All Questions
48
questions
2
votes
1
answer
79
views
A few doubts regarding the geometry and representations of spacetime diagrams [closed]
I had a couple questions regarding the geometry of space-time diagrams, and I believe that this specific example in Hartle's book will help me understand.
However, I am unable to wrap my head around ...
- 23
2
votes
1
answer
89
views
Confusion about timelike spatial coordinates
I'm pretty new to general relativity, and I'm self-studying it using Sean M. Carroll's text on the subject. In Section 2.7, he introduces the notion of closed timelike curves. He gives the example of ...
- 160
3
votes
4
answers
364
views
Regarding the signature of special relativity
in special relativity we add time as a dimension and replace euclidean space $ \mathbb{R}^4 $ with a pseudo-euclidean space $ \mathbb{R}^{1,3} $ of signature $ (1,3) $ by defining a quadratic form $\...
- 309
7
votes
2
answers
2k
views
Do the Einstein Field Equations force the metric to be Lorentzian?
In GR, we are working with Lorentzian metrics, which are examples of a pseudo-Riemannian metrics. That is, we are trying to find pseudo-Riemannian $g_{\mu\nu}$ that are solutions to the field equation ...
- 453
2
votes
2
answers
156
views
Relationship between spacelike and timelike distances in General Relativity vs. Special Relativity
In Minkowski spacetime, the distance $d_S$ between two space-like separated events $x$ and $y$ can (up to constant) be given by a distance between the two time-like separated events $z$ and $w$ where $...
- 125
3
votes
1
answer
530
views
Confusion regarding Geodesics
Suppose we have a causal curve and we can cover the causal curve by convex normal neighborhoods. We also know that, in convex normal neighborhood there will exist a unique geodesic inside the ...
- 27
0
votes
1
answer
69
views
Minkowski spacetime
I have recently become interested in special relativity. I would like to stress that I am not a physicist, but just a curious person. I read that a piecewise twice continuously differentiable curve $\...
- 186
0
votes
2
answers
93
views
A question on negative time and Minkowski Space
Can someone please explain why a point originating inside the cone can never be the cause of an event outside the cone? Is there a real life example of this? The only thing I can think of is from a ...
- 2,706
0
votes
2
answers
107
views
Light-like interval and simultaneity [closed]
Why if the interval between two events is light-like then there is no frame of reference where the events occur at either the same time? If I assume that the 2 events happen at the same time, I arrive ...
2
votes
2
answers
106
views
Is time-like separation transitive? [closed]
In other words, if events a and b are time-like separated, and events b and c are time-like separated, does it follow that events a and c are time-like separated?
Is there a straightforward proof of ...
- 29
1
vote
1
answer
72
views
Would I not notice proper space in the same way that I don't notice proper time?
I'm working to understand the metric tensor in spacetime (including 4 dimension lengths and 6 angles). I know that if I'm carrying a clock near a black hole I won't notice that my proper time is any ...
- 4,783
0
votes
1
answer
153
views
General Relativity via light cones curvature?
Is it possible to reformulate general relativity as curvature of objects' light cones instead of curvature of spacetime?
- 3
3
votes
6
answers
1k
views
What does the spacetime interval measure?
I know that the spacetime interval is the analog of the (square of the) Euclidean distance in spacetime. Also, I understand that it is an invariant quantity and determines spacetime's causal structure....
- 431
1
vote
0
answers
73
views
Signature of the Minkowski metric tensor
In special relativity, events happen in the Minkowski spacetime, with signature $(3,1)$ or $(1,3)$. I was wondering about the need of different sign for temporal and spatial coordinates. Looking ...
- 123
1
vote
2
answers
523
views
Understanding Space-time intervals and its types
I am taking Introduction to Modern Physics class. There, we were studying spacetime intervals as a subsection of Lorentz's transformation. My professor said that $\Delta x^2-c^2\Delta t^2$ is ...
- 111