Einstein's hole argument

In general relativity, space and time are inseparable from a gravitational field: no field, no spacetime. This is a lesson of Einstein's hole argument . We use a simple transformation in a Schwartzschild spacetime to illustrat e this. On the basis of the general theory of relativity... space as opposed to "wh at fills space"... has no separate existence.... There is no such thing as an empty space, i.e., a space without [a gravitational] field.... Spacetime does not claim existence on its own, but only as a structural quality of t he field. (C) 2001 American Association of Physics Teachers.