Black Hole Information and Thermodynamics pp 29-32 | Cite as
Conformal Compactifications and Penrose Diagrams
Chapter
First Online:
Abstract
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.
Space-time boundaries typically at infinite coordinate distance are mapped to lines, points, or hypersurfaces at finite distance
- 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