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Geometric Relativity (Paperback)
Loot Price: R2,182
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Geometric Relativity (Paperback)
Series: Graduate Studies in Mathematics
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Many problems in general relativity are essentially geometric in
nature, in the sense that they can be understood in terms of
Riemannian geometry and partial differential equations. This book
is centered around the study of mass in general relativity using
the techniques of geometric analysis. Specifically, it provides a
comprehensive treatment of the positive mass theorem and closely
related results, such as the Penrose inequality, drawing on a
variety of tools used in this area of research, including minimal
hypersurfaces, conformal geometry, inverse mean curvature flow,
conformal flow, spinors and the Dirac operator, marginally outer
trapped surfaces, and density theorems. This is the first time
these topics have been gathered into a single place and presented
with an advanced graduate student audience in mind; several dozen
exercises are also included. The main prerequisite for this book is
a working understanding of Riemannian geometry and basic knowledge
of elliptic linear partial differential equations, with only
minimal prior knowledge of physics required. The second part of the
book includes a short crash course on general relativity, which
provides background for the study of asymptotically flat initial
data sets satisfying the dominant energy condition.
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