Recent content by Dukon

Thank you highly for being specific with numerical results. Very helpful. Much appreciated!

Thank you for commenting h can be set to anything we want, lets make it 10m, 100m, 1000m, 1500m, so we get a start of an initial table of h, d values. I just want to know what d is given h, and then find the h that drops us from NYC to Chicago, examples like this...NYC to LA, NYC to London UK...

Let there be a person in a not yet optimally designed sled at h meters in height. Let this sled free fall but user can steer by tilting their body weight in the sled or by optimal sled shape design point it in some horizontal direction where it is wanted to go - in any horizontal direction but...

Correction to post #14 $$\eqalign{ \tau &= t \sqrt{1 - \frac{r_s}{r} } \hspace{1.7in} \ J=0 \ Q=0 \ \ {\rm Schwarzschild} \cr \tau &= t \sqrt{1 - \frac{r_s r}{\rho^2} } \hspace{1.6in} \ J\ne 0 \ Q = 0 \ \ {\rm Kerr} \cr \tau &= t \sqrt{1 - \frac{r_s}{r} + \frac{{r_Q}^2}{r^2} } \hspace{1in} \...

OIC when you say time dilation factor you mean first order in ##\tau## which means we both agree yes $$ \eqalign{ d\tau^2\ &=\ \ g_{00}\ \ dt^2 \\ d\tau\ &=\ \ \sqrt{ g_{00} }\ \ dt \\ \tau\ &=\ \ t \ \ \sqrt{ g_{00} } \\ } $$ physics aligned; language misaligned. Langauge is a true hindrance...

Actually, I think it is ok not to square it. I left ## g_{00} ## as the ##(something)## as it is written top of my post #14 without taking it as ##(something)^2##. Leaving it as I did, when push came to shove, I had to take the square root of both sides to get rid of the squares on the...

The Time Dilation formula for the Kerr-Newman metric, in terms of a number of length parameters for a position ##(r,\theta)## away from center of mass and polar axis respectively of a gravitational body of mass ##M##, polar angular momentum ##J## and electrical charge ##Q##, is independent of...

Thank you very much for sharing the steps I would not have known to take from the place on that page I would never have known to stop to find this. I will post my final result of what I call the absolute form of time dilation which reduces in the ##J=Q=0## limits to the Schwarzschild time...

Absolutely fantastic to learn. Thank you. However, as I am not GR conversant enough I drown when viewing the myriads of other points made in the literature about any metric, that for me to find the ##g_{00}## metric coefficient would take hours and days still not knowing where it is. Even on...

Using the expression for the Schwarzschild radius ##r_s## and the "starting point" Kerr expression both from post #1, then the Kerr expression in terms of ##r_s##, the position ##r## and Angular momentum modified position ##\rho## reduces to $$1 - \left( \frac{{\rm d}\tau}{{\rm d}t} \right)^2 =...

Thank you for your comments on this By starting point I mean the Kerr expressions in my first post. To me, since that was not in a simple absolute form of ##\tau## on left and ##t## on the right, I took the whole Kerr mess I found somewhere else as my Kerr starting point. After doing the...

Thank you I was just now looking how to delete my post because after I posted it, I was able to solve myself both a) and b) of my request. Your comment is helpful confirmation that what I did was correct. Glad you commented, thanks. The Kerr time dilation in the form I wanted it to be can be...

Just as the time dilation formula for the Schwarzschild metric in terms of the position ##r## away from center of mass for a gravitational body and the Schwarzschild radius ##r_s = {2GM}/{c^2}## is given by $$ \tau = t \sqrt{1 - \frac{r_s}{r} } $$ so I'd like to know the corresponding...

Uranus and Neptune have roughly an 80-19-1 $H_2$-$He_4$-$CH_4$ mixture. (Of course actual percentages vary but those are rough values for sake of this simplification argument -- unless their actual values are critical to the answer.) Uranus temperature is reported as 2K while Neptune is 20K...

Understood that vacuum fluctuations (VF) and quantum fluctuations (QF) are identical, yes. No special nuance was intended by use of QF. However, in bulk taken as a whole set of VFs they are not as ephemeral, vaporous and without physical effects and physcial reality "as you think they are" lol...