Analytic continuation of Spacetime Metrics
Analytic continuation of Spacetime Metrics
Analytic continuation of Spacetime Metrics
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Exact solutions<br />
any space-time metric can be regarded as satisfying Einstein's field equations<br />
exact solution = space-time in which the field equations are satisfied with T ab the<br />
energy-momentum tensor <strong>of</strong> some specified form <strong>of</strong> matter which obeys<br />
postulate <strong>of</strong> 'local causality' and the some energy conditions. – for empty space<br />
(T ab = 0), electromagnetic field, perfect fluid/space containing an electromagnetic<br />
field and a perfect fluid.<br />
complexity <strong>of</strong> the field equations -> solutions in spaces <strong>of</strong> high symmetry<br />
the unknown = Lorentzian metric g μν<br />
the characteristic sets are its light<br />
cones.<br />
μν<br />
,<br />
The most simple and natural problem <strong>of</strong> physics since Newton:<br />
-initial conditions and laws <strong>of</strong> evolution given. Can we predict the future?<br />
-GR: appropriate initial conditions given, can we describe the future universe?
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