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Show that if a vectorial field ça satisfies the Killing equation &B;a + $a;3 = 0, then, along a geodesic, pº$a =constant
Posted: Tue Apr 26, 2022 7:30 pm
by answerhappygod
- Show That If A Vectorial Field Ca Satisfies The Killing Equation B A A 3 0 Then Along A Geodesic Po A Constant 1 (66.43 KiB) Viewed 48 times
Show that if a vectorial field ça satisfies the Killing equation &B;a + $a;3 = 0, then, along a geodesic, pº$a =constant. This is a coordinate-invariant way of characterizing a conservation law. We only need to know if a metric supports these types of vector fields called Killing fields or Killing vectors. If & is a Killing vector and T is the energy-momentum tensor, show that JH = THVSV is a conserved quantity i.e. J'; e = 0. Interpret J when § is a Killing temporal vector .