All Questions
Tagged with metric-field or metric-tensor
3,670 questions
-2
votes
3
answers
570
views
How to obtain the line element with inverse metric coefficient than that of Schwarzschild line element?
The Schwarzschild solution could simply be expressed as
$$ds^2=-(1-2GM/r)dt^2+(1-2GM/r)^{-1}dr^2+r^2d\phi^2 \; .$$
Is it possible that we could obtained a new metric into the form as
$$ds^2=-(1-2GM/r)^...
-2
votes
1
answer
88
views
How (if) is the metric of the quantum vacuum different from the metric of the classical vacuum?
The classical vacuum, with no matter or energy in it, has a flat metric.
Meanwhile we know that the classical vacuum is a chimera. There are lots of things going on, even though it is called virtual. ...
-2
votes
1
answer
64
views
Calculate a specific $A$, $B$ in the general static spherically symmetric metric using geodesics [closed]
The Einstein field equations (EFE), leaving out $\Lambda $ for simplicity, are :
$$R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R=-\kappa T_{\mu\nu} \tag 1$$
From that, the general static, spherically symmetric ...
- 255
-2
votes
1
answer
87
views
Integral over an area of spacetime [closed]
Is it possible to evaluate this integral in spacetime?
$$\int_{\Sigma} \frac{dydz}{[a_{o}(y^{2}+z^{2})+2f_{o}y+2g_{o}z+c_{o}]^{2}}$$ where $$a_{o}c_{o}-f_{o}^{2}-g_{0}^{2}=\frac{1}{4}.$$
If it is ...
-2
votes
2
answers
118
views
What would the Second Law of Motion be in this universe?
I have a universe described by the equation:
$$ds^2=c^2d\tau^2=-c^2dt^2+[dr+a_0 td\tau]^2+r^2\Omega^2$$
What would be the second law of motion in this universe?
user32023
-2
votes
1
answer
120
views
Does this identity that applies to the metric tensor also apply to the stress-energy tensor?
Okay so if the $g_{00}$ component of the metric is $-c^2$ and $g_{11}=g_{22}=g_{33}$ and all the other other components are zero, the question is simple, would similar identities apply to the stress-...
- 387
-2
votes
1
answer
490
views
Interpretation of space time Minkowski diagram [closed]
How to interpret the following space-time diagram in the image.
I know how to interpret euclidean distance from Euclidean space diagram
- 1,586
-2
votes
1
answer
305
views
Meaning of orthogonality in SR spacetime
I had doubts about the meaning of time being orthogonal to space. I have seen several threads about the topic and my conclusions are as follows (please correct if anything is wrong):
Yes, time is ...
- 527
-2
votes
1
answer
116
views
How can I prove that $\Gamma_{kij}+\Gamma_{kji}=\partial_k g_{ij}$? [closed]
I want a simple proof of this identity:
$$\Gamma_{kij}+\Gamma_{kji}=\partial_k g_{ij}$$
If there's no answer, give me a hint or something would help to prove it, and thanks!
user257221
-2
votes
1
answer
309
views
Sphere of circumferential radius $r$
What do you then mean by constructing a sphere of circumferential radius $r$ centered on the black hole? Is that sphere a 2D surface?
- 5
-2
votes
1
answer
77
views
Write down the components of metric tensor correctly [closed]
this is a FLRW metric and I want to write down the metric tensor from this FLRW metric accurately. Can anyone please help me to do this? Thanks in advance.
\begin{equation}\tag{1}
ds^2 = a^2 ( \tau) [...
- 55
-3
votes
1
answer
123
views
From Klein-Gordon equation to Dirac equation: a wrong "derivation" [closed]
So let us start with the Klein-Gordon equation
$$\tag{KG}
(-p^\mu p_\mu + m^2)\phi = 0
$$
The idea is to "factorize" the operator $-p^\mu p_\mu + m^2$.
\begin{equation}\tag{1}
-p^\mu p_\mu + ...
- 1,664
-3
votes
1
answer
103
views
Importance of orthogonality in Minkowski space [closed]
I am currently studying Minkowski space. Orthogonality in this space is new to me. I have seen in a blog post, in 1 that states that, orthogonality is important in this space.
It will be helpful, if ...
- 103
-3
votes
1
answer
98
views
Time-ordering and Minkowski metric's negative sign [closed]
I'm coming at the following question from a mostly lay perspective (i.e. barely-undergrad physics), so please bear with the weirdness of it if possible.
I've generally been uncomfortable with the ...
- 163
-4
votes
2
answers
550
views
Why is $\vec{E}$ defined as $-\nabla\phi - \partial\vec{A}/\partial t$?
I find to obtain $\nabla\cdot \vec E= 0$ where there is no electric charge or current, I need
$$\vec E = \frac {\partial \vec A} {\partial t} - \nabla\phi ,$$
($\vec E = \nabla\phi - \frac {\...
- 33
-4
votes
2
answers
128
views
Is the equation $g_{\mu\nu} = const. + T_{\mu\nu}$ equivalent to Einstein's field equations? [closed]
Is the equation
$g_{\mu\nu} =$ diag (-1,1,1,1)$\cdot$ const. + $T_{\mu\nu}$
equivalent to Einstein's field equations?
$g_{\mu\nu}$ is the metric tensor and describes the curvature and $T_{\mu\nu}$ ...
- 61
-4
votes
1
answer
66
views
Cannot understand this identity between kronecker and metric tensor [closed]
I'm working on Lorentz generators and I am really not able to understand this relation:
$$\omega_{\rho \sigma} \eta^{\rho\mu} \delta^{\alpha}_{\nu} = \frac{1}{2}\omega_{\rho \sigma} \left(\eta^{\rho\...
- 383
-5
votes
4
answers
352
views
In Einstein's General Relativity, do the space-time dimensions curve?
In Einstein's General Relativity, do the space-time dimensions curve according to the positions of stars, planets, and masses?
- 107
-5
votes
1
answer
275
views
How is traveling back in time different from traveling at a negative velocity? [closed]
A simplified explanation of why you can't travel through space faster than the speed of light is that you are already traveling at the speed of light, through spacetime.
If you are stationary in ...
-6
votes
3
answers
134
views
What exactly is the role of the Lorentzian metric within spacetime? [closed]
I learned that twodimensional spacetime diagrams and fourdimensional spacetime manifolds are provided with Lorentzian (pseudo-Riemannian) metric. However, regarding a spacetime diagram with a light ...
- 3,151