Black holes

Black holes

Автор(ы): Townsend P. K.

06.10.2007
Год изд.: 1997
Описание: These notes were written to accompany a course taught in Part III of the Cambridge University Mathematical Tripos. There are occasional references to questions on four ‘example sheets’, which can be found in the Appendix. From the table of contents: Gravitational Collapse; Schwarzschild Black Hole; Charged Black Holes; Rotating Black Holes; Energy and Angular Momentum; Black Hole Mechanics; Hawking Radiation.
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1 Gravitational Collapse [6]
1.1 The Chandrasekhar Limit [6]
1.2 Neutron Stars [8]
2 Schwarzschild Black Hole [11]
2.1 Test particles: geodesies and affine parameterization [11]
2.2 Symmetries and Killing Vectors [13]
2.3 Spherically-Symmetric Pressure Free Collapse [15]
2.3.1 Black Holes and White Holes [18]
2.3.2 Kruskal-Szekeres Coordinates [20]
2.3.3 Eternal Black Holes [24]
2.3.4 Time translation in the Kruskal Manifold [26]
2.3.5 Null Hypersurfaces [27]
2.3.6 Killing Horizons [29]
2.3.7 Rindler spacetime [33]
2.3.8 Surface Gravity and Hawking Temperature [37]
2.3.9 Tolman Law — Unruh Temperature [39]
2.4 Carter-Penrose Diagrams [40]
2.4.1 Conformal Compactification [40]
2.5 Asymptopia [47]
2.6 The Event Horizon [49]
2.7 Black Holes vs. Naked Singularities [53]
3 Charged Black Holes [56]
3.1 Reissner-Nordstrom [56]
3.2 Pressure-Free Collapse to RN [65]
3.3 Cauchy Horizons [67]
3.4 Isotropic Coordinates for RN [70]
3.4.1 Nature of Internal oo in Extreme RN [74]
3.4.2 Multi Black Hole Solutions [75]
4 Rotating Black Holes [76]
4.1 Uniqueness Theorems [76]
4.1.1 Spacetime Symmetries [76]
4.2 The Kerr Solution [78]
4.2.1 Angular Velocity of the Horizon [84]
4.3 The Ergosphere [88]
4.4 The Penrose Process [88]
4.4.1 Limits to Energy Extraction [89]
4.4.2 Super-radiance [90]
5 Energy and Angular Momentum [93]
5.1 Covariant Formulation of Charge Integral [93]
5.2 ADM energy [94]
5.2.1 Alternative Formula for ADM Energy [96]
5.3 Komar Integrals [97]
5.3.1 Angular Momentum in Axisymmetric Spacetimes [98]
5.4 Energy Conditions [99]
6 Black Hole Mechanics [101]
6.1 Geodesic Congruences [101]
6.1.1 Expansion and Shear [106]
6.2 The Laws of Black Hole Mechanics [109]
6.2.1 Zerothlaw [109]
6.2.2 Smarr’s Formula [110]
6.2.3 First Law [112]
6.2.4 The Second Law (Hawking’s Area Theorem) [113]
7 Hawking Radiation [119]
7.1 Quantization of the Free Scalar Field [119]
7.2 Particle Production in Non-Stationary Spacetimes [123]
7.3 Hawking Radiation [125]
7.4 Black Holes and Thermodynamics [129]
7.4.1 The Information Problem [130]
A Example Sheets [132]
A.1 Example Sheet 1 [132]
A.2 Example Sheet 2 [135]
A.3 Example Sheet 3 [138]
А.4 Example Sheet 4 [141]

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