All Questions
Tagged with velocity general-relativity
59
questions
2
votes
1
answer
76
views
How to properly combine kinetic and gravitational time dilation effect?
I developed a time dilation calculator that includes both kinetic (Lorentz Factor) and gravitational (Schwarzschild Metric Formula) factors to assess the time difference between Earth and satellites. ...
0
votes
0
answers
37
views
Stationary Obversers in Brinkmann Coordinates
The four-velocity of a stationary observer is defined as $U^{u}$ = $\left (\dot{t},0,0,0 \right )$, where t is the time coordinate in some four-dimensional coordinate system, and overdot represents ...
- 100
-1
votes
2
answers
38
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Formula for adding velocities in opposed motion at relativistic speeds from the perspective of a stationary observer
I'm confused by the formula 𝑢=(𝑣+𝑣′)/(1+𝑣𝑣′/𝑐^2) whenever I apply it to a specific thought experiment.
I have a third party, stationary observer, who observers to collinear objects moving ...
- 99
0
votes
1
answer
110
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Is there a mistake in this special relativity question? Partial derivative
I’m not asking for the answer or even how to solve it — I just want to know if there has been a mistake.
Given
$$U^\alpha = (1+t^2, t^2, \sqrt{2}\,t,0)$$
Show that (using the “brute force” method)
$$...
- 93
1
vote
1
answer
697
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What is Wald talking about here in his book "General Relativity"?
I'm reading General Relativity by Robert Wald and his notation is confusing me.
On page $61$ of the book, Wald claims that by setting $c=1$ we can derive $E=mc^2$ from the following information.
(1) $...
- 113
0
votes
0
answers
51
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Is $u^{\mu} = \gamma\tfrac{dx^{\mu}}{dt}$ a 4-vector?
I understand that $c\dfrac{dx^{\mu}}{ds}$ is a 4-vector since $ds$ is a scalar. In flat space-time,
$$
ds = c\dfrac{dt}{\gamma}
$$
so $\gamma\dfrac{dx^{\mu}}{dt}$ would be a 4-vector as it is equal to ...
- 391
0
votes
1
answer
83
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In general relativity, how to get geometric velocity from 4-vector velocity field?
Currently, I‘m listening to the lecture of Prof. Hughes (https://ocw.mit.edu/courses/8-962-general-relativity-spring-2020/video_galleries/video-lectures/).
In General, I‘m able to follow the lecture, ...
- 1
2
votes
1
answer
260
views
How to get the 4-velocity of a fluid in general relativity?
If I know the energy-momentum tensor of a fluid, how to get the 4-velocity of this fluid in general relativity? Additionally, I find the 4-velocity of a fluid determined by $u_a$ which satisfies $u_a ...
- 113
2
votes
0
answers
30
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Why is the energy of a particle with $4$-momentum $p^a = mu^a$ measured by an observer with $4$-velocity $v^a$ given by $E=-p_av^a$? [duplicate]
On page 61 of his book “General Relativity”, Robert Wald says that the energy of a particle with $4$-momentum $p^a = mu^a$ measured by an observer with $4$-velocity $v^a$ is given by $E=-p_av^a$. How ...
- 669
9
votes
4
answers
1k
views
Is the four-velocity always normalized?
In the book i have reading defines the four-velocity like $$U^\mu=dx^\mu/d\tau.$$ The metric used is $\eta_{\mu\nu}=diag(-1,1,1,1)$. It is straightforward to show that the norm of the four-velocity is ...
- 171
1
vote
0
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93
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How is the pressure term being generated?
Background
So my understanding is that one can start with a stress energy tensor for many point particles:
$$T^{\alpha \beta} = \sum_{i} \frac{E}{c^2} v^{\alpha} (t) v^{\beta} (t) \delta(x-x_i(t)) $$
...
- 1,389
-1
votes
2
answers
59
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LFE: why $E=0$ implies that $|u^{\prime}|=a$ for a constant $a>0$?
Consider this easier formulation of the relativistic Lorentz force equation given by
\begin{equation}\
\left(\frac{u'}{\sqrt{1-|u'|^2}}\right)'= E(t,u)+u'\times B(t,u).
\end{equation}
Here, $E$ and $...
user316052
1
vote
1
answer
117
views
Pound-Rebka Experiment
Does anyone know if the velocity of the photons changes in the Pound-Rebka experiment?
Do the wavelength and the frequency change simultaneously, so that there is no change in the velocity, or do they ...
- 11
3
votes
2
answers
1k
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4-velocity in Schwarzschild metric
Is 4-velocity always equal to light speed in any metric? In Schwarzschild metric, the light speed with respect to a remote observer is $1 - r_{S}/r$. Should that be the 4-velocity of a falling ...
- 1,161
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votes
2
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92
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What causes things to gain the speed of nearby gravitational sources?
While I’m aware that this probably has a really simple answer, I can’t figure it out. For example, humans, apples, but also things outside of earth like the ISS travel along with the earth, at the ...
- 11