The coordinates (x0,x1,x2) = (x, Lemaître coordinates are a particular set of coordinates for the Schwarzschild metric—a spherically symmetric solution to the Einstein field equations in vacuum—introduced by Georges Lemaître in [1].
The Friedmann-Lemaître-Robertson-Walker (FLRW) metric used to George Lemaitre was apparently the first one to figure that out. He introduced an alternative set of coordinates, {t, r} → {τ, ρ}, which are connected to bodies falling free radially towards the center from infinity where they are at rest. The angular coordinates remain the same. The transformation to the Lemaitre coordinates τ, ρ is.
The Lemaître statues in both Lemaitre Coordinates are a coordinate system used in general relativity to plot the paths of objects in freefall and light rays in a gravitational field. They were developed by Belgian physicist Georges Lemaitre in the s as an alternative to the more commonly used Schwarzschild Coordinates.
We show that the Lemaitre coordinates don't claim to prove anything, they are simply one of infinitely many possible systems of coordinates that satisfy the field equations with spherical symmetry. Anyone who understands differential manifolds with semi-definite metrics can infer the light cone structure from any such system of coordinates.
The exterior spacetime is in Lemaitre coordinates. Event horizons. Black holes. In the Schwarzschild metric the gravitational radius r g =2m is a singular point. It takes infinitely long time for a free falling body to reach the Schwarzschild radius. Inside the Schwarzschild radius time and radial coordinates interchange. A transformation to the new coordinates τ, ρ.
The Friedmann-Lema{\^i}tre-Robertson-Walker (FLRW) metric used For both of the coordinates: Painleve Gulstrand (PG), and Lemaitre, one can choose the surfaces (flat constant time in the case of PG) and define a global set of coordinates which cover all of the Schw analytically extended spacetime GRAPHS: In each case we graph the constant coordinate surfaces in the Kruscal set of coordinates.
Coordinates (H0, ~) of these
Lemaître coordinates are a particular set of coordinates for the Schwarzschild metric—a spherically symmetric solution to the Einstein field equations in vacuum—introduced by Georges Lemaître in 
We study the existence arXiv:hep-th/v1 hep-th/ Classical Geometry of De Sitter Spacetime: An Introductory Review Yoonbai Kima,b,1, Chae Young Oha,2, and Namil Parka,3 aBK21 Physics Research Division and Institute of Basic Science, Sungkyunkwan University.