# nLab Minkowski space

### Context

#### Riemannian geometry

Riemannian geometry

## Surveys, textbooks and lecture notes

#### Gravity

gravity, supergravity

# Contents

## Definition

For $d-1 \in \mathbb{N}$, $d$-dimensional Minkowski space is the Lorentzian manifold whose underlying smooth manifold is the Cartesian space $\mathbb{R}^d$ and whose pseudo-Riemannian metric is at each point the Minkowski metric.

This is naturally a spacetime.

## Properties

### Isometries

The isometry group of Minkowski space is the Poincaré group. The study of Minkowski spacetime with its isometries is also called Lorentzian geometry. This is the context of the theory of special relativity.

### Gravitational stability

###### Theorem

Minkowski spacetimes is a stable? solution of the vacuum Einstein equations.

This is due to (ChristodoulouKlainerman 1993).

## References

Gravitational stability of Minkowski space is proven in

• Demetrios Christodoulou, Sergiu Klainerman, The global nonlinear stability of the Minkowski space Princeton University Press (1993)

Revised on October 30, 2013 22:31:38 by Urs Schreiber (82.169.114.243)