5
votes
Can you directly feel the effect of gravity, or only opposing forces?
You are almost completely right.
What we do not and cannot feel is a uniform gravitational force. By “uniform” here I mean in the sense of general relativity where the force of gravity is just a ...
- 109k
5
votes
Accepted
Gravitational time dilation – clock falling to event horizon
Since you're asking what the clock itself will show, if you fall from rest the proper time $\rm \tau$ from $\rm r_0$ to $\rm r$ is the same as under Newton since in this case $\rm d^2r/d\tau^2=-GM/r^2$...
- 13k
3
votes
Why Gravitational Time Dilation Equals SR Time Dilation for Objects Free-Falling from Infinity?
why do these two different mechanisms produce the same time dilation factor in this scenario?
Well, you are making an assumption here, and I recommend you let go of that assumption. Do not assume ...
- 22.6k
3
votes
Accepted
Origin of this equation attributed to Einstein
The image was taken from this pdf (thanks to comments). The original publication is:
David Bernstein, David Hobill, Edward Seidel, Larry Smarr, and John Towns, "Numerically generated ...
2
votes
Accepted
Covariant derivative acting on Dirac delta function
Let's be a bit systematic. Let $M$ be a smooth $m$-dimensional manifold. Suppose that $M$ is orientable and oriented (so that we can use $m$-forms as densities). Let $\xi:E\rightarrow M$ be a smooth ...
- 11.6k
2
votes
Accepted
Jacobian and chain rule contradiction, Geodesic equation
First of all, note that in general the Jacobian of the coordinate transformation is not identical with the coordinate transformation itself. As you mention in your first sentence, you first need to ...
- 3,273
2
votes
Difference between an orthonormal frame and normal coordinates
An orthonormal frame is exactly orthonormal everywhere, but might not be realized as the frame of any coordinate system. Normal coordinates give a frame that looks orthonormal to first order near a ...
- 1,506
2
votes
Does inflation really answer why the universe is almost flat?
You are confused by the standard way FLRW metric is written where in 3d metric you keep $a^2(t)$ as a common factor multiplied on sphere or hyperboloid metric with unit curvature radius. However, in ...
- 8,739
1
vote
Why do physicists want to apply the energy conservation law to the entire universe, when it is immune to falsification?
tenebris in kux wrote: "It cannot be applied to the universe as a whole because such an application would not be accessible to experiment"
This runs under the assumption of the Copernican ...
- 13k
1
vote
Net Time Dilation for a Free-Falling Object as Seen from Infinity
nir asked: "For an object freely falling from rest at infinity down to radius $r$, does the gravitational and velocity time dilation double up, or do they somehow cancel?"
From the ...
- 13k
1
vote
Accepted
How do you obtain the coordinates of 3D space from the FLRW metric?
If your issue is just interpreting spherical coordinates, note that you don’t actually need to define an additional spatial dimension to properly set stuff up. It is perfectly-fine to call the spatial ...
- 3,357
1
vote
Parallel transport of a vector on a $2d$ plane
Parallel vector field along a curve means that the "covariant differential of a vector along the curve vanishes" which implies
\begin{align}
\dot{A}^\mu+\Gamma^\mu_{\nu\lambda}A^\nu\dot{x}^\...
- 66
1
vote
Problem in deriving Killing equation
Question one: this is just notation for the antisymmetric part of a tensor
\begin{align}
\chi_{[a}\nabla_{b]}\chi_c\equiv\frac{1}{2}(\chi_{a}\nabla_{b}\chi_c-\chi_{b}\nabla_{a}\chi_c)
\end{align}
See ...
- 66
1
vote
Reference for property of $\psi_4$ of Newman-Penrose formalism
In vacuum we have $R_{\mu\nu}=0$ and therefore $C_{\alpha\beta\mu\nu}=R_{\alpha\beta\mu\nu}$ and so
\begin{align}
\Psi_4
&=C_{\alpha\beta\mu\nu}\tilde{k}^\alpha \bar{\tilde{m}}^\beta \tilde{k}^\mu ...
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