What about the force on an object near the event horizon though?
Imagine a huge black hole, with low gravity gradient at the event horizon. I use a rocket to hover just outside the event horizon and use a simple pendulum to measure g at my feet and g at my head. If I did that at different...
I am a bit weak on that question! But it is a stationary observer outside the event horizon, and I can't decide if it is the acceleration that a distant observer decides is being experienced at the event horizon, or if it is the oberver at the event horizon that experiences that acceleration.
I think I missed a 2 in my original post. The Schwartzschild radius is 2GM/c^2.
I do believe the Newtonian formula for Gravitational pull applies down to the event horizon, i.e. acceleration due to gravity = GM/r^2 still. Substitute r=Schwartzschild radius and you get the acceleration at...
I continue to do a few math computations to understand this, and I just looked at gravity within a disc of matter.
Now while gravity at radius R within a sphere of matter experiences zero pull from the spherical shells at radius greater than R, unless I have a bug in my prgram, this is not...
gravitational pull = GM/r^2 at static radius r outside the event horizon
substitute schwartzschild radius r = GM/c^2
and you get c^4/GM as the gravitational pull at the event horizon.
For modest BHs (small M) this is enormous. But for ginormous M, it becomes tolerable.
Then it seems you agree that there IS a singularity at the event horizon, at least to an observer who is not in free fall. And the catastrophic stretching is nothing to do with the rocket thrust, as in my example, that would only have to be g=9.81m/s^2, as here on earth.
I am just getting round to taking another look at the Kruskal extension. The last time I looked, I had many problems with it, at least the way it was presented, as it had quantities under square root signs that became negative. And that wasn't the only problem. It basically transforms only the r...
What I was saying is that, from a certain perspective, the event horizon can appear one-dimensional; if you imagine its area appearing to be zero (instead of a sphere) while its thickness or depth appears to be infinite instead of zero, then it morphs to a straight line in the radial direction...
I think you must be talking about an observer in free fall into the BH.
However, consider a BH of mass 1.237e43 Kg, which is still only about 1e-15 the mass of our universe. The gravitational acceleration at the event horizon is c^4/GM, which you will find is our regular 9.81 m/s^2 with the...
Yes, it is absurd, but not stupid. It may be absurd AND correct.
I have tried to imagine a convoy of spacecraft heading directly towards a BH.
Far from the hole, they were equispaced and traveling at the same speed, one behind another. If you were in one of the middle ones, what would you...
Those claiming there is no singularity at the event horizon should be asked the following question:
If your head was inside the event horizon and your feet were outside, could you wiggle your toes?
If not, I suspect you would find that rather disconcerting, and some catastrophe would...
If you go down a mineshaft, gravity reduces because the pull of gravity is due only to matter between r=0 and the radius R you are at, and force due to all matter outside that radius R where you are integrates to zero. Assume, perfectly spherical, uniform matter density distribution.
But now...
Spacetime doesn't have to "hold" anything in orbit. The orbital trajectories are the natural paths a body will follow when NO forces are applied.
We just have to restate Netwon's fisrt law:
Original says: "Every body remains in its state of rest or uniform motion in a straight line unless...
If the number of poles is much lower than the number of data samples, a version of Prony would be suggested. Many improvements to Prony's algorithm have been made since 1795. The "smallest eigenvector" method of Howard J Price is better than Prony's original method. Still better is the optimum...