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A spacetime can be foliated by spacelike hypersurfaces which are related by an isometry ##\partial_t##.
1. Why is ##\partial_{t}## called an isometry of the spacetime?
2. How are the spacelike hypersurfaces related by the isometry ##\partial_{t}##?
1. Why is ##\partial_{t}## called an isometry of the spacetime?
2. How are the spacelike hypersurfaces related by the isometry ##\partial_{t}##?