This answer to my own question is the best example of which I know that seems to show that the maximally extended Schwarzschild spacetime is of some interest other than as a purely mathematical object. This is based on a physics.SE answer by Ted Bunn, which was a summary of a longer article he and Matthew McIrvin wrote. Theirs was about a Reissner-Nordstrøm spacetime and dealt with electric charge, but I've modified it (hopefully in a correct way) to relate to the less esoteric and more physically realistic Schwarzschild spacetime. I would be interested if other people could provide better motivation for the notion of maximal extension than what I've given here.

People often ask how the gravitational field of a black hole can escape out past the event horizon, or, in a more sophisticated formulation, how the information about its mass can get out. For a black hole that forms by physical collapse, the answer is that there is information in an external observer's past light cone about how much mass fell in -- this information comes from the mass that went into the gravitational collapse.

But the Schwarzschild spacetime is a lot simpler than one formed by gravitational collapse, and we would like to have a valid answer for it as well. The answer here is that we form the maximal extension, which includes a white hole singularity. The information about the mass is on the observer's past light cone, which contains this singularity.

This answer to my own question is the best example of which I know that seems to show that the maximally extended Schwarzschild spacetime is of some interest other than as a purely mathematical object. This is based on a physics.SE answer by Ted Bunn, which was a summary of a longer article he and Matthew McIrvin wrote. Theirs was about a Reissner-Nordstrøm spacetime and dealt with electric charge, but I've modified it (hopefully in a correct way) to relate to the less esoteric and more physically realistic Schwarzschild spacetime. I would be interested if other people could provide better motivation for the notion of maximal extension than what I've given here.

People often ask how the gravitational field of a black hole can escape out past the event horizon, or, in a more sophisticated formulation, how the information about its mass can get out. For a black hole that forms by physical collapse, the answer is that there is information in an external observer's past light cone about how much mass fell in -- this information comes from the mass that went into the gravitational collapse.

But the Schwarzschild spacetime is a lot simpler than one formed by gravitational collapse, and we would like to have a valid answer for it as well. The answer here is that we form the maximal extension, which includes a white hole singularity. The information about the mass is on the observer's past light cone, which contains this singularity.

This answer to my own question is the best example of which I know that seems to show that the maximally extended Schwarzschild spacetime is of some interest other than as a purely mathematical object. This is based on a physics.SE answer by Ted Bunn, which was a summary of a longer article he and Matthew McIrvin wrote. Theirs was about a Reissner-Nordstrøm spacetime and dealt with electric charge, but I've modified it (hopefully in a correct way) to relate to the less esoteric and more physically realistic Schwarzschild spacetime. I would be interested if other people could provide better motivation for the notion of maximal extension than what I've given here.

People often ask how the gravitational field of a black hole can escape out past the event horizon, or, in a more sophisticated formulation, how the information about its mass can get out. For a black hole that forms by physical collapse, the answer is that there is information on an external observer's past light cone about how much mass fell in -- this information comes from the mass that went into the gravitational collapse.

But the Schwarzschild spacetime is a lot simpler than one formed by gravitational collapse, and we would like to have a valid answer for it as well. The answer here is that we form the maximal extension, which includes a white hole singularity. The information about the mass is on the observer's past light cone, which contains this singularity.

This answer to my own question is the best example of which I know that seems to show that the maximally extended Schwarzschild spacetime is of some interest other than as a purely mathematical object. This is based on a physics.SE answer by Ted Bunn, which was a summary of a longer article he and Matthew McIrvin wrote. Theirs was about a Reissner-Nordstrøm spacetime and dealt with electric charge, but I've modified it (hopefully in a correct way) to relate to the less esoteric and more physically realistic Schwarzschild spacetime. I would be interested if other people could provide better motivation for the notion of maximal extension than what I've given here.

People often ask how the gravitational field of a black hole can escape out past the event horizon, or, in a more sophisticated formulation, how the information about its mass can get out. For a black hole that forms by physical collapse, the answer is that there is information in an external observer's past light cone about how much mass fell in -- this information comes from the mass that went into the gravitational collapse.

But the Schwarzschild spacetime is a lot simpler than one formed by gravitational collapse, and we would like to have a valid answer for it as well. The answer here is that we form the maximal extension, which includes a white hole singularity. The information about the mass is on the observer's past light cone, which contains this singularity.