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Advanced General RelativityGravity Waves, Spinning Particles, and Black Holes$
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Claude Barrabès and Peter A. Hogan

Print publication date: 2013

Print ISBN-13: 9780199680696

Published to Oxford Scholarship Online: September 2013

DOI: 10.1093/acprof:oso/9780199680696.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 16 October 2021

Minkowskian space–time

Minkowskian space–time

(p.1) 1 Minkowskian space–time
Advanced General Relativity
Oxford University Press

The relationship between the proper, orthochronous Lorentz group, the special linear group of 2×2 matrices with complex entries and unit determinant, and the group of fractional linear transformations of the extended complex plane is explicitly described with examples. The existence of non-singular and singular Lorentz transformations is explained as are infinitesimal Lorentz transformations and their close similarity to electromagnetic fields. This chapter demonstrates how a natural generalization of Lorentz transformations leads to a construction of an impulsive gravitational wave.

Keywords:   Lorentz group, singular Lorentz transformations, infinitesimal Lorentz transformations, impulsive gravitational wave

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