# Tag Info

### Where is the Lorentz signature enforced in general relativity?

4-dimensional Lorenzian manifold was the most natural way to express the invariance of light velocity (Maxwell's wave equation), in terms of metric $$ds^2=c^2 dt^2-dx^2-dy^2-dz^2$$ For Herman ...
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### Curvature of Hilbert space

Hilbert space is infinite dimensional space, by default it is continuous, has no curvature, and extends indefinitely in all directions. It also lacks any edges where the space ends, or wraps around on ...
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### Where is the Lorentz signature enforced in general relativity?

The Lorentzian signature of the metric is "baked into" the local causal structure (the set of "light cones", one at each event) of spacetime, which plays a role in the initial ...
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### Where is the Lorentz signature enforced in general relativity?

The Lorentz signature is just part of the theory; for example in a weak-field limit, we should reduce to special relativity, which is described using Lorentz signature (in order to talk about light, ...
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### Where is the Lorentz signature enforced in general relativity?

Quoted from Pseudo-Riemannian manifold - Lorentzian manifold: A principal premise of general relativity is that spacetime can be modeled as a 4-dimensional Lorentzian manifold of signature $(-,+,+,+)$...
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1 vote

### Could time be a secondary effect due to curvature of space?

Are there cases where time is curved independent from space? To my knowledge not. Einstein field equations (EFE) are just about this dependency. In case of Schwarzschild exterior solution the metric ...
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### Could time be a secondary effect due to curvature of space?

You can't have curvature in 1 dimension: it is a line and always locally flat, with $R^a{}_{bcd} = R^0{}_{000} =0$. So it doesn't make sense to ask about 'time being curved'. If you want to consider ...
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### Could 2D spacetime be seen as an embedded manifold?

If you mean "embedded in $\mathbb{R}^3$ with a Euclidean metric", then the answer is no. Suppose that such an embedding exists. Consider the neighborhood of a point $P$ on the submanifold. ...
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1 vote
Accepted

### Linear Momentum in General Relativity

Is there a metric that describes this case? Yes. It is the Schwarzschild metric (valid outside of the gravitating body if we are talking about something like a star). When written in the form where ...
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### How to simplify the process of calculating spacetime geodesics?

I guess you may be making a reasonable point here, when speaking about this particular metric. Assume the space-time is split into $(t , \, x) \, \in \, \mathbb{R} \times M_3$, where $M_3$ is one of ...
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