nLab
Minkowski space

Definition

For $d-1\in \mathbb{N}$, $d$-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).

Related entries

• spacetime

  • super Minkowski space

  • Schwarzschild spacetime

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)