Physics, Astronomy & Cosmology / Re: Does The Gravity Of A Black Hole Travel Faster Than The Speed Of Light ?« on: 22/06/2022 02:00:15 »
Space and the way things behave in space follows the physical laws of science. Changing co-ordinates can't change that.Agree, but this contradicts what you said before. I had needed (and got) some clarification before knowing which one was the contradictory one. It concerns your alternate metric with T = x + t.
Consider dropping a scientist and well stocked lab into some arbitrary place and time in the Universe.This suggests that the 'way things behave in space' can be changed by a coordinate change. They're apparently performing experiments to empirically demonstrate an abstraction (their alternate choice). No experiment will show that, because as you say, the choice of abstraction can't change the way things physically (empirically) behave. One can tell the metric isn't Minkowskian simply with a pencil and paper. The experiments will all be unaltered by the choice.
Specifically, they can choose to use some arbitrary co-ordinates but they will know and can tell that the metric isn't Minkowski in those co-ordinates - it it will only take them a few experiments to determine that.
We seem to have a fundamental disagreement about the line between arbitrary abstraction and objective (and classical) physical fact.
However, some co-ordinate systems make things seem unnatural when expressed in those co-ordinates. E.g. Objects move around in circles in some some co-ordinates but physically they are always obeying Newton's laws, it's just that the chosen co-ordinates don't describe an inertial frame.Newton's laws are local simplifications and what might be a natural coordinate system for local description will be inevitably entirely unnatural for one's larger purpose. Yet again, we're not discussing local physics here, so choosing a nice neat local CS is inappropriate (not a natural choice). Most of your post focused on this 'LIF', but the 'L' there makes it unnatural for a non-'L' description unless spacetime remains effectively flat between observer and measured event, which in this scenario is not at all the case. Your scientist with the well stocked lab isn't considering anything in the lab, and he isn't even taking any actual measurements. The question wasn't 'what will the distant observer measure?'.
There's no disagreement here. The original sentence had the phrase "if they hold still" in it and the distant scientist is located on a surface of constant radial co-ordinate r, their entire worldline is on that surface. For the distant scientist, the proper time interval they experience (between two events in their worldline) = the difference in the Schwarzschild co-ordinate time, t, between those two events.[/quote]OK, I see what you mean. The same could be said worldline a meter above the event horizon, despite the objective massive dilation of the lower time relative to the distant time.Quote from: Eternal StudentThat Schwarzschild time, t, isn't unimportant or arbitrary to the scientist. That co-ordinate t is what they will experience as local time (if they hold still).This is wrong. How does one 'experience' any kind of abstract time? One experiences proper time. That's the only time that's physical. One does not 'experience' the time for some worldline not in one's presence.
Yes, in answering 'when does the rock cross the EH?', I was using time T (not t) to express the simultaneity since T is not singular. It may take some arithmetic, but one can very much compute distant-observer-t from a given T, even if T isn't something the guy's clock on the wall measures.
As shown on the Kruskal diagram (which was produced in paintbrush and took what seemed like hours before you criticize it again for not showing irrelevant details like the singularity).Fantastic job then. I never managed reasonable curves with the primitive tools I have. I'd have just grabbed one from the web.
Anyway, the event with the rock crossing over the EH is never in the past light cone of the distant scientistOf course not. It wouldn't be an EH if it was.
So that event never causes an effect for the distant scientist.None claimed.
This is getting to the crux of matter: We orbit around Sagittarius-A* which seems to be a big black hole, so we are that distant scientist, following a worldline that lies (more or less) at constant Schwarzschild radius r. Is it possible for that black hole to engulf a rock and grow, so that it's mass parameter is now larger, during a finite amount of time for us scientists?Hard to say, since the question is abstract, not physical. Your scientist might pick a metric that is singular at the EH, but that metric cannot actually describe the situation. The LIF doesn't work when there's gravity involved at all. The Schwarzschild metric doesn't work in anything but a static black hole. Even the distant orbiting thing violates that if it has any mass.
So I think I discussed this before. Absent a metric describing an infalling mass, one has to simply approximate and imagine it, possibly giving wrong answers. More below, but your comments are on point.
Will the mass parameter of Sgr-A ever change in my lifetime?If it didn't, it wouldn't have a mass parameter in the first place. Based on that alone, you have only two choices, a singular infalling metric that either allows mass at all, or one that doesn't. The rock (and everything else in its history) goes in or it doesn't. Keep in mind that the question isn't physical. It is strictly an abstract one unless one asserts physicality to a particular abstraction.
(Assuming that I do not ever get off planet earth and do something like travel fast or travel toward the black hole etc). It makes little practical difference if the gravity we experience from the centre of the galaxy is always caused by a black hole of Mass parameter M plus a small rock close to the event horizon with mass m, or if eventually we just experience the gravity from a Black hole with mass parameter M+m.A black hole with no mass at all, but a lot of crap almost in it is (must be) empirically indistinguishable from a black hole of mass <a lot of crap>. Thus we will very much experience M+m because m is there, inside or not. What we experience isn't abstract.
However, there is a small difference, one is symmetric, the other is not.Yes! That's a huge problem with plan B above (it all stuck on the surface). Suppose we start with a solar mass black hole (about 3km). Now we take a concrete cylinder 100m in diameter and massing 100 stars. It's a super-long cylinder. We jam that thing into the small black hole and it all sticks to the non-rotating surface in one place. That puts all the mass off to one side, not centered at all. That would violate the whole no-hair thing. The black hole (after the bar thrown in) is still stationary in the frame of the system CoM, (which is nowhere near where the small black hole was at first). Where is the mass? All on the one side, or centered on the radius? It can't be the former since an off-center mass would be empirically detectable, not just an abstraction. Right? No? My logical seems a little naive/Newtonian, so maybe I'm just doing the mathematics wrong.
So maybe a tiny mass gets stuck, but the next tiny mass (on the same side??) grows the EH, swallowing the first. You drop in a big rock, and all but the trailing bit gets in, at least relative to this chosen metric.
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