Here, " maximally extended " refers to the idea that the spacetime should not have any " edges ": for any possible trajectory of a free-falling particle ( following a geodesic ) in the spacetime, it should be possible to continue this path arbitrarily far into the particle's future or past, unless the trajectory hits a gravitational singularity like the one at the center of the black hole's interior.

Here, " maximally extended " refers to the idea that the spacetime should not have any " edges ": for any possible trajectory of a free-falling particle ( following a geodesic ) in the spacetime, it should be possible to continue this path arbitrarily far into the particle's future, unless the trajectory hits a gravitational singularity like the one at the center of the black hole's interior.

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