Einsteins Theory of Relativity 10 Internal Schwarzschild Metric
- Slides: 36
Einstein‘s Theory of Relativity 10. Internal Schwarzschild Metric, Stellar Structure Equations Ulrich R. M. E. Geppert 2/21/2021 U. R. M. E. Zielona Gora 1
remark on Schwarzschild metric proof 2/21/2021 U. R. M. E. Zielona Gora 2
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classical, nonrelativistic stellar structure equations 2/21/2021 U. R. M. E. Zielona Gora 4
Schwarzschild metric in the form Einstein equations in the form 2/21/2021 ⇐ relativistic Euler and continuity equation of a liquid in a gravitational field U. R. M. E. Zielona Gora 5
remark on Euler equation: in detail: 2/21/2021 U. R. M. E. Zielona Gora 6
2/21/2021 U. R. M. E. Zielona Gora 7
proof: 2/21/2021 now U. R. M. E. Zielona Gora 8
in more detail analogue 2/21/2021 U. R. M. E. Zielona Gora 9
f 2/21/2021 U. R. M. E. Zielona Gora 10
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insertion: contraction of Christoffel symbols, determinant of metric tensor 2/21/2021 U. R. M. E. Zielona Gora 12
why: ? 2/21/2021 U. R. M. E. Zielona Gora 13
antisymmetric tensor, see GR_1 2/21/2021 U. R. M. E. Zielona Gora 14
two identical indices 2/21/2021 U. R. M. E. Zielona Gora 15
back to determination of metric coefficient: 2/21/2021 U. R. M. E. Zielona Gora 16
(see GR_9, slide 31, Eq. B) 2/21/2021 U. R. M. E. Zielona Gora 17
insert this, and this Tolman, Oppenheimer, Volkoff 2/21/2021 U. R. M. E. Zielona Gora 18
slide 6: hydrostatic stellar equilibrium, derived from Newton‘s field equation 2/21/2021 U. R. M. E. Zielona Gora 19
joins this solution smoothly to the external Schwarzschild solution? 2/21/2021 U. R. M. E. Zielona Gora 20
2/21/2021 U. R. M. E. Zielona Gora 21
up to now 2 stellar structure equations: 3 fields but only 2 equations 2/21/2021 U. R. M. E. Zielona Gora 22
e. g. : General relativistic treatment of thermal, magnetic and rotational evolution of isolated neutron stars with crustal magnetic fields D. Page 1, U. Geppert 2, and T. Zannias 3 2/21/2021 U. R. M. E. Zielona Gora 23
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relativistic stars with constant density simplest case: - spherical symmetric, i. e. no rotation no magnetic field 2/21/2021 U. R. M. E. Zielona Gora 27
TOV-equation with (1) and (2): 2/21/2021 U. R. M. E. Zielona Gora 28
R r 2/21/2021 U. R. M. E. Zielona Gora 29
(little exercise? ) 2/21/2021 U. R. M. E. Zielona Gora 30
stability of a constant density star: gravitational collapse 2/21/2021 U. R. M. E. Zielona Gora → time dependent metric 31
⇒ central pressure in non-relativistic stars remains finite 2/21/2021 U. R. M. E. Zielona Gora 32
reminder GR_6, slide 17 2/21/2021 U. R. M. E. Zielona Gora 33
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volume in internal Schwarzschildmetric 2/21/2021 U. R. M. E. Zielona Gora 35
2/21/2021 U. R. M. E. Zielona Gora 36
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