They are called FLRW solutions (at least by Wikipedia). One important class of solutions was discovered in the 1920's. If there is no space and there is no time, but only spacetime, why do people talk about space expanding? Is spacetime expanding?Д®ach solution of Einstein's equation describes a possible geometry of spacetime. I have a similar question (if not the same question really). The speed of light (or anything else) only becomes unambiguous when it is 'local' to the observer. If a photon is at some distance away from a particle, then the speed in relation to that particle is not well defined it can depends on how you put co-ordinates on spacetime and there's no one way to do that. To makes things even worse, the idea of being 'at rest' or having a certain speed is actually ambiguous when particles are separated from each other. The speed of light is measured locally as the speed at which a photon moves past any other particle. Two particles that are at rest with respect to each other might actually start to move closer together as a result of the expansion of space this depends on the nature of the expansion. You can identify a point with a particle but if you pick two particles, the expansion of space does not work like a force to drive them apart. A point is an abstraction you need some way of identifying a point and probably what you want is not a 'point' in space and time but a 'worldline', or a trajectory. But don't we already know that the speed if light is the only constant? Now if the space expanded the two points are further away and not a light second apart. So take two points, maybe of a distance of one light second.

Time speed up