I am busy with an effort to show how the energy density parameters evolve over time in an update of the LightCone7 calculator. See the posts on the thread Steps on the way to Lightcone cosmological calculator. As part of this effort, I ran into some difficulties with deciding how to find and...
The full power series for the Schwarzschild portion of perihelion shift is given in Mathpages as:
where L = a(1-\epsilon^2), a the semi-minor axis and \epsilon the eccentricity. This implies that as \epsilon tends to zero, the perihelion shift tends to a non-vanishing 6\pi m/a + some much...
LIGO reported the announced event with a redshift of 0.6 < z < 1.3. With no em radiation event reported
(AFAIK), does anyone know how they have determined the redshift?
I understand how they could measure the pre-merger, chirp and ring-down frequencies with good accuracy. In order to determine...
The LightCone7 cosmological calculator has been under collaboratively development on this forum for over three years now. It has sprouted a branch following Marcus' definition of a 'natural timescale of the present universe' - the long term Hubble time, which we collaboratively labelled one...
If we restrict ourselves to a homogeneous, spatially flat LCDM universe model, the Friedman equations can be written a very simple form. Marcus posted several threads in a collaborative effort to develop the simplified approach. Here is a summary of the parts that seem the most informative, to...
In this thread, I would like to discuss: "which is more natural for a simple cosmological model: taking the long term Hubble time as a timescale (as Marcus has done), or taking the Hubble time as a timescale". I will start by paraphrasing Marcus' OP and replacing his '##\Lambda##-timescale' with...
In an old (2008) thread, DrGreg posted this transformation from a Minkowski chart to a Rindler chart
He also wrote:
My question: using these photon worldlines, does a two-way radar measurement give a valid radar distance between two points in the Rindler frame, as per this zoomed...
MTW section 25, from eq. 25.16 onwards, derives an orbital equation (with G=c=1, u = M/r, E and L Schwarzschild constants for energy and angular momentum respectively):
\left(\frac{du}{d\phi}\right)^2 = \frac{M^2}{L^2}(E^2-1) + \frac{2M^2}{L^2}u - u^2 + 2u^3
This equation is readily...
We are trying to find the relative velocity in a Lemaitre observer's frame, when said observer passes an observer dropped from rest at Painleve radius r_0. I have searched for related previous posts, found some, but none that clarified this particular situation.
Let the passing happens at 0 < r...
I have often thought about how the one-way speed of light can be measured without having to use synchronized clocks, which tends to be controversial because the clocks are normally synchronized by using one-way light in the first place. Recently, Don Lincoln of Fermi-Lab suggested a method to...
Since 2006/7, David Wiltshire published a number of papers on his "http://arxiv.org/abs/1102.2045" [Broken]", as he calls it lately (2010/11), apparently changing from the original "Fractal Bubble (FB) universe" name. I suspect that this change was due to it being confused with the "Hubble...
Here is an interesting observation, which I would like to know the validity of.
The momentum of a relativistic 'cosmological' particle in a homogeneous universe can be written as ^{[1]}
L = \gamma m a v_{pec} = K
where \gamma=(1-v_{pec}^2/c^2)^{-0.5}, m the rest mass, v_{pec} the peculiar...
The "False Twin Paradox"
I have no problems with the resolution of the classical 'Twin Paradox', but the following "False Twin Paradox" does have me puzzled. (If it was discussed and explained elsewhere, please just point me there.)
Instead of the usual accelerating twin at the turnaround...
The use of gravity-assist flybys of planets are well known for interplanetary missions. My question: can a Sun flyby be used to gain orbital energy relative to the Galactic center for interstellar missions?
I assume one must first attain solar escape velocity by other means, since bound...
Same topic, new question, I think, so please suppress the Arghh!!!s. This is about detection of 'tidal gravity' effects inside a uniformly accelerated lab in free space.
As I understand it, if you release a spherical test particle cloud to 'free-fall from rest' inside a uniformly accelerated...
The main attraction of the Loedel spacetime diagram is that it treats the reference frame and the first moving frame symmetrically and hence they have identical scales in geometric units. The Minkowski diagram uses different scales for the orthogonal and the non-orthogonal axes, where the time...
I've scanned some literature, but could not find a description of the mechanism that causes the "thin vertical wind"* from the accretion disk of a quasar. Can someone please explain or point me to an accessible paper?
*Elvis M., 2000, Astrophysical Journal 545, 63
I understand that light can be in an unstable orbit at Schwarzschild radial coordinate r=3M (geometric units) around a Schwarzschild black hole. I also understand that the local* circular orbital speed of a massive particle around the hole is
v_o = r\frac{d\phi}{dt} =...
MTW section 27.7 states:
It then proceeds to derive the relationships: \rho_m a^3 = constant and \rho_v a^4 = constant that pervect has shown before.
My question: does this mean one cannot push the basic Friedmann equations that were discussed so exhaustively in the locked thread...
The Einstein cross (G2237+030) shows 4 reasonably symmetrically spaced images of the very distant quasar, indicating that our alignment with the galactic nucleus to quasar line is fairly good.
How is that it does not show an Einstein ring instead of the cross?
Here's something that puzzled me for some time: why are space-proper-time (SPT) diagrams not used more frequently? I did search this forum for the term, but without success. It may be known under some other technical term that I don't know about.
I'm using the term with the meaning as per...
Relativity is not a thing your nominal engineer ever needs. Some engineers have a curiosity that drives them to find out what they can about the topic. Some read all the popular books and still have little 'handles' on it. Most just ignore it, unless their work somehow requires it.
There are...