# nLab Minkowski space

### Context

#### Riemannian geometry

Riemannian geometry

## Applications

#### Gravity

gravity, supergravity

# Contents

## Definition

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

This is naturally a spacetime.

## Properties

###### 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)