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Gravitational collapse of the dust sphere
What we do?
Energy-momentum tensor for spherically symmetric matter is , here is energy density function and pressure (just dust). Einstein equations are
Energy-momentum tensor for spherically symmetric matter is
, here 
is energy density function and pressure p = 0 (just dust). Einstein equations are r - 
= 8
kT, where r - Ricci tensor, s - Ricci scalar, k - gravitational constant (here light velocity c = 1).
Energy-momentum tensor for spherically symmetric matter is
, here is energy density function and pressure p = 0 (just dust). Einstein equations are r - = 8kT, where r - Ricci tensor, s - Ricci scalar, k - gravitational constant (here light velocity c = 1).Calculate Einstein tensor and corresponding equations for dust sphere metric. Verify that corresponding space-time has axial symmetry and it is not stationary.
Solution:
| Connection[id] | id - variable - connection identifier. | ||
| Coframe[id1→ expr1,id2→ expr2,...idn→ exprn] | id - identifier for indexed variable - the coframe 1-forms,
n - dimension of working manifold (a variable or integer),
idi
|
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Dust sphere metric:
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