phenomenon 45.24 Compact objects exist above every cold-support limit

open in the book · parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1062 · p. 1297

phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt

Rests on

depends_on proposition 45.22 The view from outside: exponential freezing ¶
- depends_on proposition 45.21 Radial plunge: the cycloid ¶
  - depends_on proposition 45.6 Radial equation and effective potential ¶
    - depends_on proposition 13.141 The invariant of a Killing vector along a geodesic ¶
      - depends_on definition 13.149 Metric compatibility ¶
      - depends_on definition 13.146 Parallel transport and autoparallels ¶
      - depends_on proposition 13.140 Killing's equation ¶
      - proves proof ch:11-manifolds-tensors-curvature@proof-38 ¶
    - depends_on proposition 40.3 Normalization of the four-velocity ¶
      - depends_on definition 38.6 Minkowski metric and interval ¶
      - depends_on equation 40.2 eq:rdyn-fourvelocity ¶
      - proves proof ch:04-relativistic-dynamics@proof-1 ¶
    - depends_on theorem 45.1 Schwarzschild solution ¶
      - depends_on equation 13.306 eq:mfd-riemann ¶
      - depends_on postulate 43.1 Geodesic motion ¶
      - depends_on theorem 13.150 Levi-Civita connection and contorsion ¶
      - proves proof ch:04-schwarzschild-black-holes@proof-1 ¶
    - proves proof ch:04-schwarzschild-black-holes@proof-3 ¶
  - proves proof ch:04-schwarzschild-black-holes@proof-12 ¶
- depends_on remark 45.3 Gravitational redshift from the static metric ¶
- proves proof ch:04-schwarzschild-black-holes@proof-13 ¶
depends_on theorem 45.23 Oppenheimer–Snyder collapse ¶
- depends_on proposition 45.21 Radial plunge: the cycloid ¶ ↺
- depends_on theorem 45.4 Jebsen–Birkhoff ¶
  - depends_on equation 13.306 eq:mfd-riemann ¶ ↺
  - depends_on theorem 45.1 Schwarzschild solution ¶ ↺
  - proves proof ch:04-schwarzschild-black-holes@proof-2 ¶
- proves proof ch:04-schwarzschild-black-holes@prooflink-1 ¶
depends_on theorem 45.27 Penrose; imported ¶
- depends_on definition 45.25 Trapped surface ¶
proves proof ch:04-schwarzschild-black-holes@proof-14 ¶

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type	direction	node	provenance	where
`cites`	→	Observation of Gravitational Waves from a Binary Black Hole Merger	derived	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1069
`cites`	→	GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs	derived	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1069
`cites`	→	On Continued Gravitational Contraction	derived	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1076
`cites`	→	X-Ray Properties of Black-Hole Binaries	derived	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1067
`depends_on`	→	The view from outside: exponential freezing	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1078
`depends_on`	→	Oppenheimer–Snyder collapse	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1078
`depends_on`	→	Penrose; imported	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1078
`proves`	←	ch:04-schwarzschild-black-holes@proof-14	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1081