## General Theory of RelativityEinstein's general theory of relativity requires a curved space for the description of the physical world. If one wishes to go beyond superficial discussions of the physical relations involved, one needs to set up precise equations for handling curved space. The well-established mathematical technique that accomplishes this is clearly described in this classic book by Nobel Laureate P.A.M. Dirac. Based on a series of lectures given by Dirac at Florida State University, and intended for the advanced undergraduate, |

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### Contents

1 Special Relativity | 1 |

2 Oblique Axes | 3 |

3 Curvilinear Coordinates | 5 |

4 Nontensors | 8 |

5 Curved Space | 9 |

6 Parallel Displacement | 10 |

7 Christoffel Symbols | 12 |

8 Geodesics | 14 |

20 Tensor Densities | 36 |

21 Gauss and Stokes Theorems | 38 |

22 Harmonic Coordinates | 40 |

23 The Electromagnetic Field | 41 |

24 Modification of the Einstein Equations by the Presence of Matter ... | 43 |

25 The Material Energy Tensor | 45 |

26 The Gravitational Action Principle | 48 |

27 The Action for a Continuous Distribution of Matter ... | 50 |

9 The Stationary Property of Geodesics | 16 |

10 Covariant Differentiation | 17 |

11 The Curvature Tensor | 20 |

12 The Condition for Flat Space | 22 |

13 The Bianci Relations | 23 |

14 The Ricci Tensor | 24 |

15 Einsteins Law of Gravitation | 25 |

16 The Newtonian Approximation | 26 |

17 The Gravitational Red Shift | 29 |

18 The Schwarzchild Solution | 30 |

19 Black Holes | 32 |

28 The Action for the Electromagnetic Field | 54 |

29 The Action for Charged Matter | 55 |

30 The Comprehensive Action Principle | 58 |

31 The PseudoEnergy Tensor of the Gravitational Field ... | 61 |

32 Explicit Expression for the PseudoTensor | 63 |

33 Gravitational Waves | 64 |

34 The Polarization of Gravitational Waves | 66 |

35 The Cosmological Term | 68 |

71 | |

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### Common terms and phrases

action density action principle antisymmetric becomes Bianci relation change of coordinates Christoffel symbol coefficient components condition conservation constant contravariant vector coordinate system corresponding covariant derivative covariant differentiation covariant vector curvature curved space curvilinear coordinates cyc perm denote distribution of matter downstairs suffix dx1 dx2 dx3 Einstein equation Einstein’s law electromagnetic field empty space energy and momentum equations for empty expression field equations field quantity flat space formula four-dimensional function gives gravitational field Hence hold integral invariant Lagrangian Let us suppose Let us take lower suffixes Maxwell equation metric multiply nontensor null vector number of dimensions oblique axes parallel displacement particle pseudo-tensor rectilinear result Ricci tensor right-hand side satisfies scalar field Schwarzschild solution second derivatives Section shift sin2 special relativity static surface symmetrical system of coordinates term theorem timelike upstairs vanishes velocity of light world line zero