Global Geometry of Space-Times with Shells

Victor Aleksandrovich Berezin and Vyacheslav Ivanovich Dokuchaev
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia

Series: Physics Research and Technology
BISAC: SCI051000




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In this book, the complete classification of the possible types of spherically symmetric global geometries for two types of electrically charged shells are explored. These include the charged shell as a single source of the gravitational field, when internal space-time is flat, and external space-time is the Reissner–Nordstrom metric; and the neutralizing shell with an electric charge opposite to the charge of the internal source with the Reissner–Nordstrom metric and with the Schwarzschild metric outside the shell.

Starting from Israel equations for the spherically symmetric thin shells, this book introduce the effective potential and shows how it can be used in constructing, without further thorough investigation, the corresponding Carter–Penrose diagrams describing clearly the global geometry of the composite space-time manifolds. This book demonstrates how this new method works by considering all possible configurations for the neutral thin dust shell immersed into different types of Reissner–Nordstrom electro-vacuum manifolds. (Imprint: Nova)

List of Figures

List of Notations


Chapter 1 - Introduction (pp. 1-4)

Chapter 2 - Conformal Carter–Penrose Diagrams (pp. 5-10)

Chapter 3 - Thin Shell Formalism (pp. 11-14)

Chapter 4 - Charged Shell with Minkowski Space-time Inside (pp. 15-26)

Chapter 5 - Neutralizing Shell (pp. 27-36)

Chapter 6 - Neutralizing Shell — Capacitor (pp. 37-88)

Chapter 7 - Reissner–Nordstr¨om Metric with Neutral Shell (pp. 89-92)

Chapter 8 - Preliminaries (pp. 93-102)

Chapter 9 - The Effective Potential Method (pp. 103-116)

Chapter 10 - Global Geometries for the Combined Systems (pp. 117-156)


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"One can never learn too much about elementary solutions of General Relativity. In this book, the authors provide a general global description, using Israel matching conditions, of spherically symmetric spacetimes with thin shell sources, charged or neutral, in spacetimes that are themselves asymptotically Schwarzschild or Reissner-Nordstrom, and have various charged/neutral interiors. This book will provide an authoritative, useful, basis for further explorations of the Einstein-Maxwell system, and its extensions both to wider models and more complex sources.” - Stanley Deser, PhD., Professor Emeritus of Physics, Brandeis University, USA

"Thin shells and surface layers are increasingly used to model gravitational collapse and phase transitions in general relativity and cosmology. However, a textbook treatment of these topics is still hard to find in the current literature. This book nicely fills the gap. The techniques are illustrated by focusing on the dynamics of charged spherical shells in a variety of backgrounds. Recommended for students and practitioners who want to add this useful tool to their armory.” - Werner Israel, Adjunct Professor, University of Victoria, Canada

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