An overview of general relativity and space-time:
"This textbook equips Masters' students studying Physics and Astronomy with the necessary mathematical tools to understand the basics of General Relativity and its applications. It begins by reviewing classical mechanics with a more geometrically oriented language, continues with Special R...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton ; London ; New York
CRC Press
2022
|
| Ausgabe: | First edition |
| Schriftenreihe: | Series in astronomy and astrophysics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "This textbook equips Masters' students studying Physics and Astronomy with the necessary mathematical tools to understand the basics of General Relativity and its applications. It begins by reviewing classical mechanics with a more geometrically oriented language, continues with Special Relativity and, then onto a discussion on the pseudo-Riemannian space-times. Applications span from the inner and outer Schwarzschild solutions to gravitational wave, black holes, spherical relativistic hydrodynamics, and Cosmology. The goal is to limit the abstract formalization of the problems, to favor a hands-on approach with a number of exercises, without renouncing to a pedagogical derivation of the main mathematical tools and findings"-- |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xv, 255 Seiten Illustrationen, Diagramme, Karten |
| ISBN: | 9780367683047 9780367692889 |
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| 100 | 1 | |a Vittorio, Nicola |d 1954- |e Verfasser |0 (DE-588)1284127133 |4 aut | |
| 245 | 1 | 0 | |a An overview of general relativity and space-time |c Nicola Vittorio |
| 250 | |a First edition | ||
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press |c 2022 | |
| 264 | 4 | |c © 2023 | |
| 300 | |a xv, 255 Seiten |b Illustrationen, Diagramme, Karten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Series in astronomy and astrophysics | |
| 500 | |a Includes bibliographical references and index | ||
| 520 | 3 | |a "This textbook equips Masters' students studying Physics and Astronomy with the necessary mathematical tools to understand the basics of General Relativity and its applications. It begins by reviewing classical mechanics with a more geometrically oriented language, continues with Special Relativity and, then onto a discussion on the pseudo-Riemannian space-times. Applications span from the inner and outer Schwarzschild solutions to gravitational wave, black holes, spherical relativistic hydrodynamics, and Cosmology. The goal is to limit the abstract formalization of the problems, to favor a hands-on approach with a number of exercises, without renouncing to a pedagogical derivation of the main mathematical tools and findings"-- | |
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Datensatz im Suchindex
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| adam_text | Contents List of Figures............................................................................................................... xiii List of Boxes.................................................................... .............................................. xv Part I Chapter 1 From Forces to Curvature Space and Time: The Classical View.............................................. 3 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 Chapter 2 From Space and Time to Space-Time............................................. 19 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 Chapter 3 Introduction............... ................................................................ 3 MetricSpace...............................................................................3 Homogeneity and Isotropy of Space......................................... 4 Covariant or Contravariant Vector Components..................... 6 Motion of a Free Test-Particle.................................................. 8 Inertial Frames and Galileo’s Relativity Principle.................10 The Derivative of a Vector................. ..................................... 10 Velocity of Interactions and Second Newton’s Law............. 13 Homogeneity of Time: Energy Conservation........................ 14 Homogeneity of Space: The Third Newton’s Law............... 14 Planetary Motions.................................................................... 15 Non-Inertial Reference Frames................... 17 Introduction................ .................... 19 A Metric Space-
Time................................... ......................... 19 Homogeneity and Isotropy of the Minkowski Space-Time 21 Ordinary vs. Hyperbolic Rotations........................................ 23 Hyperbolic Rotations vs. Drag Velocities.............................. 24 Lorentz Transformations: A Graphical Approach............... 25 Proper Time and Proper Length................ ............................. 27 Motion of a Free Test-Particle............................................... 29 Four-Velocity and Four-Acceleration Vectors........ ..............30 Geodesics in Minkowski Space-Time................................... 31 Four-Momentum................................. 32 Relativistic Velocity Composition Law................................. 33 From Inertial to Non-Inertial Reference Frames............................. 35 3.1 3.2 Introduction.............................................................................. 35 Linear vs. Non-Linear Coordinate Transformations............ 35 vii
viii Contents 3.3 3.4 3.5 3.6 3.7 3.8 Chapter 4 Pseudo-Riemannian Spaces................................................................ 47 4.1 4.2 4.3 4.4 4.5 4.6 4.7 Chapter 5 Introduction.............................................................................. 47 Manifolds................................................................................. 47 How to Move to The Tangent Plane?..................................... 50 Vector Fields............................................................................ 51 Tensors..................................................................................... 53 How to Recognize Tensors..................................................... 54 General Covariance................................................................. 56 The Riemann-Christoffel Curvature Tensor..................................... 57 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 Chapter 6 Motion of a Free Test-Particle in a RotatingFrame.............. 37 Geodesics in a Generic Space-Time...................................... 39 Geodesic Motion in the Rotating ReferenceFrame..............40 Something More on Proper Time.......................................... 41 Clock Synchronization........................................................... 42 Proper Spatial Distances........................................................ 44 Introduction.............................................................................. 57 Parallel Transport in Curved Space: The 2DCase................ 57 More About the Christoffel
Symbols..................................... 59 Parallel Transport in Curved Manifolds................................60 Covariant Derivative and Covariant Differential.................. 61 Covariant Derivatives are Tensors......................................... 61 More on Geodesics................................................................. 62 More on Covariant Derivative............................................... 63 Covariant Derivative of a Tensor........................................... 64 The Riemann-Christoffel Curvature Tensor......................... 65 Second Covariant Derivatives.................................................67 Symmetries of the Riemann-Christoffel Tensor................... 67 From Non-inertial Frames to Gravity: Thè Equivalence Principle.................................................................. 71 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 Introduction...............................................................................71 The Equivalence Principle...................................................... 71 Switching Off Gravity: The Free-Fall.................................... 72 “Creating Gravity”: Non-Inertial Frames.............................. 73 The Gravity Case: A Metric Space.........................................75 The Motion of a Test-Particle in a Gravitational Field........ 77 Geodesic Deviation.................................................................. 78 Link Between Geometry and Dynamics................................ 79 Riemann-Christoffel Tensor in the Rotating Frame............. 81 Riemann-
Christoffel Tensor and Gravity........................ 81
Contents Part II Chapter 7 ix From Curvature to Observations Observational Test of the Equivalence Principle.............................. 85 7.1 7.2 7.3 7.4 7.5 7.6 7.7 Chapter 8 Field Equations in the “vacuum”....................................................... 95 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 Chapter 9 Introduction................ ............................................................ 95 Field Equations in the ’‘Vacuum”: Requirements................ 95 The Ricci Tensor...................................................................... 96 Gravitational Field Eqnations in the “Vacuum”.................. 97 The Einstein Tensor...,.............................................................99 Hilbert’s Action.......... ...................... 100 The Action for a Cosmological Constant........................... 102 The Geometry of Space-Time in the “Vacuum”................. 103 Test-Particles in the Schwarzschild Space-Time........................... 109 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 Chapter 10 Introduction..............................................................................85 Inertial vs. Gravitational Masses........................................... 85 Gravitational Time Dilation................................................... 86 The Global Positioning System - GPS................................. 86 Gravitational Redshift,...................... 87 The Long Gravitational Redshift Hunt................................. 88 The Nordtvedt Rffect..............................................................89
Introduction................. ...................... 109 The Schwarzschild Solution for a Point Mass................... 109 The “Embedding” Procedure................................................ 110 The Jebsen-Birķhoff Theorem........... ................................. Ill First Integrals in the Schwarzschild Space-Time................ 112 Energy Conservation ip GR.................................................. 113 The Radial Infall............................. ...;................................. 114 Orbits in a Schwarzschild Geometry. ................................. 115 Stable Circular Orbits: a д/З................ 118 The Case of a Non-Radial Infall: a - /3.......................... 119 Photons in the Schwarzschild Space-Time .. .......................119 The Classical Tests of General Relativity...................................... 123 10.1 10.2 10.3 10.4 10.5 10.6 10.7 Introduction................ ?............ 123 Planetary Motion.................................................................. 123 The Perihelion Shift of Mercury.................. 125 Light Ray’s Deflection.................. .......................................126 Gravitational Lensing................................. 130 The Schwarzschild Metric in Totally Isotropic Form.......133 Light Travel Lime in a Schwarzschild Geometry............. 134
x Chapter 11 Contents Gravitational Waves in the “Vacuum”............................................ 139 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10 11.11 11.12 Part III Chapter 12 From Singularities to Cosmological Scales Schwarzschild Black Holes...............................................................159 12.1 12.2 12.3 12.4 12.5 12.6 Chapter 13 Introduction............................................................................ 159 Singularities of the Schwarzschild Metric.......................... 159 Conformally-Flat Coordinates............................................. 161 Kruskal-Szekeres vs. Schwarzschild Coordinates............. 164 The Kruskal-Szekeres Plane............................................ 166 The Schwarzschild Black Hole........................................... 170 Field Equations in Non-“Empty” Space-Times.............................. 173 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 13.11 Chapter 14 Introduction........................................................................... 139 Linearized Gravity................................................................139 Gauge Transformations........................................................ 140 The Lorentz Gauge...............................................................141 Gravitational Waves............................................................. 142 TT Gauge.............................................................................. 144 Gauge Invariant Approach.................................................. 145 Field
Equations..................................................................... 147 Effects of a Gravitational Wave.......................................... 149 Interferometers...................................................................... 151 The Direct Detection of Gravitational Waves....................153 The Indirect Evidence for Gravitational Waves............... 154 Introduction............................................................................173 Field Equations: Requirements........................................... 173 Conservation Laws for a Relativistic Fluid....................... 174 The Matter Energy-Momentum Tensor..............................174 The EM Energy-Momentum Tensor................................... 177 An Isotropic Radiation Field...............................................179 Field Equations Inside a Matter/Energy Distribution...... 180 The Reissner-Nordstrom Solution...................................... 181 Orbits in a Reissner-Nordstrom Geometry........................ 184 Free-Fall on the Reissner-Nordstrom Black Hole........ . 185 The Ken Solution.................................................................188 Further Applications of the Field Equations.................................. 193 14.1 14.2 14.3 Introduction....................... 193 The Inner Schwarzschild Space-Time............................... 193 Proper vs. Observable Mass................................................ 198
Contents xi 14.4 14.5 Chapter 15 Theoretical Cosmology.................................................................... 209 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 15.10 15.11 15.12 15.13 15.14 15.15 15.16 15.17 15.18 Chapter 16 Introduction.......................................................................... 209 An Isotropic and Homogeneous Matter Distribution...... 209 The FLRW Metric............................................................... 210 The Spatial Sector of the FLRW Space-Time.................. 211 The Friedmann Equations................................................... 212 Equation of Motions........................................................... 213 Cosmological Parameters...................................................214 The De Sitter Model........................................................... 215 The Closed Friedmann Universe....................................... 215 The Open Friedmann Universe.......................................... 216 The Einstein-De Sitter Universe........................................ 217 A Flat, Λ-Dominated Universe.......................................... 217 Hņ and the Age of the Universe......................................... 218 The Cosmological Redshift............................................... 219 Comoving Distances........................................................... 221 The Proper Angular Diameter Distance........................... 222 The Proper Luminosity Distance....................................... 223 SNe La and Dark
Energy....................................................225 The Hot Big-Bang........................................................... 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 16.10 16.11 Appendix A Spherical Relativistic Hydrodynamics............................... 200 The Gravitational Collapse................................................. 205 227 Introduction......................................................................... 227 TheCMB.............................................................................227 A Radiation-Dominated Universe.....................................228 The Neutron-to-Baryon Ratio............................................ 229 Av’s Cosmic Background................................................. 230 Primordial Nucleosynthesis............................................... 231 Primordial Abundance of Light Nuclei........................... 232 The Recombination of the Primordial Plasma................. 234 The Puzzles of the Standard Model.................................. 235 An Early Accelerated Phase?............................................. 237 Cosmic Inflation..................................................................238 Exercises............................................................................................ 241 References________ ...-------------- -------------- ------------ -—------------------------- 247 Index, 253
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| adam_txt |
Contents List of Figures. xiii List of Boxes. . xv Part I Chapter 1 From Forces to Curvature Space and Time: The Classical View. 3 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 Chapter 2 From Space and Time to Space-Time. 19 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 Chapter 3 Introduction. . 3 MetricSpace.3 Homogeneity and Isotropy of Space. 4 Covariant or Contravariant Vector Components. 6 Motion of a Free Test-Particle. 8 Inertial Frames and Galileo’s Relativity Principle.10 The Derivative of a Vector. . 10 Velocity of Interactions and Second Newton’s Law. 13 Homogeneity of Time: Energy Conservation. 14 Homogeneity of Space: The Third Newton’s Law. 14 Planetary Motions. 15 Non-Inertial Reference Frames. 17 Introduction. . 19 A Metric Space-
Time. . 19 Homogeneity and Isotropy of the Minkowski Space-Time 21 Ordinary vs. Hyperbolic Rotations. 23 Hyperbolic Rotations vs. Drag Velocities. 24 Lorentz Transformations: A Graphical Approach. 25 Proper Time and Proper Length. . 27 Motion of a Free Test-Particle. 29 Four-Velocity and Four-Acceleration Vectors. .30 Geodesics in Minkowski Space-Time. 31 Four-Momentum. 32 Relativistic Velocity Composition Law. 33 From Inertial to Non-Inertial Reference Frames. 35 3.1 3.2 Introduction. 35 Linear vs. Non-Linear Coordinate Transformations. 35 vii
viii Contents 3.3 3.4 3.5 3.6 3.7 3.8 Chapter 4 Pseudo-Riemannian Spaces. 47 4.1 4.2 4.3 4.4 4.5 4.6 4.7 Chapter 5 Introduction. 47 Manifolds. 47 How to Move to The Tangent Plane?. 50 Vector Fields. 51 Tensors. 53 How to Recognize Tensors. 54 General Covariance. 56 The Riemann-Christoffel Curvature Tensor. 57 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 Chapter 6 Motion of a Free Test-Particle in a RotatingFrame. 37 Geodesics in a Generic Space-Time. 39 Geodesic Motion in the Rotating ReferenceFrame.40 Something More on Proper Time. 41 Clock Synchronization. 42 Proper Spatial Distances. 44 Introduction. 57 Parallel Transport in Curved Space: The 2DCase. 57 More About the Christoffel
Symbols. 59 Parallel Transport in Curved Manifolds.60 Covariant Derivative and Covariant Differential. 61 Covariant Derivatives are Tensors. 61 More on Geodesics. 62 More on Covariant Derivative. 63 Covariant Derivative of a Tensor. 64 The Riemann-Christoffel Curvature Tensor. 65 Second Covariant Derivatives.67 Symmetries of the Riemann-Christoffel Tensor. 67 From Non-inertial Frames to Gravity: Thè Equivalence Principle. 71 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 Introduction.71 The Equivalence Principle. 71 Switching Off Gravity: The Free-Fall. 72 “Creating Gravity”: Non-Inertial Frames. 73 The Gravity Case: A Metric Space.75 The Motion of a Test-Particle in a Gravitational Field. 77 Geodesic Deviation. 78 Link Between Geometry and Dynamics. 79 Riemann-Christoffel Tensor in the Rotating Frame. 81 Riemann-
Christoffel Tensor and Gravity. 81
Contents Part II Chapter 7 ix From Curvature to Observations Observational Test of the Equivalence Principle. 85 7.1 7.2 7.3 7.4 7.5 7.6 7.7 Chapter 8 Field Equations in the “vacuum”. 95 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 Chapter 9 Introduction. . 95 Field Equations in the ’‘Vacuum”: Requirements. 95 The Ricci Tensor. 96 Gravitational Field Eqnations in the “Vacuum”. 97 The Einstein Tensor.,.99 Hilbert’s Action. . 100 The Action for a Cosmological Constant. 102 The Geometry of Space-Time in the “Vacuum”. 103 Test-Particles in the Schwarzschild Space-Time. 109 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 Chapter 10 Introduction.85 Inertial vs. Gravitational Masses. 85 Gravitational Time Dilation. 86 The Global Positioning System - GPS. 86 Gravitational Redshift,. 87 The Long Gravitational Redshift Hunt. 88 The Nordtvedt Rffect.89
Introduction. . 109 The Schwarzschild Solution for a Point Mass. 109 The “Embedding” Procedure. 110 The Jebsen-Birķhoff Theorem. . Ill First Integrals in the Schwarzschild Space-Time. 112 Energy Conservation ip GR. 113 The Radial Infall. .;. 114 Orbits in a Schwarzschild Geometry. . 115 Stable Circular Orbits: a д/З. 118 The Case of a Non-Radial Infall: a -\/3. 119 Photons in the Schwarzschild Space-Time . .119 The Classical Tests of General Relativity. 123 10.1 10.2 10.3 10.4 10.5 10.6 10.7 Introduction. ?. 123 Planetary Motion. 123 The Perihelion Shift of Mercury. 125 Light Ray’s Deflection. .126 Gravitational Lensing. 130 The Schwarzschild Metric in Totally Isotropic Form.133 Light Travel Lime in a Schwarzschild Geometry. 134
x Chapter 11 Contents Gravitational Waves in the “Vacuum”. 139 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10 11.11 11.12 Part III Chapter 12 From Singularities to Cosmological Scales Schwarzschild Black Holes.159 12.1 12.2 12.3 12.4 12.5 12.6 Chapter 13 Introduction. 159 Singularities of the Schwarzschild Metric. 159 Conformally-Flat Coordinates. 161 Kruskal-Szekeres vs. Schwarzschild Coordinates. 164 The Kruskal-Szekeres Plane. 166 The Schwarzschild Black Hole. 170 Field Equations in Non-“Empty” Space-Times. 173 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 13.11 Chapter 14 Introduction. 139 Linearized Gravity.139 Gauge Transformations. 140 The Lorentz Gauge.141 Gravitational Waves. 142 TT Gauge. 144 Gauge Invariant Approach. 145 Field
Equations. 147 Effects of a Gravitational Wave. 149 Interferometers. 151 The Direct Detection of Gravitational Waves.153 The Indirect Evidence for Gravitational Waves. 154 Introduction.173 Field Equations: Requirements. 173 Conservation Laws for a Relativistic Fluid. 174 The Matter Energy-Momentum Tensor.174 The EM Energy-Momentum Tensor. 177 An Isotropic Radiation Field.179 Field Equations Inside a Matter/Energy Distribution. 180 The Reissner-Nordstrom Solution. 181 Orbits in a Reissner-Nordstrom Geometry. 184 Free-Fall on the Reissner-Nordstrom Black Hole. . 185 The Ken Solution.188 Further Applications of the Field Equations. 193 14.1 14.2 14.3 Introduction. 193 The Inner Schwarzschild Space-Time. 193 Proper vs. Observable Mass. 198
Contents xi 14.4 14.5 Chapter 15 Theoretical Cosmology. 209 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 15.10 15.11 15.12 15.13 15.14 15.15 15.16 15.17 15.18 Chapter 16 Introduction. 209 An Isotropic and Homogeneous Matter Distribution. 209 The FLRW Metric. 210 The Spatial Sector of the FLRW Space-Time. 211 The Friedmann Equations. 212 Equation of Motions. 213 Cosmological Parameters.214 The De Sitter Model. 215 The Closed Friedmann Universe. 215 The Open Friedmann Universe. 216 The Einstein-De Sitter Universe. 217 A Flat, Λ-Dominated Universe. 217 Hņ and the Age of the Universe. 218 The Cosmological Redshift. 219 Comoving Distances. 221 The Proper Angular Diameter Distance. 222 The Proper Luminosity Distance. 223 SNe La and Dark
Energy.225 The Hot Big-Bang. 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 16.10 16.11 Appendix A Spherical Relativistic Hydrodynamics. 200 The Gravitational Collapse. 205 227 Introduction. 227 TheCMB.227 A Radiation-Dominated Universe.228 The Neutron-to-Baryon Ratio. 229 Av’s Cosmic Background. 230 Primordial Nucleosynthesis. 231 Primordial Abundance of Light Nuclei. 232 The Recombination of the Primordial Plasma. 234 The Puzzles of the Standard Model. 235 An Early Accelerated Phase?. 237 Cosmic Inflation.238 Exercises. 241 References_ .-------------- -------------- ------------ -—------------------------- 247 Index, 253 |
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| id | DE-604.BV048691201 |
| illustrated | Illustrated |
| index_date | 2024-07-03T21:27:30Z |
| indexdate | 2024-07-10T09:46:15Z |
| institution | BVB |
| isbn | 9780367683047 9780367692889 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034065408 |
| oclc_num | 1370400772 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-703 |
| owner_facet | DE-19 DE-BY-UBM DE-703 |
| physical | xv, 255 Seiten Illustrationen, Diagramme, Karten |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Series in astronomy and astrophysics |
| spelling | Vittorio, Nicola 1954- Verfasser (DE-588)1284127133 aut An overview of general relativity and space-time Nicola Vittorio First edition Boca Raton ; London ; New York CRC Press 2022 © 2023 xv, 255 Seiten Illustrationen, Diagramme, Karten txt rdacontent n rdamedia nc rdacarrier Series in astronomy and astrophysics Includes bibliographical references and index "This textbook equips Masters' students studying Physics and Astronomy with the necessary mathematical tools to understand the basics of General Relativity and its applications. It begins by reviewing classical mechanics with a more geometrically oriented language, continues with Special Relativity and, then onto a discussion on the pseudo-Riemannian space-times. Applications span from the inner and outer Schwarzschild solutions to gravitational wave, black holes, spherical relativistic hydrodynamics, and Cosmology. The goal is to limit the abstract formalization of the problems, to favor a hands-on approach with a number of exercises, without renouncing to a pedagogical derivation of the main mathematical tools and findings"-- Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Raum-Zeit (DE-588)4302626-6 gnd rswk-swf Space and time / Mathematical models Allgemeine Relativitätstheorie (DE-588)4112491-1 s Raum-Zeit (DE-588)4302626-6 s DE-604 Erscheint auch als Online-Ausgabe 978-1-003-14125-9 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034065408&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vittorio, Nicola 1954- An overview of general relativity and space-time Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Raum-Zeit (DE-588)4302626-6 gnd |
| subject_GND | (DE-588)4112491-1 (DE-588)4302626-6 |
| title | An overview of general relativity and space-time |
| title_auth | An overview of general relativity and space-time |
| title_exact_search | An overview of general relativity and space-time |
| title_exact_search_txtP | An overview of general relativity and space-time |
| title_full | An overview of general relativity and space-time Nicola Vittorio |
| title_fullStr | An overview of general relativity and space-time Nicola Vittorio |
| title_full_unstemmed | An overview of general relativity and space-time Nicola Vittorio |
| title_short | An overview of general relativity and space-time |
| title_sort | an overview of general relativity and space time |
| topic | Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Raum-Zeit (DE-588)4302626-6 gnd |
| topic_facet | Allgemeine Relativitätstheorie Raum-Zeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034065408&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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