UID:
almafu_9961262409602883
Format:
1 online resource (xvi, 70 pages) :
,
illustrations.
Edition:
1st ed. 2023.
ISBN:
9783031429484
,
3031429486
Series Statement:
SpringerBriefs in Physics,
Content:
This book offers a primer on the fundamentals and applications of the Geroch-Held-Penrose (GHP) calculus, a powerful formalism designed for spacetimes that occur frequently in the teaching of General Relativity. Specifically, the book shows in detail the power of the calculus when dealing with spherically symmetric spacetimes. After introducing the basics, a new look at all the classical spherically symmetric black hole solutions is given within the GHP formalism. This is then employed to give new insights into the Tolman-Oppenheimer-Volkoff equations for stellar structure, including a derivation of new exact anisotropic fluid solutions. Finally, a re-writing of some essential features of black hole thermodynamics within the GHP formalism is performed. The book is based on the authors' lecture notes, used in their undergraduate and graduate lectures and while supervising their upper undergraduate and graduate students. To fully benefit from this concise primer, readers only need an undergraduate background in general relativity.
Note:
Part I. Fundamentals -- Chapter 1. Basics of General Relativity -- Chapter 2. The Newman-Penrose formalism -- Chapter 3. Tools for the GHP formalism -- Chapter 4. The GHP equations, Bianchi identities and commutator relations -- Chapter 5. The Penrose-Rindler equation -- Part II. Applications -- Chapter 6. Spherically symmetric electro-vacuum solutions: a GHP approach -- Chapter 7. Self-gravitating spheres and fluid distributions: a GHP approach -- Chapter 8. Black hole thermodynamics through the GHP calculus -- Part III. Conclusions -- Chapter 9. Conclusions and Outlook.
Additional Edition:
ISBN 9783031429477
Language:
English
DOI:
10.1007/978-3-031-42948-4
