Conformal Compactifications and Penrose Diagrams

  • Dieter LüstEmail author
  • Ward Vleeshouwers
Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)


Typical space-time metrics, e.g. \(\mathbb {R}^{1,3}\) or Schwarzschild space, are infinite in coordinate extension. This means that there are boundaries of our space-time at infinite coordinate distance in this coordinate system. To make such space-times more manageable we perform so-called conformal compactifications, which is a transformation of our original coordinate system such that:
  1. 1.

    Space-time boundaries typically at infinite coordinate distance are mapped to lines, points, or hypersurfaces at finite distance

  2. 2.

    The conformal structure is kept intact, in particular, we require that light rays travel at 45\(^{\circ }\).


Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Arnold-Sommerfeld-CenterLudwig-Maximilians-UniversitaetMunichGermany
  2. 2.Institute for Theoretical PhysicsUtrecht UniversityUtrechtThe Netherlands

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