All Questions
10
questions
0
votes
2
answers
65
views
What is $r$ in a metric signature in general relativity? If $v$ and $p$ are the time and spatial coordinates?
The Wikipedia article on metric signatures says that the signature of a metric can be written $(v,p,r)$, where $v$ is the number of positive eigenvalues, $p$ is the number of negative eigenvalues, and ...
- 4,509
1
vote
1
answer
167
views
What does it mean that the metric is static?
I'm reading the paper Regular phantom black holes where in page 2 (left column) the authors write that "the metric is static where $A(\rho)>0$".
Does anyone know what they mean with the ...
- 2,478
0
votes
1
answer
155
views
Is the zero 4-vector lightlike? [closed]
I'm not sure whether the zero 4-vector can be considered lightlike, spacelike, or timelike in special relativity. Can anybody give me some insight?
- 468
0
votes
1
answer
936
views
Minkowski vs. Lorentz metric
Can anyone help me to understand the difference between Minkowski and Lorentzian metric?
They appear to me to be the very same: $$\langle x,y\rangle=-x_1\cdot y_1+x_2\cdot y_2+\ldots+x_n\cdot y_n.$$
...
- 255
0
votes
1
answer
197
views
How do 'locally Euclidean' and 'Lorentzian' requirements in manifolds reconcile?
In GR, we define our manifolds to be locally Euclidean. However, we also demand that our metric tensor have a Lorentzian signature. Since the metric tensor is a measure of curvature, doesn't the first ...
- 579
1
vote
1
answer
1k
views
Meaning of 1+1 dimensions
I came across the notion of 1+1 dimensions in a condensed matter context and, in particular, while studying bosonization, which relates to 1D quantum systems. Indeed, the Wikipedia article about it ...
- 1,396
8
votes
4
answers
992
views
Definition of spacetime in GR: what is the underlying set of the spacetime manifold?
In all the references/textbooks that I have looked at, the precise definition of spacetime is never really clear. By gathering the hypothesis that we need to make, I get the following definition: $$\...
- 1,044
5
votes
3
answers
1k
views
When exactly is a dimension spatial?
I every so often hear claims like:
M-Theory predicts that there are 10 spatial dimensions!
Now I'm not really sure what these claims mean. There are three spatial dimensions that I normally observe ...
1
vote
2
answers
613
views
Distinction between spacetime and vacuum
In GR, is spacetime just a mathematical abstraction, and in reality, it's the vacuum - whatever that is!!- is what curves, bends, and warps? In other words, is the distinction between spacetime and ...
16
votes
4
answers
6k
views
What is 'past null infinity'?
For example, in the sentence "there is no incoming radiation at past null infinity".
- 2,283