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MeJennifer
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How do you calculate the proper time and the proper distance for an object free falling into a black hole from the event horizon to the singularity?
Well but is the value r that simple? What does r represent here?pervect said:This gives dr/dtau = sqrt(2m/r), which is easily solved to find r as a function of proper time, giving a result for the above "easy" case which is
r = constant * (tau^2)^(1/3), tau = -infinty ... 0
So r starts out at infinity at tau = -infinty, and decreases to 0 at tau=0 in this solution. The proper time will be infinite if you start at r=infinty, but it will be finite if you start at finite r.
It is simply the distance traveled for the free falling object.pervect said:I'm not sure what "proper distance" would be - the "proper time" has a clear interpretation as the time that the falling observer reads on his watch.
I understand that.pervect said:r is the Schwarzschild r coordinate. The set of points of a given, constant value of r can be thought of as a sphereical shell around the black hole, one that has a surface area of 4*pi*r^2. r=0 occurs at the central singularity. r=2M (or in non-geometric units, r = 2GM/c^2) is the "event horizon".
Well don't worry everybody seems to do so and then with a straight face declare the value of proper time as if it is a done deal.pervect said:I suppose I should mention that the calculation in my previous post assumes that the interior metric is Schwarzschild, something that strictly speaking isn't likely to be true (it's probalby a BKL metric inside the horizon, though it's Schwarzschild outside the horizon).
Well exactly, then how can anyone support using r in the calculation for proper time? If we use r we use coordinate distance.pervect said:The free-falling particle is not in a single inertial frame, and the space-time is curved, so I don't see how one can sensibly define a proper distance.
Well since we apparently can use a metric to calculate the proper time of an object in free fall from the event horizon to the singularity what is the argument that we cannot calculate the proper distance traveled between the event horizon and the singularity?Pervect said:The free-falling particle is not in a single inertial frame, and the space-time is curved, so I don't see how one can sensibly define a proper distance.
MeJennifer said:I understand that.
But the issue that I do not understand is how you can use the r coordinate to calculate proper time. Clearly the r coordinate does not translate in some linear measure of distance for a free falling test particle.
Well don't worry everybody seems to do so and then with a straight face declare the value of proper time as if it is a done deal.
To me it is not, but that is probably because I do not understand it
Well exactly, then how can anyone support using r in the calculation for proper time? If we use r we use coordinate distance.Well since we apparently can use a metric to calculate the proper time of an object in free fall from the event horizon to the singularity what is the argument that we cannot calculate the proper distance traveled between the event horizon and the singularity?
The proper time for an object to fall into a black hole is the amount of time measured by an observer who is falling along with the object. This time is relative and can vary depending on the observer's position and velocity.
The proper time for an object falling into a black hole will appear to slow down as the object approaches the event horizon. This is due to the intense gravitational pull of the black hole, which causes time dilation. An outside observer will see time for the falling object appear to slow down significantly as it gets closer to the event horizon.
No, an object cannot survive falling into a black hole. The immense gravitational forces inside a black hole are strong enough to tear apart any object, including atoms and subatomic particles.
There is no minimum or maximum time for an object to fall into a black hole. The time it takes for an object to reach the event horizon depends on its initial velocity and the mass of the black hole. However, once an object passes the event horizon, it will reach the singularity at the center of the black hole in a finite amount of time.
No, once an object has passed the event horizon of a black hole, it is impossible for it to escape. The gravitational pull of a black hole is so strong that not even light can escape, hence the name "black hole". Any object that falls past the event horizon is destined to reach the singularity at the center of the black hole.