# General Relativity

Is it accurate to claim that space-time curvature in general relativity means a curvature of a space-time with a Minkowski pseudo-metric?

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Locally, and with the right coodinates.

pervect
Staff Emeritus
That doesn't sound right.

I'd suggest saying that SR is done with a Minkowskian metric, while GR has a more general space-time with a Lorentzian metric.

The flat Minkowskian metric is a special case of the more general Lorentzian metric (whcih is not necessarily flat).

A manifold with either a Lorentzian or Minkowskian metric is a pseudo-Riemannian manifold because the metric tensor is not positive definte (those pesky minus signs).

The flat Minkowskian metric is a special case of the more general Lorentzian metric (whcih is not necessarily flat).
Ok, that definition makes sense.

A manifold with either a Lorentzian or Minkowskian metric is a pseudo-Riemannian manifold because the metric tensor is not positive definte (those pesky minus signs).
Right, and so can we take a collection of local Lorentzian patches and form a curved space-time, which is thus as agreed upon also Lorentzian, and with maintaining a causal connection?

In other words, is "bending" a space with a Lorentzian metric unproblematic in terms of extending the causal structures?

Sorry!
Wikipedia:
A principal assumption of general relativity is that spacetime can be modeled as a Lorentzian manifold of signature (3,1).