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- Thread starter MeJennifer
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- #2

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Locally, and with the right coodinates.

- #3

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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).

- #4

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

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?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).

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

- #5

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Wikipedia:

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