Recent content by Dema

Thank you very much for your effort and patience, now all this stuff sounds much clearer to me! Bye D.

Thanks again. Now I understood more deeply the meaning of the factor ##\sqrt{1 - 3M / R}##. Therefore, would it be correct to say that the 2 formulas ##A=\sqrt{g_{tt} + 2\Omega g_{\phi t}+\Omega^2 g_{\phi \phi}}## and ##A=\alpha\cdot\sqrt{1-v_{\pm}^2}## are equivalent only for the special case...

Thanks, this is exactly what I understood. Now I would like to come back to my original questions (see post #1): are the 2 Doppler shift factors, for a source on a circular orbit around a BH, ##A=\sqrt{g_{tt} + 2\Omega g_{\phi t}+\Omega^2 g_{\phi \phi}}## and...

If the gravitational factor is given by ##1 / \sqrt{1-2GM / c^2 R}##, why should it not appear trivially constant, as it depends only on the radius R of the circular orbit? Thanks D.

Thank you again for having showed me the right way to do the calculation. I think now I got it. As you suggested, I tried to apply it for a source on a circular orbit in the equatorial plane of a Schwarzschild BH, by considering a ring of static observers at radius R and an observer at rest at...

Thank you very much for your suggestion. I took some days to review the relativistic Doppler effect on some textbooks and I recognized the mistake I did in my previous evaluation, at least when the emitting body is moving on a straight line: I didn't take into account the special relativity time...

Thank you for the clarification. I tried to work out a way to include this in the definition of ##A##. On the simpler situation in which the emitting body is moving on a straight line (i.e. in a 1-dimensional problem) the duration observed by the far observer should be ##\Delta T_{\text{inf}}...

True, but if I already assume that the distance of the faraway observer is much greater than the orbit diameter, (approximation already needed to guarantee that ##g_{tt} \approx 0 ##) than the difference in time travel of pulses due to the displacement on the orbit wouldn't be negligible as...

Hmmm... the easiest way I can conceive is the following. Let me assume for the moment that the metric is Schwartzschild (the BH does not rotate) and coordinates are the usual Schwartzschild ones (## t, r, \theta, \phi##) Let's now assume that the orbiting observer emits a single light pulse...

Thank you for the replies and clarifications. I'll try to do my best to explain what I mean by "time reduction factor". I would say that "time reduction factor" can be defined as the ratio of time durations of the same phenomenon as measured by a clock carried by an observer orbiting the BH...

Thank you for the clarification, I was a bit too quick in my explanation. I understand there is no concept such velocity observed at infinity in GR and in the formula ##\frac{d \tau}{ dt}= \sqrt{g_{\mu \nu} \dot{x^{\mu}} \dot{x^{\nu}}}## the derivatives are those of coordinates with respect...

Hello, I’d have a question regarding two apparently different formulas for the time reduction factors for observers in orbit around a rotating black hole, as reported in this nice thread: Equation for time dilation of body in orbit around Kerr black hole? The first one is: $$A=\sqrt{g_{tt} +...