Pub Date : 2021-11-02DOI: 10.1093/oso/9780192895646.003.0007
A. Steane
The theory of weak gravitational waves is discussed at length. The transverse traceless gauge is described, and the behaviour of plane wave solutions obtained. The impact of a wave on physical objects, and hence methods for their detection, are calculated. The laser interferometric gravitational wave detector is described. Sources such as binary stars are considered. The compact source approximation is employed, and the quadrupole formula relating the wave amplitude to the quadrupole of the source is obtained. Energy flux in gravitational waves is calculated by two methods, one more general, the other giving further physical insight. The total emitted power is obtained. These are lengthy calculations but they are presented in full. Finally they are applied in detail to a binary star with elliptical orbtis (the Hulse Taylor binary) and to a black hole merger detected by the LIGO interferometers.
{"title":"Gravitational waves","authors":"A. Steane","doi":"10.1093/oso/9780192895646.003.0007","DOIUrl":"https://doi.org/10.1093/oso/9780192895646.003.0007","url":null,"abstract":"The theory of weak gravitational waves is discussed at length. The transverse traceless gauge is described, and the behaviour of plane wave solutions obtained. The impact of a wave on physical objects, and hence methods for their detection, are calculated. The laser interferometric gravitational wave detector is described. Sources such as binary stars are considered. The compact source approximation is employed, and the quadrupole formula relating the wave amplitude to the quadrupole of the source is obtained. Energy flux in gravitational waves is calculated by two methods, one more general, the other giving further physical insight. The total emitted power is obtained. These are lengthy calculations but they are presented in full. Finally they are applied in detail to a binary star with elliptical orbtis (the Hulse Taylor binary) and to a black hole merger detected by the LIGO interferometers.","PeriodicalId":365636,"journal":{"name":"Relativity Made Relatively Easy Volume 2","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132039096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-02DOI: 10.1093/oso/9780192895646.003.0028
A. Steane
An introduction to Lagrangian methods for classical fields in flat spacetime and then in curved spacetime. The Euler-Lagrange equations for Lagrangian densities are obtained, and applied to the wave, Klein-Gordan, Weyl, Dirac, Maxwell and Proca equations. The canonical energy tensor is obtained. Conservation laws and Noether’s theorem are described. An example of the treatment of Interactions is given by presenting the the QED Lagrangian. Finally, covariant Lagrangian methods are described, and the Einstein field eqution is derived from the Einstein-Hilbert action.
{"title":"Lagrangian mechanics for fields","authors":"A. Steane","doi":"10.1093/oso/9780192895646.003.0028","DOIUrl":"https://doi.org/10.1093/oso/9780192895646.003.0028","url":null,"abstract":"An introduction to Lagrangian methods for classical fields in flat spacetime and then in curved spacetime. The Euler-Lagrange equations for Lagrangian densities are obtained, and applied to the wave, Klein-Gordan, Weyl, Dirac, Maxwell and Proca equations. The canonical energy tensor is obtained. Conservation laws and Noether’s theorem are described. An example of the treatment of Interactions is given by presenting the the QED Lagrangian. Finally, covariant Lagrangian methods are described, and the Einstein field eqution is derived from the Einstein-Hilbert action.","PeriodicalId":365636,"journal":{"name":"Relativity Made Relatively Easy Volume 2","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126092428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-02DOI: 10.1093/oso/9780192895646.003.0003
A. Steane
This chapter discusses some physical effects related to two simple metrics: the RIndler metric and the uniform static field. The purpose is to illustrate the methods by applying them in an exact calculation which is not too taxing. The Christoffel symbols and curvature tensors are obtained, and some example geodesics are calculated. The force experienced by a fisherman fishing in the RIndler metric is calculated.
{"title":"An introductory example: the uniform static field","authors":"A. Steane","doi":"10.1093/oso/9780192895646.003.0003","DOIUrl":"https://doi.org/10.1093/oso/9780192895646.003.0003","url":null,"abstract":"This chapter discusses some physical effects related to two simple metrics: the RIndler metric and the uniform static field. The purpose is to illustrate the methods by applying them in an exact calculation which is not too taxing. The Christoffel symbols and curvature tensors are obtained, and some example geodesics are calculated. The force experienced by a fisherman fishing in the RIndler metric is calculated.","PeriodicalId":365636,"journal":{"name":"Relativity Made Relatively Easy Volume 2","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124706189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-02DOI: 10.1093/oso/9780192895646.003.0026
A. Steane
The universe at very early times, before the GUT era, is discussed. The entropy problem is described. The horizon and flatness problems are subsumed into the general problem of finding plausible models of the physics of the Planck era or the era immediately after it. An outline of inflationary cosmology is given, including quantitative treatment of a scalar inflaton field, treated in both a classical and quantum approach, in order to find the average dynamics and the spectrum of perturbations, respectively.
{"title":"The very early universe","authors":"A. Steane","doi":"10.1093/oso/9780192895646.003.0026","DOIUrl":"https://doi.org/10.1093/oso/9780192895646.003.0026","url":null,"abstract":"The universe at very early times, before the GUT era, is discussed. The entropy problem is described. The horizon and flatness problems are subsumed into the general problem of finding plausible models of the physics of the Planck era or the era immediately after it. An outline of inflationary cosmology is given, including quantitative treatment of a scalar inflaton field, treated in both a classical and quantum approach, in order to find the average dynamics and the spectrum of perturbations, respectively.","PeriodicalId":365636,"journal":{"name":"Relativity Made Relatively Easy Volume 2","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124035518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-02DOI: 10.1093/oso/9780192895646.003.0021
A. Steane
The chapter presents the Penrose process, Hawking radiation, entropy and the laws of black hole thermodynamics. The Penrose process is derived and the area theorem is stated. A heuristic argument for the Hawking effect is given, emphasising a correct grasp of the concepts and the nature of the result. The Hawking effect and the Unruh effect are further discussed and linked together in a precise calculation. Evaporation of black holes is described. The information paradox is presented.
{"title":"Black hole thermodynamics","authors":"A. Steane","doi":"10.1093/oso/9780192895646.003.0021","DOIUrl":"https://doi.org/10.1093/oso/9780192895646.003.0021","url":null,"abstract":"The chapter presents the Penrose process, Hawking radiation, entropy and the laws of black hole thermodynamics. The Penrose process is derived and the area theorem is stated. A heuristic argument for the Hawking effect is given, emphasising a correct grasp of the concepts and the nature of the result. The Hawking effect and the Unruh effect are further discussed and linked together in a precise calculation. Evaporation of black holes is described. The information paradox is presented.","PeriodicalId":365636,"journal":{"name":"Relativity Made Relatively Easy Volume 2","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115031971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-02DOI: 10.1093/oso/9780192895646.003.0005
A. Steane
A complete theory of weak-field gravity is described: the linearized approximation. This is a form of first-order perturbation theory. The concept of a gauge transformation, as applied to the curvature tensor and the field equation, is explained, and it is shown how to reduce the field equation to a wave equation in the Lorenz gauge (under the linear approximation). Thus a huge variety of gravitational calculations become accessible.
{"title":"Linearized General Relativity","authors":"A. Steane","doi":"10.1093/oso/9780192895646.003.0005","DOIUrl":"https://doi.org/10.1093/oso/9780192895646.003.0005","url":null,"abstract":"A complete theory of weak-field gravity is described: the linearized approximation. This is a form of first-order perturbation theory. The concept of a gauge transformation, as applied to the curvature tensor and the field equation, is explained, and it is shown how to reduce the field equation to a wave equation in the Lorenz gauge (under the linear approximation). Thus a huge variety of gravitational calculations become accessible.","PeriodicalId":365636,"journal":{"name":"Relativity Made Relatively Easy Volume 2","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121418512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-02DOI: 10.1093/oso/9780192895646.003.0024
A. Steane
The growth of structure by gravitational collapse from initially small perturbations is described. The Jeans instability is calculated. The structure equations are obtained and solved in various cases (radiation-dominated, matter-dominated and others) via a linearized treatment. Hence the main features of the growth of density perturbations are obtained. The observed spectrum in the present is used to infer the primordial spectrum. The scale-invariant (Harrison-Zol’dovich) spectrum is described. The process of baryon acoustic oscillations is outlined and the sound horizon is defined. The chapter concludes with brief notes on galaxy formatiom.
{"title":"The growth of structure","authors":"A. Steane","doi":"10.1093/oso/9780192895646.003.0024","DOIUrl":"https://doi.org/10.1093/oso/9780192895646.003.0024","url":null,"abstract":"The growth of structure by gravitational collapse from initially small perturbations is described. The Jeans instability is calculated. The structure equations are obtained and solved in various cases (radiation-dominated, matter-dominated and others) via a linearized treatment. Hence the main features of the growth of density perturbations are obtained. The observed spectrum in the present is used to infer the primordial spectrum. The scale-invariant (Harrison-Zol’dovich) spectrum is described. The process of baryon acoustic oscillations is outlined and the sound horizon is defined. The chapter concludes with brief notes on galaxy formatiom.","PeriodicalId":365636,"journal":{"name":"Relativity Made Relatively Easy Volume 2","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125142553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-02DOI: 10.1093/oso/9780192895646.003.0029
A. Steane
Concluding remarks, in part about the enduring significance of General Relativity, and in part about current and future lines of research.
结束语，部分是关于广义相对论的持久意义，部分是关于当前和未来的研究方向。
{"title":"Conclusion","authors":"A. Steane","doi":"10.1093/oso/9780192895646.003.0029","DOIUrl":"https://doi.org/10.1093/oso/9780192895646.003.0029","url":null,"abstract":"Concluding remarks, in part about the enduring significance of General Relativity, and in part about current and future lines of research.","PeriodicalId":365636,"journal":{"name":"Relativity Made Relatively Easy Volume 2","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134368378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-02DOI: 10.1093/oso/9780192895646.003.0009
A. Steane
The vector, the dual vector (one-form), components and inner products are defined and discussed. The difference between a vector and a one-form is carefully drawn out, with examples and diagrams. Contravariant and covariant components are described, and the way in which the metric can relate them is carefully explained. The transformation of vector components under a change of coordinate basis is derived.
{"title":"Vectors on manifolds","authors":"A. Steane","doi":"10.1093/oso/9780192895646.003.0009","DOIUrl":"https://doi.org/10.1093/oso/9780192895646.003.0009","url":null,"abstract":"The vector, the dual vector (one-form), components and inner products are defined and discussed. The difference between a vector and a one-form is carefully drawn out, with examples and diagrams. Contravariant and covariant components are described, and the way in which the metric can relate them is carefully explained. The transformation of vector components under a change of coordinate basis is derived.","PeriodicalId":365636,"journal":{"name":"Relativity Made Relatively Easy Volume 2","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124756111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-02DOI: 10.1093/oso/9780192895646.003.0023
A. Steane
The chapter deals with the large-scale dynamics of the universe. First the Friedmann equations are obtained from the Einstein field equation, and they are interpreted with the aid of a Newtonian comparison. Then the application to the universe modelled as a collection of ideal fluids is described. Density parameters and the equation of the state are defined, and the main features of the evolution of matter, radiation and the vacuum are obtained. Analytic solutuions in various simple cases are found. Dark matter and dark energy are defined through their observational evidence. The particle horizon is defined and discussed. The density and temperature at last scattering are calculated by a model involving Thomson scattering, expansion, and the Saha equation.
{"title":"Cosmological dynamics","authors":"A. Steane","doi":"10.1093/oso/9780192895646.003.0023","DOIUrl":"https://doi.org/10.1093/oso/9780192895646.003.0023","url":null,"abstract":"The chapter deals with the large-scale dynamics of the universe. First the Friedmann equations are obtained from the Einstein field equation, and they are interpreted with the aid of a Newtonian comparison. Then the application to the universe modelled as a collection of ideal fluids is described. Density parameters and the equation of the state are defined, and the main features of the evolution of matter, radiation and the vacuum are obtained. Analytic solutuions in various simple cases are found. Dark matter and dark energy are defined through their observational evidence. The particle horizon is defined and discussed. The density and temperature at last scattering are calculated by a model involving Thomson scattering, expansion, and the Saha equation.","PeriodicalId":365636,"journal":{"name":"Relativity Made Relatively Easy Volume 2","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116820143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：