Space-Time Curvature in General Relativity

[MeJennifer]

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

 

[quantum123]

Locally, and with the right coodinates.

 

[pervect]

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).

 

[MeJennifer]

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?

 

[quantum123]

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