theorem 44.27 Newtonian correspondence of the field equations
open in the book ·
parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1136
· p. 1274
Rests on
-
depends_on
definition 44.15
Dust
¶
-
depends_on
definition 40.2
Four-velocity
¶
-
depends_on
definition 38.12
Proper time
¶
-
depends_on
definition 38.6
Minkowski metric and interval
¶
- depends_on proposition 38.5 The invariant interval ¶
- depends_on proposition 38.5 The invariant interval ¶ ↺
-
depends_on
definition 38.6
Minkowski metric and interval
¶
-
depends_on
definition 40.1
Four-vector
¶
- depends_on definition 38.6 Minkowski metric and interval ¶ ↺
- depends_on equation 38.14 eq:lor-invariance-condition ¶
-
depends_on
definition 38.12
Proper time
¶
-
depends_on
phenomenon 40.6
Mass–energy equivalence
¶
- depends_on equation 40.4 eq:rdyn-E-p ¶
- proves proof ch:04-relativistic-dynamics@proof-3 ¶
-
depends_on
definition 40.2
Four-velocity
¶
-
depends_on
proposition 44.26
Newtonian limit of geodesic motion
¶
- depends_on postulate 43.1 Geodesic motion ¶
- proves proof ch:03-einstein-field-equations@proof-14 ¶
-
depends_on
proposition 44.4
Trace-reversed form
¶
-
depends_on
postulate 44.3
Einstein field equations
¶
-
depends_on
definition 44.2
Einstein tensor
¶
-
depends_on
definition 13.153
Contractions
¶
- depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶
- depends_on theorem 13.152 Riemann tensor; Ricci identity with torsion ¶
-
depends_on
definition 13.153
Contractions
¶
-
depends_on
definition 44.2
Einstein tensor
¶
- proves proof ch:03-einstein-field-equations@proof-1 ¶
-
depends_on
postulate 44.3
Einstein field equations
¶
- proves proof ch:03-einstein-field-equations@proof-15 ¶
Supports
- depends_on corollary 44.35 The field equations are essentially unique ¶
- depends_on phenomenon 49.6 A maximum mass for a cold degenerate star ¶
- depends_on phenomenon 49.16 Pulsars: clocks at nuclear density ¶
- depends_on phenomenon 49.14 A neutron star is observed being born ¶
- depends_on proposition 44.29 Linearized field equations ¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
cites |
→ | Die Feldgleichungen der Gravitation | derived | parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1152 |
depends_on |
→ | Dust | declared | parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1153 |
depends_on |
→ | Newtonian limit of geodesic motion | declared | parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1153 |
depends_on |
→ | Trace-reversed form | declared | parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1153 |
depends_on |
← | The field equations are essentially unique | declared | parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1465 |
depends_on |
← | A maximum mass for a cold degenerate star | declared | parts/05-general-relativity-cosmology/08-compact-stars.tex:383 |
depends_on |
← | Pulsars: clocks at nuclear density | declared | parts/05-general-relativity-cosmology/08-compact-stars.tex:1049 |
depends_on |
← | A neutron star is observed being born | declared | parts/05-general-relativity-cosmology/08-compact-stars.tex:895 |
depends_on |
← | Linearized field equations | declared | parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1265 |
proves |
← | ch:03-einstein-field-equations@proof-15 | declared | parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1157 |