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Singularity Theory and Gravitational Lensing

  • Arlie O. Petters
  • Harold Levine
  • Joachim Wambsganss

Part of the Progress in Mathematical Physics book series (PMP, volume 21)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 3-14
    3. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 15-21
  3. Astrophysical Aspects

    1. Front Matter
      Pages 23-23
    2. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 25-117
    3. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 119-141
    4. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 143-168
  4. Mathematical Aspects

    1. Front Matter
      Pages 169-169
    2. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 171-208
    3. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 209-286
    4. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 287-325
    5. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 327-392
    6. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 393-418
    7. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 419-444
    8. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 445-465
    9. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 467-485
    10. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 487-501
    11. Arlie O. Petters, Harold Levine, Joachim Wambsganss
      Pages 503-559
  5. Back Matter
    Pages 561-603

About this book

Introduction

This monograph, unique in the literature, is the first to develop a mathematical theory of gravitational lensing. The theory applies to any finite number of deflector planes and highlights the distinctions between single and multiple plane lensing.

Introductory material in Parts I and II present historical highlights and the astrophysical aspects of the subject. Among the lensing topics discussed are multiple quasars, giant luminous arcs, Einstein rings, the detection of dark matter and planets with lensing, time delays and the age of the universe (Hubble’s constant), microlensing of stars and quasars.

The main part of the book---Part III---employs the ideas and results of singularity theory to put gravitational lensing on a rigorous mathematical foundation and solve certain key lensing problems. Results are published here for the first time.

Mathematical topics discussed: Morse theory, Whitney singularity theory, Thom catastrophe theory, Mather stability theory, Arnold singularity theory, and the Euler characteristic via projectivized rotation numbers. These tools are applied to the study of stable lens systems, local and global geometry of caustics, caustic metamorphoses, multiple lens images, lensed image magnification, magnification cross sections, and lensing by singular and nonsingular deflectors.

Examples, illustrations, bibliography and index make this a suitable text for an undergraduate/graduate course, seminar, or independent these project on gravitational lensing. The book is also an excellent reference text for professional mathematicians, mathematical physicists, astrophysicists, and physicists.

Keywords

Mathematica geometry gravitation gravity quasars universe

Authors and affiliations

  • Arlie O. Petters
    • 1
  • Harold Levine
    • 2
  • Joachim Wambsganss
    • 3
  1. 1.Department of MathematicsDuke UniversityDurhamUSA
  2. 2.Department of MathematicsBrandeis UniversityWalthamUSA
  3. 3.Astrophysikalisches Institut PotsdamUniversität PotsdamPotsdamGermany

Bibliographic information