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.
Arvustused
The authors' aims in this book is to make the formalism of Penrose and Rindler more accessible . If this short book persuades readers that the (compacted) spin-coeffcient formalism is worth knowing, entices them to delve into Penrose and Rindler, and appreciate the charms and power of the two-component spinor formalism and its derivatives, then it will prove valuable indeed. (Peter R. Law, Mathematical Reviews, July, 2024)
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.
Pedro Bargueño is an associate research professor at the Department of Applied Physics, Alicante University (Spain). His work mainly involves gravitational physics, with emphasis in black holes. He received two Ph. Ds, one from Salamanca University (Spain) in 2010 and other from Complutense University (Madrid, Spain) in 2012. After serving as a Juan de la Cierva researcher at Complutense University (2011-2013), he joined Los Andes University (Colombia), where he got his tenure as an associate professor (2014-2019). He joined the Group of Relativistic Astrophysics at the Department of Applied Physics, Alicante University, in 2019. Prof. Bargueño has authored or coauthored more than eighty publications in internationally recognized journals. He has mentored two postdoctoral researchers and supervised two PhD students, six MSc students and around twenty undergrads.
Ernesto Contreras is a theoretical physicist and professor at the Universidad San Francisco de Quito,Department of Physics, Quito, Ecuador. His wide-ranging interests include: General Relativity, Quantum Field Theory, High Energy Physics, Knot Theory and Quantum Gravity.
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