Professor Ray d'Inverno is Emeritus Professor in General Relativity at the University of Southhampton. A pioneer in the use of computer algebra in general relativity, Professor d'Inverno developed the early system LAM (Lisp Algebraic Manipulator), which was a precursor to Sheep, the system most used to date in the study of exact solutions and their invariant classification. He also developed the 2+2 formalism for analysing the initial value problem in general relativity. The formalism has also been used to provide a possible route towards a canonical quantization programme for the theory. In addition, he worked in numerical relativity (solving Einstein's equations numerically on a computer) and with others set up the CCM (Cauchy-Characteristic Matching) approach, which is still used in this increasingly important field.James Vickers is an Emeritus Professor of Mathematics at the University of Southampton and has published extensively on general relativity. His early research was on the structure of weak singularities in relativity and more recently he has given proofs of both the Penrose and Hawking singularity theorems for low-regularity spacetimes. These show that the singularities predicted by these theorems must be accompanied by unbounded curvature. He has also worked on the asymptotic structure of space-time and used spinors to prove the positivity of the Bondi mass.

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• 1: The Organisation of the Book A: Special Relativity 2: The k-Calculus 3: The Key Attributes of Special Relativity 4: The Elements of Relativistic Mechanics B: The Formalism of Tensors 5: Tensor Algebra 6: Tensor Calculus 7: Integration, Variation, and Symmetry C: General Relativity 8: Special Relativity Revisited 9: The Principles of General Relativity 10: The Field equations of General Relativity 11: General Relativity from a Variational Principle 12: The Energy-Momentum Tensor 13: The Structure of the Field Equations 14: The 3+1 and 2+2 Formalisms 15: The Schwarzschild sSlution 16: Classical Experimental Tests of General Relativity D: Black Holes 17: Non-Rotating Black Holes 18: Maximal Extension and Conformal Compactification 19: Charged Black Holes 20: Rotating Black Holes E: Gravitational Waves 21: Linearized Gravitational Waves and their Detection 22: Exact Gravitational Waves 23: Radiation from an Isolated Source F: Cosmology 24: Relativistic Cosmology 25: The Classical Cosmological Models 26: Modern Cosmology Answers to Exercises Selected Bibliography Index

Professor Ray d'Inverno is Emeritus Professor in General Relativity at the University of Southhampton. A pioneer in the use of computer algebra in general relativity, Professor d'Inverno developed the early system LAM (Lisp Algebraic Manipulator), which was a precursor to Sheep, the system most used to date in the study of exact solutions and their invariant classification. He also developed the 2+2 formalism for analysing the initial value problem in general relativity. The formalism has also been used to provide a possible route towards a canonical quantization programme for the theory. In addition, he worked in numerical relativity (solving Einstein's equations numerically on a computer) and with others set up the CCM (Cauchy-Characteristic Matching) approach, which is still used in this increasingly important field.James Vickers is an Emeritus Professor of Mathematics at the University of Southampton and has published extensively on general relativity. His early research was on the structure of weak singularities in relativity and more recently he has given proofs of both the Penrose and Hawking singularity theorems for low-regularity spacetimes. These show that the singularities predicted by these theorems must be accompanied by unbounded curvature. He has also worked on the asymptotic structure of space-time and used spinors to prove the positivity of the Bondi mass.

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• 1: The Organisation of the Book A: Special Relativity 2: The k-Calculus 3: The Key Attributes of Special Relativity 4: The Elements of Relativistic Mechanics B: The Formalism of Tensors 5: Tensor Algebra 6: Tensor Calculus 7: Integration, Variation, and Symmetry C: General Relativity 8: Special Relativity Revisited 9: The Principles of General Relativity 10: The Field equations of General Relativity 11: General Relativity from a Variational Principle 12: The Energy-Momentum Tensor 13: The Structure of the Field Equations 14: The 3+1 and 2+2 Formalisms 15: The Schwarzschild sSlution 16: Classical Experimental Tests of General Relativity D: Black Holes 17: Non-Rotating Black Holes 18: Maximal Extension and Conformal Compactification 19: Charged Black Holes 20: Rotating Black Holes E: Gravitational Waves 21: Linearized Gravitational Waves and their Detection 22: Exact Gravitational Waves 23: Radiation from an Isolated Source F: Cosmology 24: Relativistic Cosmology 25: The Classical Cosmological Models 26: Modern Cosmology Answers to Exercises Selected Bibliography Index

Professor Ray d'Inverno is Emeritus Professor in General Relativity at the University of Southhampton. A pioneer in the use of computer algebra in general relativity, Professor d'Inverno developed the early system LAM (Lisp Algebraic Manipulator), which was a precursor to Sheep, the system most used to date in the study of exact solutions and their invariant classification. He also developed the 2+2 formalism for analysing the initial value problem in general relativity. The formalism has also been used to provide a possible route towards a canonical quantization programme for the theory. In addition, he worked in numerical relativity (solving Einstein's equations numerically on a computer) and with others set up the CCM (Cauchy-Characteristic Matching) approach, which is still used in this increasingly important field.James Vickers is an Emeritus Professor of Mathematics at the University of Southampton and has published extensively on general relativity. His early research was on the structure of weak singularities in relativity and more recently he has given proofs of both the Penrose and Hawking singularity theorems for low-regularity spacetimes. These show that the singularities predicted by these theorems must be accompanied by unbounded curvature. He has also worked on the asymptotic structure of space-time and used spinors to prove the positivity of the Bondi mass.

Select Guide Rating

• 1: The Organisation of the Book A: Special Relativity 2: The k-Calculus 3: The Key Attributes of Special Relativity 4: The Elements of Relativistic Mechanics B: The Formalism of Tensors 5: Tensor Algebra 6: Tensor Calculus 7: Integration, Variation, and Symmetry C: General Relativity 8: Special Relativity Revisited 9: The Principles of General Relativity 10: The Field equations of General Relativity 11: General Relativity from a Variational Principle 12: The Energy-Momentum Tensor 13: The Structure of the Field Equations 14: The 3+1 and 2+2 Formalisms 15: The Schwarzschild sSlution 16: Classical Experimental Tests of General Relativity D: Black Holes 17: Non-Rotating Black Holes 18: Maximal Extension and Conformal Compactification 19: Charged Black Holes 20: Rotating Black Holes E: Gravitational Waves 21: Linearized Gravitational Waves and their Detection 22: Exact Gravitational Waves 23: Radiation from an Isolated Source F: Cosmology 24: Relativistic Cosmology 25: The Classical Cosmological Models 26: Modern Cosmology Answers to Exercises Selected Bibliography Index