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General relativity:

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Main Author:	Bartelmann, Matthias 1965- (Author)
Format:	Book
Language:	English
Published:	Heidelberg Heidelberg University Publishing [2019]
Series:	Lecture notes Physik
Subjects:	Allgemeine Relativitätstheorie Gravitationswellen Kosmologie Schwarze Löcher Theoretische Physik Lehrbuch
Online Access:	Volltext Inhaltsverzeichnis Inhaltsverzeichnis
Physical Description:	x, 234 Seiten Illustrationen, Diagramme 26 cm, 654 g
ISBN:	3947732600 9783947732609
DOI:	10.17885/heiup.534

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MARC


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adam_text	CONTENTS 1 INTRODUCTION 1 1.1 THE IDEA BEHIND GENERAL RELATIVITY ................................ 1 1.2 FUNDAMENTAL PROPERTIES OF G R A V ITY ................................ 4 1.3 CONSEQUENCES OF THE EQUIVALENCE PRINCIPLE ................... 7 1.4 FUTILE ATTEMPTS .............................................................. 9 2 DIFFERENTIAL GEOMETRY I 15 2.1 DIFFERENTIABLE MANIFOLDS ............................................... 15 2.2 THE TANGENT S P A C E ........................................................... 18 2.3 DUAL VECTORS AND T E N S O R S ............................................... 24 2.4 THE M ETRIC........................................................................ 27 3 DIFFERENTIAL GEOMETRY II 31 3.1 CONNECTIONS AND COVARIANT DERIVATIVES ......................... 31 3.2 G EODESICS........................................................................ 34 3.3 C U RV ATU RE........................................................................ 38 3.4 RIEMANNIAN CO N N ECTIO N S............................................... 42 4 PHYSICS IN GRAVITATIONAL FIELDS 47 4.1 MOTION OF PA RTIC LE S ......................................................... 47 4.2 MOTION OF L I G H T .............................................................. 49 4.3 ENERGY-MOMENTUM (NON-)CONSERVATION ......................... 54 4.4 THE NEWTONIAN L I M I T ..................................................... 58 5 DIFFERENTIAL GEOMETRY III 63 VIII CONTENTS 5.1 THE LIE DERIVATIVE............................................................ 63 5.2 KILLING VECTOR FIE LD S ........................................................ 68 5.3 DIFFERENTIAL FO RM S ............................................................ 69 5.4 INTEGRATION........................................................................ 73 6 EINSTEINS FIELD EQUATIONS 77 6.1 THE PHYSICAL MEANING OF CURVATURE ............................... 77 6.2 EINSTEINS FIELD EQ U A TIO N S............................................... 82 6.3 LAGRANGIAN FORM ULATION .................................................. 84 6.4 THE ENERGY-MOMENTUM T E N S O R ...................................... 86 7 WEAK GRAVITATIONAL FIELDS 91 7.1 LINEARISED THEORY OF GRAVITY............................................ 91 7.2 GAUGE TRANSFORM ATIONS .................................................. 93 7.3 NEARLY NEWTONIAN GRAVITY............................................... 95 7.4 GRAVITATIONAL W A V ES ........................................................ 100 8 THE SCHWARZSCHILD SOLUTION 111 8.1 CARTANS STRUCTURE EQUATIONS............................................ I L L 8.2 STATIONARY AND STATIC SP A C E TIM E S .................................. 115 8.3 THE SCHWARZSCHILD SOLUTION............................................ 116 8.4 SOLUTION OF THE FIELD E Q U A TIO N S ...................................... 120 9 THE SCHWARZSCHILD SPACETIME 127 9.1 ORBITS IN THE SCHWARZSCHILD SPACETIM E ......................... 127 9.2 COMPARISON TO THE KEPLER PRO B LEM ............................... 130 9.3 PERIHELION SHIFT AND LIGHT DEFLECTION ............................... 133 9.4 SPINS IN THE SCHWARZSCHILD S P A C E TIM E ......................... 137 10 SCHWARZSCHILD BLACK HOLES 143 10.1 THE SINGULARITY AT R = 2 M ............................................... 143 10.2 THE KRUSKAL CONTINUATION............................................... 147 CONTENTS IX 10.3 PHYSICAL MEANING OF THE KRUSKAL CONTINUATION ............ 152 10.4 REDSHIFT APPROACHING THE SCHWARZSCHILD RADIUS .... 156 11 CHARGED, ROTATING BLACK HOLES 161 11.1 THE REISSNER-NORDSTROM SOLUTION .................................. 161 11.2 THE KERR-NEWMAN SOLUTION............................................ 164 11.3 MOTION NEAR A KERR BLACK H O L E ...................................... 172 11.4 ENTROPY AND TEMPERATURE OF A BLACK H O L E ...................... 177 12 HOMOGENEOUS, ISOTROPIC COSMOLOGY 183 12.1 SPHERICALLY-SYMMETRIC SPACETIM ES ............................... 183 12.2 HOMOGENEOUS AND ISOTROPIC SP A C E TIM E S ...................... 187 12.3 FRIEDMANNS E Q U A TIO N S .................................................. 191 12.4 DENSITY EVOLUTION AND R E D S H IF T ..................................... 194 13 RELATIVISTIC ASTROPHYSICS 199 13.1 LIGHT B U N D LE S ................................................................. 199 13.2 GRAVITATIONAL LE N S IN G ..................................................... 201 13.3 THE TOLMAN-OPPENHEIMER-VOLKOFF SO LU TIO N ................ 206 13.4 THE MASS OF NON-ROTATING NEUTRON S TA R S ......................... 209 A ELECTRODYNAMICS 213 A.L ELECTROMAGNETIC FIELD TENSOR ......................................... 213 A.2 MAXWELLS E Q U A TIO N S ..................................................... 213 A. 3 LAGRANGE DENSITY AND ENERGY-MOMENTUM TENSOR .... 214 B DIFFERENTIAL GEOMETRY 217 B. L MANIFOLD .................................................................... 217 B.2 TANGENT AND DUAL SPACES ............................................... 217 B.3 T E N S O R S ........................................................................... 218 B.4 COVARIANT DERIVATIVE........................................................ 219 B.5 PARALLEL TRANSPORT AND GEODESICS ..................................... 220 B.6 TORSION AND CURVATURE..................................................... 220 B.7 PULL-BACK, LIE DERIVATIVE, KILLING FIELDS ........................ 221 B.8 DIFFERENTIAL FO RM S ........................................................... 223 B.9 CARTANS STRUCTURE EQUATIONS ........................................... 224 B.10 DIFFERENTIAL OPERATORS AND INTEGRATION............................ 225 C PENROSE-CARTER DIAGRAMS 227
adam_txt	CONTENTS 1 INTRODUCTION 1 1.1 THE IDEA BEHIND GENERAL RELATIVITY . 1 1.2 FUNDAMENTAL PROPERTIES OF G R A V ITY . 4 1.3 CONSEQUENCES OF THE EQUIVALENCE PRINCIPLE . 7 1.4 FUTILE ATTEMPTS . 9 2 DIFFERENTIAL GEOMETRY I 15 2.1 DIFFERENTIABLE MANIFOLDS . 15 2.2 THE TANGENT S P A C E . 18 2.3 DUAL VECTORS AND T E N S O R S . 24 2.4 THE M ETRIC. 27 3 DIFFERENTIAL GEOMETRY II 31 3.1 CONNECTIONS AND COVARIANT DERIVATIVES . 31 3.2 G EODESICS. 34 3.3 C U RV ATU RE. 38 3.4 RIEMANNIAN CO N N ECTIO N S. 42 4 PHYSICS IN GRAVITATIONAL FIELDS 47 4.1 MOTION OF PA RTIC LE S . 47 4.2 MOTION OF L I G H T . 49 4.3 ENERGY-MOMENTUM (NON-)CONSERVATION . 54 4.4 THE NEWTONIAN L I M I T . 58 5 DIFFERENTIAL GEOMETRY III 63 VIII CONTENTS 5.1 THE LIE DERIVATIVE. 63 5.2 KILLING VECTOR FIE LD S . 68 5.3 DIFFERENTIAL FO RM S . 69 5.4 INTEGRATION. 73 6 EINSTEINS FIELD EQUATIONS 77 6.1 THE PHYSICAL MEANING OF CURVATURE . 77 6.2 EINSTEINS FIELD EQ U A TIO N S. 82 6.3 LAGRANGIAN FORM ULATION . 84 6.4 THE ENERGY-MOMENTUM T E N S O R . 86 7 WEAK GRAVITATIONAL FIELDS 91 7.1 LINEARISED THEORY OF GRAVITY. 91 7.2 GAUGE TRANSFORM ATIONS . 93 7.3 NEARLY NEWTONIAN GRAVITY. 95 7.4 GRAVITATIONAL W A V ES . 100 8 THE SCHWARZSCHILD SOLUTION 111 8.1 CARTANS STRUCTURE EQUATIONS. I L L 8.2 STATIONARY AND STATIC SP A C E TIM E S . 115 8.3 THE SCHWARZSCHILD SOLUTION. 116 8.4 SOLUTION OF THE FIELD E Q U A TIO N S . 120 9 THE SCHWARZSCHILD SPACETIME 127 9.1 ORBITS IN THE SCHWARZSCHILD SPACETIM E . 127 9.2 COMPARISON TO THE KEPLER PRO B LEM . 130 9.3 PERIHELION SHIFT AND LIGHT DEFLECTION . 133 9.4 SPINS IN THE SCHWARZSCHILD S P A C E TIM E . 137 10 SCHWARZSCHILD BLACK HOLES 143 10.1 THE SINGULARITY AT R = 2 M . 143 10.2 THE KRUSKAL CONTINUATION. 147 CONTENTS IX 10.3 PHYSICAL MEANING OF THE KRUSKAL CONTINUATION . 152 10.4 REDSHIFT APPROACHING THE SCHWARZSCHILD RADIUS . 156 11 CHARGED, ROTATING BLACK HOLES 161 11.1 THE REISSNER-NORDSTROM SOLUTION . 161 11.2 THE KERR-NEWMAN SOLUTION. 164 11.3 MOTION NEAR A KERR BLACK H O L E . 172 11.4 ENTROPY AND TEMPERATURE OF A BLACK H O L E . 177 12 HOMOGENEOUS, ISOTROPIC COSMOLOGY 183 12.1 SPHERICALLY-SYMMETRIC SPACETIM ES . 183 12.2 HOMOGENEOUS AND ISOTROPIC SP A C E TIM E S . 187 12.3 FRIEDMANNS E Q U A TIO N S . 191 12.4 DENSITY EVOLUTION AND R E D S H IF T . 194 13 RELATIVISTIC ASTROPHYSICS 199 13.1 LIGHT B U N D LE S . 199 13.2 GRAVITATIONAL LE N S IN G . 201 13.3 THE TOLMAN-OPPENHEIMER-VOLKOFF SO LU TIO N . 206 13.4 THE MASS OF NON-ROTATING NEUTRON S TA R S . 209 A ELECTRODYNAMICS 213 A.L ELECTROMAGNETIC FIELD TENSOR . 213 A.2 MAXWELLS E Q U A TIO N S . 213 A. 3 LAGRANGE DENSITY AND ENERGY-MOMENTUM TENSOR . 214 B DIFFERENTIAL GEOMETRY 217 B. L MANIFOLD . 217 B.2 TANGENT AND DUAL SPACES . 217 B.3 T E N S O R S . 218 B.4 COVARIANT DERIVATIVE. 219 B.5 PARALLEL TRANSPORT AND GEODESICS . 220 B.6 TORSION AND CURVATURE. 220 B.7 PULL-BACK, LIE DERIVATIVE, KILLING FIELDS . 221 B.8 DIFFERENTIAL FO RM S . 223 B.9 CARTANS STRUCTURE EQUATIONS . 224 B.10 DIFFERENTIAL OPERATORS AND INTEGRATION. 225 C PENROSE-CARTER DIAGRAMS 227
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spelling	Bartelmann, Matthias 1965- Verfasser (DE-588)141554185 aut General relativity Matthias Bartelmann, Institut für Theoretische Astrophysik Universität Heidelberg Heidelberg Heidelberg University Publishing [2019] x, 234 Seiten Illustrationen, Diagramme 26 cm, 654 g txt rdacontent n rdamedia nc rdacarrier Lecture notes Physik Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Allgemeine Relativitätstheorie Gravitationswellen Kosmologie Schwarze Löcher Theoretische Physik (DE-588)4123623-3 Lehrbuch gnd-content Allgemeine Relativitätstheorie (DE-588)4112491-1 s DE-604 Erscheint auch als Online-Ausgabe, PDF 978-3-947732-59-3 https://doi.org/10.17885/heiup.534 Verlag kostenfrei Volltext B:DE-101 application/pdf https://d-nb.info/1193505593/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032337016&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Bartelmann, Matthias 1965- General relativity Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd
subject_GND	(DE-588)4112491-1 (DE-588)4123623-3
title	General relativity
title_auth	General relativity
title_exact_search	General relativity
title_exact_search_txtP	General relativity
title_full	General relativity Matthias Bartelmann, Institut für Theoretische Astrophysik Universität Heidelberg
title_fullStr	General relativity Matthias Bartelmann, Institut für Theoretische Astrophysik Universität Heidelberg
title_full_unstemmed	General relativity Matthias Bartelmann, Institut für Theoretische Astrophysik Universität Heidelberg
title_short	General relativity
title_sort	general relativity
topic	Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd
topic_facet	Allgemeine Relativitätstheorie Lehrbuch
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