nLab Minkowski space

Context

Riemannian geometry

Riemannian geometry

Surveys, textbooks and lecture notes

Gravity

gravity, supergravity

Spacetimes

black hole spacetimesvanishing angular momentumpositive angular momentum
vanishing chargeSchwarzschild spacetimeKerr spacetime
positive chargeReissner-Nordstrom spacetimeKerr-Newman spacetime

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 Herrmann Minkowski.

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 March 9, 2015 12:38:34 by Urs Schreiber (89.15.236.31)