the accelerating expansion of the universe. It was first found by Georges Lemaître in 1933 and Richard Tolman in 1934 and later investigated by Hermann Bondi in 1947.