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Spacetime

Foundations of General Relativity and Differential Geometry

  • Book
  • © 1999

Overview

Authors:
  1. Marcus Kriele

    1. Fachbereich Mathematik, Sekr. MA 8-3, Technische Universität Berlin, Berlin, Germany

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  • The unique feature of this textbook on General Relativity is its treatment of causility and the singularity theorems and their implications for astrophysics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Physics Monographs (LNPMGR, volume 59)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XIX
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  2. Local theory of space and time

    Pages 1-45

  3. Analysis on manifolds

    Pages 47-149

  4. Space and time from a global point of view

    Pages 151-169

  5. Pseudo-Riemannian manifolds

    Pages 171-254

  6. General relativity

    Pages 255-286

  7. Robertson-Walker cosmology

    Pages 287-305

  8. Spherical symmetry

    Pages 307-355

  9. Causality

    Pages 357-382

  10. Singularity theorems

    Pages 383-424

  11. Back Matter

    Pages 425-436
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Keywords

About this book

One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-’ We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations" and "causality weak "shell very crossing These singularities". add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one,should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach.

Authors and Affiliations

  • Fachbereich Mathematik, Sekr. MA 8-3, Technische Universität Berlin, Berlin, Germany

    Marcus Kriele

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