# nLab Minkowski space

Contents

### 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

Named after Hermann Minkowski.