Spacetime, geometry and gravitation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2009
|
| Series: | Progress in Mathematical Physics
56 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 355 S. graph. Darst. |
| ISBN: | 9783764399702 |
Staff View
MARC
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| 245 | 1 | 0 | |a Spacetime, geometry and gravitation |c Pankaj Sharan |
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| 490 | 1 | |a Progress in Mathematical Physics |v 56 | |
| 650 | 4 | |a Allgemeine Relativitätstheorie | |
| 650 | 4 | |a Geometry | |
| 650 | 4 | |a Gravitation | |
| 650 | 4 | |a Relativity (Physics) | |
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Record in the Search Index
| _version_ | 1804140665804685312 |
|---|---|
| adam_text | CONTENTS PREFACE NOTATION AND CONVENTIONS I SPACETIME 1 1 INTRODUCTION 3
1.1 INERTIAL AND NON-INERTIAL FRAMES 4 1.2 SPACE AND TIME 11 1.3
LINEARLY ACCELERATED FRAME 16 1.4 NEED FOR THE RIEMANNIAN GEOMETRY 19
1.5 GENERAL THEORY OF RELATIVITY 20 1.6 TUTORIAL 23 1.7 LITERATURE 33 2
WHAT IS CURVATURE? 39 2.1 CONCEPT OF CURVATURE 39 2.2 THEOREMA
EGREGIUNF OF GAUSS 42 2.3 THE GAUSS EQUATION 44 2.4 THE GEODESIC
EQUATION 46 2.5 HISTORICAL NOTE ON RIEMANN 48 2.6 TUTORIAL ON SURFACES
49 3 GENERAL RELATIVITY BASICS 55 3.1 RIEMANNIAN SPACE 55 3.2 GENERAL
RELATIVITY 57 3.3 SOLVING THE EINSTEIN EQUATION 58 3.4 PARTICLE
TRAJECTORIES 59 3.5 PATH OF LIGHT RAYS 59 3.6 WEAK FIELD AND NEWTONIAN
LIMIT 59 3.7 TUTORIAL ON INDEXED QUANTITIES 61 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/992291763 DIGITALISIERT DURCH 7.12
TUTORIAL 129 VI CONTENTS 4 SPHERICALLY SYMMETRIC GRAVITATIONAL FIELD 65
4.1 THE SCHWARZSCHILD SOLUTION 65 4.2 CONSERVED QUANTITIES 67 4.3
PLANETARY MOTION 68 4.4 DEFLECTION OF LIGHT IN A GRAVITATIONAL FIELD 73
4.5 GRAVITATIONAL LENSING 76 4.6 TUTORIAL 77 II GEOMETRY 81 5 VECTORS
AND TENSORS 83 5.1 VECTOR SPACES 83 5.2 TENSOR PRODUCT 86 5.3 WEDGE OR
EXTERIOR PRODUCT 91 5.4 TUTORIAL 95 6 INNER PRODUCT 97 6.1 DEFINITION 97
6.2 ORTHONORMAL BASES 98 6.3 CORRESPONDENCE BETWEEN V AND V* 100 6.4
INNER PRODUCT IN F* 102 6.5 ORIENTATION AND CARTAN TENSOR 104 6.6 HODGE
*-OPERATOR 105 6.7 MINKOWSKI SPACE 109 6.8 TUTORIAL ILL 7 ELEMENTARY
DIFFERENTIAL GEOMETRY 115 7.1 COORDINATES AND FUNCTIONS 115 7.2 CURVES
AND TANGENT VECTORS 117 7.3 TANGENT SPACE 119 7.4 VECTOR FIELDS ON A
MANIFOLD 120 7.5 LOCAL BASIS FIELDS 122 7.6 LIE BRACKET 123 7.7
COTANGENT SPACE 123 7.8 TENSOR FIELDS 125 7.9 DEFINING TENSORS FIELDS
125 7.10 DIFFERENTIAL FORMS AND EXTERIOR DERIVATIVE 126 7.11 CLOSED AND
EXACT DIFFERENTIAL FORMS 128 CONTENTS VII 8 CONNECTION AND CURVATURE 133
8.1 DIRECTIONAL DERIVATIVE 133 8.2 TRANSFORMATION FORMULA FOR F* 136
8.3 GEODESIES 138 8.4 COVARIANT DERIVATIVE 139 8.5 ABSTRACT DEFINITION
140 8.6 TORSION TENSOR 141 8.7 CARTAN EQUATIONS 142 8.8 CURVATURE 2-FORM
145 8.9 RIEMANN-CHRISTOFFEL CURVATURE TENSOR 146 8.10 COMPONENTS OF THE
CURVATURE TENSOR 148 8.11 COVARIANT DERIVATIVE OF TENSOR FIELDS 148 8.12
TRANSPORT ROUND A CLOSED CURVE 152 8.13 TUTORIAL 152 9 RIEMANNIAN
GEOMETRY 155 9.1 RIEMANNIAN SPACE 155 9.2 LEVI-CIVITA CONNECTION 158 9.3
BIANCHI IDENTITY IN COMPONENTS 161 9.4 SYMMETRY PROPERTIES OF THE
CURVATURE TENSOR 163 9.5 RICCI, EINSTEIN AND WEYL TENSORS 165 9.6
GEODESIES 167 9.7 CALCULATING CONNECTION MATRIX 169 9.8 COVARIANT
RIEMANN TENSOR R(W.Z:X,Y) 171 9.9 ISOMETRIES AND KILLING VECTOR FIELDS
172 9.10 TUTORIAL 175 10 ADDITIONAL TOPICS IN GEOMETRY 181 10.1 MAPPINGS
BETWEEN MANIFOLDS 181 10.2 INTEGRAL CURVES OF A VECTOR FIELD 185 10.3
LIE DERIVATIVE 186 10.4 SUBMANIFOLDS 190 10.5 FROBENIUS THEOREM 191 10.6
INDUCED METRIC 192 10.7 HYPERSURFACE 192 10.8 HOMOGENEOUS AND ISOTROPIE
SPACES 193 10.9 MAXIMALLY SYMMETRIC SPACES 195 10.10 INTEGRATION 200
10.1 VIII CONTENTS III GRAVITATION 209 11 THE EINSTEIN EQUATION 211 11.1
STRESS-ENERGY-MOMENTUM TENSOR 212 11.2 RELATIVISTIC PERFECT FLUID 216
11.3 INTERPRETATION OF T» V . V = 0 219 11.4 ELECTROMAGNETIC FIELDS 219
11.5 ACTION PRINCIPLE 221 11.6 DIFFEOMORPHIC INVARIANCE 228 11.7
TUTORIAL 230 12 GENERAL FEATURES OF SPACETIME 237 12.1 SIGNATURE AND
TIME ORIENTABILITY 237 12.2 LOCAL FLATNESS 238 12.3 STATIC AND
STATIONARY SPACETIMES 240 12.4 FERMI TRANSPORT 241 12.5 FERMI-WALKER
TRANSPORT 244 12.6 PENROSE DIAGRAMS 246 12.7 SOLUTIONS OF EINSTEIN
EQUATIONS 249 12.8 TUTORIAL 250 13 WEAK GRAVITATIONAL FIELDS 257 13.1
EINSTEIN TENSOR FOR WEAK FIELDS 257 13.2 -FIXING A GAUGE 259 13.3 THE
SOLUTION 260 13.4 STATIC MASS DISTRIBUTION 260 13.5 SLOWLY ROTATING MASS
DISTRIBUTION 264 13.6 GRAVI-MAGNETIC EFFECTS 266 13.7 ENERGY AND
MOMENTUM 269 13.8 ENERGY PSUEDO-TENSOR 270 13.9 ENERGY-MOMENTUM FOR AN
ISOLATED SYSTEM 272 13.10 T V UP TO SECOND-ORDER 273 13.11
GRAVITATIONAL WAVES 274 13.12 DETECTION OF GRAVITATIONAL WAVES 280 13.13
TUTORIAL 282 14 SCHWARZSCHILD AND KERR SOLUTIONS 287 14.1 THE
SCHWARZSCHILD SOLUTION 288 14. CONTENTS IX 15 COSMOLOGY 317 15.1 THE
UNIVERSE 317 15.2 FRIEDMAN EQUATIONS 320 15.3 COSMOLOGICAL CONSTANT 322
15.4 MODELS OF THE UNIVERSE 323 15.5 HISTORY OF THE UNIVERSE 325 15.6
TUTORIAL ON THE FRW METRIC 325 16 SPECIAL TOPICS 329 16.1 THE GAUSS
EQUATION 329 16.2 THE GAUSS AND CODACCI EQUATIONS 333 16.3 BASES ON M
AND S 335 16.4 THE RAYCHAUDHURI EQUATION 341 INDEX 351
|
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| ctrlnum | (OCoLC)310400814 (DE-599)DNB992291763 |
| dewey-full | 539.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-sort | 3539.7 |
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| discipline | Physik Mathematik |
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| id | DE-604.BV035749015 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:03:36Z |
| institution | BVB |
| isbn | 9783764399702 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018609090 |
| oclc_num | 310400814 |
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| owner | DE-384 DE-83 DE-634 |
| owner_facet | DE-384 DE-83 DE-634 |
| physical | XIV, 355 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in Mathematical Physics |
| series2 | Progress in Mathematical Physics |
| spelling | Sharan, Pankaj Verfasser aut Spacetime, geometry and gravitation Pankaj Sharan Basel [u.a.] Birkhäuser 2009 XIV, 355 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in Mathematical Physics 56 Allgemeine Relativitätstheorie Geometry Gravitation Relativity (Physics) Space and time Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 s DE-604 Progress in Mathematical Physics 56 (DE-604)BV013823265 56 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018609090&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sharan, Pankaj Spacetime, geometry and gravitation Progress in Mathematical Physics Allgemeine Relativitätstheorie Geometry Gravitation Relativity (Physics) Space and time Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| subject_GND | (DE-588)4112491-1 |
| title | Spacetime, geometry and gravitation |
| title_auth | Spacetime, geometry and gravitation |
| title_exact_search | Spacetime, geometry and gravitation |
| title_full | Spacetime, geometry and gravitation Pankaj Sharan |
| title_fullStr | Spacetime, geometry and gravitation Pankaj Sharan |
| title_full_unstemmed | Spacetime, geometry and gravitation Pankaj Sharan |
| title_short | Spacetime, geometry and gravitation |
| title_sort | spacetime geometry and gravitation |
| topic | Allgemeine Relativitätstheorie Geometry Gravitation Relativity (Physics) Space and time Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| topic_facet | Allgemeine Relativitätstheorie Geometry Gravitation Relativity (Physics) Space and time |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018609090&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013823265 |
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