# Tag Info

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### How does the covariant derivative satisfy the Leibniz rule?

Assuming that $T$ and $S$ are supposed to be $(1,0)$ tensor fields we can see that Eq. (2) is wrong immediately, because the expression $\nabla (S)^{ \nu \rho}$ has the wrong indices (it should have ...

### The limit of GR with infinite speed of light $c$

what would the universe be like if gravity was curvature but c was infinite? The equivalence principle holds in Newtonian gravity. So you can geometrize standard Newtonian gravity. That is called ...
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### Is it possible to describe every possible spacetime in Cartesian coordinates?

As the choice of coordinates is arbitrary, can't I just "postulate" to use cartesian coordinates to describe any possible spacetime? If by cartesian coordinates you mean a set of four ...

### Physical meaning of each component of the metric tensor in GR

It is perhaps better to exercise with simpler examples before deal with GR to have an intuition on the metric tensor. Plane coordinates $xy$ with non-orthogonal axis leads to a metric with non-zero ...

### Is it true to say that there is a single electric field and it is inhabited by and affected by all charges in the universe?

It's a model. "All models are wrong, some are useful." So, the question is what the use of this idea is. There is some insight here: to achieve the isolated electric fields of textbooks ...

### Is it possible to describe every possible spacetime in Cartesian coordinates?

I think you have a mixup between global and local properties here. Using differential geometry language, a space-time is a 4-dimensional manifold with a Lorentzian metric. It is a theorem in ...

### How comes that we use space and time together in one manifold?

Start off with 3D vectors. If you have a vector in one set of coordinates, then rotate the coordinate axes, you end up with the same vector needing to be expressed in the new coordinate system. A ...

### How comes that we use space and time together in one manifold?

Let's suppose a 2D (1 + 1) non relativistic world, and a distance $d$ and time interval $t$ between 2 events in a given frame. Any space-time metric $f(t,d) \neq f(t)$ would not be invariant, because ...

### How comes that we use space and time together in one manifold?

Michaelson and Morley demonstrated that light has always the same speed in all frames of reference. The simplest answer to your question, then, is that if you are in a model with absolute time and ...

### Questions about E. Minguzzi's article on Synchronization (arXiv:1009.3005)

Thank you for the interest in the paper. Let me mention that this work has not been published so far because soon after I posted it I worked on another version that expanded it while rearranging some ...

### Another dimensions

Dimensions denote the number of variables needed to describe exactly where something is located. But this happens inside some given space (like the Earth's surface which is 2 dimensional or the ...
1 vote

### Compactification of Minkowski spacetime

$r'$ is just the angular position on the cylinder's surface. In the Penrose diagram (Fig. 17.9), it's the horizontal coordinate. From comments, I think you're confused because there is a second copy ...
1 vote

### Compactification of Minkowski spacetime

Although in the cylinderical diagram the time coordiante $t'$ has the range $$-\infty < t' < \infty$$ the relavent range is only from $$-\pi< t' < \pi$$ As such, the conformally ...
1 vote

### According the theory of general relativity, what is the role of causality in the changes of the curvature of spacetime?

Yes. This has to do with energy conditions and how the causal structure of the spacetime are linked. While the causal structure is usually somewhat axiomatic, in that the causal principle and ...
1 vote
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### How to get metric tensor components?

The metric tensor is a bilinear map that takes in vectors of the tangent space to the manifold. We can expand the metric tensor as $$g(X_i, X_j) = g_{ij}dx^idx^j$$ Now, say the metric is a function of ...

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