The Geroch-Held-Penrose Calculus

Beschreibung

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.
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.
Includes a substantial foreword by Roger Penrose Provides a comprehensive and pedagogical review of the Geroch-Held-Penrose calculus Serves as a "hands on" of the GHP formalism within spherical symmetry

Autor*in

Pedro Bargueño

Themen in »The Geroch-Held-Penrose Calculus«

Geroch-Held-Penrose formalism Newman-Penrose formalism Spacetime calculus Spherically symmetric spacetimes Exact anisotropic fluid solutions Stellar structure

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“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)

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