Geometry of black holes:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Oxford
Oxford University Press
[2020]
|
| Schriftenreihe: | International series of monographs on physics
169 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032403397&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xiv, 389 Seiten Illustrationen, Diagramme |
| ISBN: | 9780198855415 |
Internformat
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0202 PHY 964 2021 B 1985 |
|---|---|
| DE-BY-TUM_katkey | 2600400 |
| DE-BY-TUM_location | 02 |
| DE-BY-TUM_media_number | 040009528263 |
| _version_ | 1821936226640330754 |
| adam_text | Contents PART I GLOBAL LORENTZIAN GEOMETRY 1 Basic notions 1.1 Conventions 1.2 Topology and manifolds 1.3 Lorentzian manifolds 1.4 The Levi-Civita connection,curvature 1.5 Geodesics 1.6 Moving frames 3 3 3 6 8 11 12 2 Elements of causality 2.1 Time orientation 2.2 Normal coordinates 2.3 Causal paths 2.4 Futures, pasts 2.5 Extendible and inextendiblepaths 2.5.1 Maximally extended geodesics 2.6 Accumulation curves 2.6.1 Achronal causal curves 2.7 Causality conditions 2.8 Global hyperbolicity 2.9 ^-Domains of dependence 2.10 Cauchy horizons 2.10.1 Semi-convexity 2.10.2 Points of differentiability 2.10.3 Alexandrov differentiability 2.11 Cauchy surfaces, time functions 21 21 24 31 35 44 46 47 52 53 56 61 67 69 72 78 79 3 Some applications 3.1 Conformal completions 3.2 Null splitting theorems 3.3 Topological censorship 3.3.1 Horizon topology 3.3.2 Trapped surfaces 3.3.3 Causality in spacetimes with boundary 3.3.4 Spacetimes with timelike boundary 3.3.5 Kaluza-Klein asymptotics 3.3.6 Spacetimes with uniform Kaluza-Klein ends 3.3.7 Weakly future trapped surfaces areinvisible 3.3.8 Spacetimes with a conformal completion at null infinity 3.4 Incompleteness theorems 3.5 Area theorem 3.5.1 Hawking and Ellis’s area theorem 3.6 Causality and wave equations PART II 4 85 85 88 89 90 90 92 92 95 97 101 104 108 109 112 113 BLACK HOLES An introduction to black holes 117
xii Contents 4.1 4.2 4.3 4.4 4.5 4.6 4.7 5 Black holes as astrophysical objects The Schwarzschild solution and its extensions 4.2.1 The singularity r = 0 4.2.2 Eddington-Finkelstein extension 4.2.3 The Kruskal-Szekeres extension 4.2.4 Other coordinate systems, higher dimensions 4.2.5 Some geodesics 4.2.6 The Flamm paraboloid 4.2.7 Fronsdal’s embedding 4.2.8 Conformal Carter-Penrose diagrams 4.2.9 Weyl coordinates Some general notions 4.3.1 Isometries 4.3.2 Killing horizons 4.3.3 Surface gravity 4.3.4 Zeroth law 4.3.5 The orbit-space geometry near Killing horizons 4.3.6 Near-horizon geometry 4.3.7 Asymptotically flat stationary metrics 4.3.8 Domains of outer communications, event horizons 4.3.9 Adding bifurcation surfaces 4.3.10 Black strings and branes Extensions 4.4.1 Distinct extensions 4.4.2 Inextendibility 4.4.3 Uniqueness of a class of extensions The Reissner-Nordström metrics The Kerr metric 4.6.1 Komar integrals 4.6.2 Non-degenerate solutions (a2 m2):bifurcate horizons 4.6.3 Surface gravity, thermodynamical identities 4.6.4 Carter’s time machine 4.6.5 Extreme case a2 = m2 4.6.6 Maximal slices 4.6.7 The Ernst map for the Kerr metric 4.6.8 The orbit-space metric 4.6.9 Kerr-Schild coordinates 4.6.10 Dain coordinates 4.6.11 Weyl coordinates Majumdar-Papapetrou multi-black holes Further selected solutions 5.1 The Kerr-de Sitter/anti-de Sitter metrics (with C.Ölz) 5.1.1 Asymptotic behaviour 5.1.2 The axis 5.1.3 The ‘singular ring’ Σ = 0 5.1.4 Killing horizons 5.1.5 The number and nature of Killing horizons 5.1.6 Extensions across Killing horizons 5.1.7 Principal null
directions 5.2 The Kerr-Newman֊(anti-)de Sitter metrics (withC. Ölz) 5.2.1 The ‘ring singularity’ 5.2.2 Extensions across Killing horizons 117 124 128 129 132 136 142 143 145 146 147 149 149 150 151 153 158 159 164 166 166 167 167 168 168 170 172 174 181 182 186 187 188 190 191 191 192 193 194 195 200 200 203 205 205 206 207 208 213 213 214 215
Contents xiii 5.3 5.4 5.5 5.2.3 The number and nature of horizons, Λ 0 5.2.4 The number and nature of horizons, Λ 0 Emparan-Reall ‘black rings’ 5.3.1 The region x є {£ւ,£շ} 5.3.2 Signature 5.3.3 The rotation axis у = ξι 5.3.4 Asymptotic flatness 5.3.5 The limits у -¥ ±oo 5.3.6 Ergoregion 5.3.7 Black ring 5.3.8 Some further properties 5.3.9 A Kruskal-Szekeres type extension 5.3.10 Global structure 5.3.11 Other coordinate systems Rasheed’s metrics 5.4.1 Zeros of the denominators 5.4.2 Regularity at the outer Killing horizonH+ 5.4.3 Asymptotic behaviour 5.4.4 Global charges Birmingham metrics 5.5.1 ‘Thermodynamics’ 5.5.2 Curvature 5.5.3 Euclidean Birmingham (Schwarzschild-(anti-)de Sitter) metrics 5.5.4 Horowitz-Myers-type metrics 215 220 221 223 224 225 225 228 229 229 230 235 237 241 242 244 247 248 249 250 251 252 255 257 6 Extensions, conformal diagrams 6.1 Causality for a class of block-diagonal metrics 6.1.1 Riemannian aspects 6.1.2 Causality 6.2 The building blocks 6.2.1 Two-dimensional Minkowski spacetime 6.2.2 Higher dimensional Minkowski spacetime 6.2.3 ƒ F՜1 diverging at both ends 6.2.4 ƒ F՜1 diverging at one end only 6.2.5 Birmingham metrics with A 0 and m = 0 6.3 Putting things together 6.3.1 Four-blocks gluing 6.3.2 Two-blocks gluing 6.4 General rules 6.5 Black holes / white holes 6.6 Birmingham metrics 6.6.1 Cylindrical solutions 6.6.2 Naked singularities 6.6.3 Spatially periodic time-symmetric initialdata 259 259 260 261 262 263 264 266 267 268 269 270 274 275 276 277 277 278 278 7 Projection diagrams 7.1 The definition 7.2 Simplest examples 7.3 The Kerr
metrics 7.3.1 Uniqueness of extensions 7.3.2 Two-dimensional submanifolds of Kerrspacetime 7.3.3 The orbit-space metric on Л?/ J(l) 7.4 The Kerr-Newman metrics 280 280 282 284 288 289 291 291
xiv Contents 7.5 7.6 7.7 8 7.4.1 The Kerr-de Sitter metrics 7.4.2 The Kerr-Newman-de Sitter metrics 7.4.3 The Kerr-Newman-anti-de Sitter metrics The Emparan-Reall metrics The Pomeransky-Senkov metrics U(l) x U(l) symmetry with compact Cauchy horizons 7.7.1 Building blocks and periodic identifications 7.7.2 Taub-NUT metrics Dynamical black holes 8.1 Robinson-Trautman spacetimes 8.1.1 m 0 8.1.2 m 0 8.1.3 A^O 8.2 Initial data sets with trapped surfaces 8.2.1 Brill-Lindquist initial data 8.2.2 The ‘many Schwarzschild’ initial data 8.2.3 Black holes and conformal gluing methods 8.3 Black holes without Seri 8.3.1 The shortcomings of the conformal approach 8.3.2 Numerical black holes 8.3.3 Naive black holes 8.4 Apparent horizons 8.4.1 Quasi-local black holes 8.5 Christodoulou’s trapped surfaces 8.6 Small perturbations of the Schwarzschild metric 293 295 298 299 304 306 307 308 312 312 314 317 318 321 321 322 323 324 324 325 326 328 329 333 334 Appendices A The Lie derivative В Covariant derivatives C Curvature C.l Bianchi identities C.2 Pair interchange symmetry C.3 Curvature of product metrics C.4 Analyticity of isometries D Exterior algebra D.l Hodge duality E Null hyperplanes F The geometry of null hypersurfaces G The general relativistic Cauchy problem H A collection of identities H.l ADM notation H.2 Some commutators H.3 Bianchi identities H.4 Linearizations H.5 Warped products H.6 Conformal transformations H.7 Laplacians on tensors H.8 Stationary metrics 337 337 338 341 344 346 348 349 350 353 354 356 363 364 364 364 365 365 365 366 367 367 References 368 Index 385
|
| any_adam_object | 1 |
| author | Chruściel, Piotr T. 1957- |
| author_GND | (DE-588)11348156X |
| author_facet | Chruściel, Piotr T. 1957- |
| author_role | aut |
| author_sort | Chruściel, Piotr T. 1957- |
| author_variant | p t c pt ptc |
| building | Verbundindex |
| bvnumber | BV046995622 |
| classification_rvk | US 2200 |
| classification_tum | PHY 964 |
| ctrlnum | (OCoLC)1192521489 (DE-599)KXP172707646X |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV046995622 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T19:06:48Z |
| institution | BVB |
| isbn | 9780198855415 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032403397 |
| oclc_num | 1192521489 |
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| physical | xiv, 389 Seiten Illustrationen, Diagramme |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | Oxford University Press |
| record_format | marc |
| series | International series of monographs on physics |
| series2 | International series of monographs on physics |
| spellingShingle | Chruściel, Piotr T. 1957- Geometry of black holes International series of monographs on physics Schwarzes Loch (DE-588)4053793-6 gnd Geometrische Methode (DE-588)4156715-8 gnd |
| subject_GND | (DE-588)4053793-6 (DE-588)4156715-8 |
| title | Geometry of black holes |
| title_auth | Geometry of black holes |
| title_exact_search | Geometry of black holes |
| title_full | Geometry of black holes Piotr T. Chruściel |
| title_fullStr | Geometry of black holes Piotr T. Chruściel |
| title_full_unstemmed | Geometry of black holes Piotr T. Chruściel |
| title_short | Geometry of black holes |
| title_sort | geometry of black holes |
| topic | Schwarzes Loch (DE-588)4053793-6 gnd Geometrische Methode (DE-588)4156715-8 gnd |
| topic_facet | Schwarzes Loch Geometrische Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032403397&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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Teilbibliothek Physik
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