theorem 45.49 Hawking temperature; imported

open in the book · parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1865 · p. 1305

Rests on

depends_on proposition 45.46 The first law ¶
- depends_on proposition 45.43 Static acceleration and surface gravity ¶
  - depends_on theorem 45.30 Kerr solution; imported ¶
    - 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 ¶
  - depends_on theorem 45.1 Schwarzschild solution ¶ ↺
  - proves proof ch:04-schwarzschild-black-holes@proof-20 ¶
- depends_on proposition 45.45 Irreducible mass and the Christodoulou–Smarr mass formula ¶
  - depends_on lemma 45.44 Horizon area ¶
    - depends_on proposition 45.31 Horizons and the extremal bound ¶
      - depends_on theorem 45.30 Kerr solution; imported ¶ ↺
      - proves proof ch:04-schwarzschild-black-holes@proof-15 ¶
    - proves proof ch:04-schwarzschild-black-holes@proof-21 ¶
  - depends_on proposition 45.31 Horizons and the extremal bound ¶ ↺
  - proves proof ch:04-schwarzschild-black-holes@proof-22 ¶
- proves proof ch:04-schwarzschild-black-holes@proof-23 ¶
depends_on proposition 45.43 Static acceleration and surface gravity ¶ ↺

Supports

depends_on proposition 45.51 Evaporation: scale and timescale ¶

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`	→	Particle creation by black holes	derived	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1882
`depends_on`	→	The first law	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1883
`depends_on`	→	Static acceleration and surface gravity	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1883
`depends_on`	←	Evaporation: scale and timescale	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1928