Tagged Questions
2
votes
1answer
42 views
“WLOG” re Schwarzschild geodesics
Why, when studying geodesics in the Schwarzschild metric, one can WLOG set
$$\theta=\frac{\pi}{2}$$
to be equatorial? I assume it is so because when digging around the internet, most references seem ...
6
votes
1answer
128 views
Are group representations possible when the solution space is not a vector space?
As far as I understand, the motivation for using representation theory in high energy physics is as follows. Assume that a theory has some (internal or external) symmetry group which acts on a vector ...
4
votes
1answer
366 views
Physical significance of Killing vector field along geodesic
Let us denote by $X^i=(1,\vec 0)$ the Killing vector field and by $u^i(s)$ a tangent vector field of a geodesic, where $s$ is some affine parameter.
What physical significance do the scalar quantity ...
2
votes
1answer
72 views
Killing Vectors of BTZ black hole and their calculation in general
I was wondering what are the Killing vectors of BTZ black hole and how to guess them easily? Will it be the same as of AdS? What then will be Killing vectors for AdS-Schwarzschild e.g.?
2
votes
3answers
181 views
Are the principles of space-time homogeneity and Isotropy independent of one another?
Einstein in deriving the Lorentz transformations, used the principles of space-time homogeneity and Isotropy. Does space-time isotropy follow from space-time homogeneity or are they completely ...
1
vote
1answer
129 views
Symmetries of spacetime and objects over it
I guess according to mathematical didactic, we first think of spacetime as a set and we reason about elements of its topology and then it's furthermore equipped with a metric. Appearently it is this ...
0
votes
0answers
104 views
Time reversal symmetry and reversal of vectors
Firstly: I have been told that under time reversal transformations, i.e. $t\rightarrow -t$, vector fields must change sign. Why is this? I haven't found this in the literature, any references?
...
3
votes
2answers
351 views
Lorentz invariance of the 3 + 1 decomposition of spacetime
Why is allowed decompose the spacetime metric into a spatial part + temporal part like this for example
$$ds^2 ~=~ (-N^2 + N_aN^a)dt^2 + 2N_adtdx^a + q_{ab}dx^adx^b$$
($N$ is called lapse, $N_a$ is ...
4
votes
2answers
333 views
Deriving Birkhoff's Theorem
I am trying to derive Birkhoff's theorem in GR as an exercise: a spherically symmetric gravitational field is static in the vacuum area. I managed to prove that $g_{00}$ is independent of t in the ...
2
votes
2answers
158 views
What are the limitations of the FLRW metric?
I was wondering, given how in any other area of life making an explosion spherically symmetric is more or less impossible is there any reason to expect that the universe is? I appreciate that the FLRW ...
6
votes
3answers
130 views
From Manifold to Manifold?
Tensor equations are supposed to stay invariant in form wrt coordinate transformations where the metric is preserved. It is important to take note of the fact that invariance in form of the tensor ...
