Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: syhprum on 10/12/2017 18:24:27
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When I fall from a quasi infinite distance to a normal body such as a planet or star when I reach the surface I will be travelling at the escape velocity.
The event horizon of a black hole by definitition has an escape velocity of "c" would I be travelling at this speed SR would seem to forbid it.
It is observed that if I go into orbit I join a circulating halo of hot particles but what if I head straight in?
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That all depends upon the value of the potential at the event horizon. Not all black holes are identical. The escape velocity can be the same for all because of the inverse square nature of the gradient. It simply determines the required energy to escape to infinity. If this energy cannot be reach then any path away from the horizon will ultimately end up returning to the horizon. Since at all event horizons the energy for escape to infinity is infinite nothing gets out. This is different from the final inward instantaneous velocity at the horizon.
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Whether you can escape or not is defined by the ratio of your kinetic energy and your mass.
If your mass is zero and your kinetic energy is not zero, you can hover at the event horizon.
If your mass is small and your kinetic energy is large, you can escape from the vicinity of the event horizon.
We know that an object can bounce back from the vicinity of the event horizon, therefore we know that the kinetic energy/mass ratio of an object falling near an event horizon is large.
Maybe we can deduce the speed from the kinetic energy/mass ratio.
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Energy is a function of time. Time is dilated as velocity increases. So energy must also be dilated. The energy of the gravitational field itself may become dilated as the potential decreases. This would have to be taken into account in any calculation. But first you must determine if it is in fact true.
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Energy is a function of time
Idiot level explanation, please, Jeffrey.
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Energy is a function of time
Idiot level explanation, please, Jeffrey.
units of energy include a time term (for instance s–2 term in the equation 1 J = 1 kg m2 s–2
so if time and space are distorting, then energy, which has time and space terms must also change with the distortion (unless changes in m and s cancel out--I don't know off hand how spacial and temporal distortions are related around a black hole)
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Energy is a function of time
Idiot level explanation, please, Jeffrey.
units of energy include a time term (for instance s–2 term in the equation 1 J = 1 kg m2 s–2
so if time and space are distorting, then energy, which has time and space terms must also change with the distortion (unless changes in m and s cancel out--I don't know off hand how spacial and temporal distortions are related around a black hole)
It all depends upon whether or not there is such a thing as relativistic mass.
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How fast am I travelling when I cross the event horizon of a black hole?
Like everything in Relativity, it depends on your frame of reference!
- If you are a distant observer, with a powerful telescope that can see the victim plummeting towards a stellar-mass black hole, you would see them approach about 1/3 the speed of light
- If you are a distant observer, with an even more powerful far-infrared microscope that can see the victim plummeting towards a stellar-mass black hole, you would see them radiating far-infrared photons from a point just outside the event horizon, long after they should have crossed it (based on their velocity farther out). This is because of the extreme time dilation just near the event horizon. (By "long after", I mean "nanoseconds after", not "hours after").
- If you are the Olympic diver taking the ultimate plunge, you would not see the black hole approaching you (it is black, after all), but if you had a powerful telescope, you would see severe distortion of the starfield as this 10km-wide space expands to meet you at relativistic speeds (near 1/3 the speed of light).
- If you are the feet of the Olympic diver approaching a stellar-mass black hole, you would see the diver's head accelerate away from you at the speed of an aeroplane: spaghettification, as the acceleration due to gravity is very different between head and feet.
See: https://en.wikipedia.org/wiki/Spaghettification
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Thank you for this reference
https://en.wikipedia.org/wiki/Spaghettification
this would seem to be the best explanation yet as to what happens, I believe it is due to "spaghettification" that the velocity is limited to1/3 "c" .
Would a very dense object such as a stellar mass black hole falling into a super massive one attain a higher velocity ?
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Would a very dense object such as a stellar mass black hole falling into a super massive one attain a higher velocity ?
A black hole is a very small target in a large volume of space. Statistically, most collisions will not be falling directly into the black hole, but will "miss", and take an elliptical (or hyperbolic) path around the black hole. So the tangential/orbital velocity is what matters, rather than the radial velocity.
However, when two black holes are in orbit, they radiate significant amounts of energy in the form of gravitational waves. This radiation is most intense when the two bodies are closest. Paradoxically, this has the effect of reducing the farthest separation on their orbit. This results in "circularising" the orbit, over very many orbital passes.
They now radiate gravitational waves intensely throughout their circular orbit, and the radius of the orbit shrinks, until they eventually merge.
The first gravitational waves detected were from the merger of two black holes around 30 solar masses each.
Across the 0.2-second duration of the detectable signal, the relative tangential (orbiting) velocity of the black holes increased from 30% to 60% of the speed of light. The orbital frequency of 75 Hz (half the gravitational wave frequency) means that the objects were orbiting each other at a distance of only 350 km by the time they merged.
As always, this orbital velocity (and orbital frequency) will differ depending on the frame of reference of the observer!
See: https://en.wikipedia.org/wiki/First_observation_of_gravitational_waves#Astrophysical_origin
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units of energy include a time term (for instance s–2 term in the equation 1 J = 1 kg m2 s–2
I see that, but then I ask: does the fact that time is included in our measurement of the work done by an amount (unit) of energy, mean that energy itself has a time component?
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E = mc^2 has a time component in the speed of light. This is 1 light second divided by 1 second. It could equally well have been 1 Planck length divided by 1 Planck time. This rest energy has to be considered separately from kinetic energy, 1/2mv^2.
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Not quite on topic, perhaps, but it does involve black holes.
https://www.laboratoryequipment.com/news/2017/12/how-strong-are-black-holes-really?et_cid=6206921&et_rid=517749120&type=cta&et_cid=6206921&et_rid=517749120&linkid=https%3a%2f%2fwww.laboratoryequipment.com%2fnews%2f2017%2f12%2fhow-strong-are-black-holes-really%3fet_cid%3d6206921%26et_rid%3d%%subscriberid%%%26type%3dcta
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Not quite on topic, perhaps, but it does involve black holes.
https://www.laboratoryequipment.com/news/2017/12/how-strong-are-black-holes-really?et_cid=6206921&et_rid=517749120&type=cta&et_cid=6206921&et_rid=517749120&linkid=https%3a%2f%2fwww.laboratoryequipment.com%2fnews%2f2017%2f12%2fhow-strong-are-black-holes-really%3fet_cid%3d6206921%26et_rid%3d%%subscriberid%%%26type%3dcta
Sag A* is the black hole at the centre of our galaxy. The gas cloud G2 survived its encounter with this object so fields being dilated near a black hole makes perfect sense.
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How much would G2's escape have been influenced by the fact that it is not just gas; but has a very large star at its centre?
What effect would the star's presence have on the field dilation?
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Whether you can escape or not is defined by the ratio of your kinetic energy and your mass.
If your mass is zero and your kinetic energy is not zero, you can hover at the event horizon.
If your mass is small and your kinetic energy is large, you can escape from the vicinity of the event horizon.
We know that an object can bounce back from the vicinity of the event horizon, therefore we know that the kinetic energy/mass ratio of an object falling near an event horizon is large.
Maybe we can deduce the speed from the kinetic energy/mass ratio.
I derive gamma, the relativistic factor of change, I leave deriving the speed from the gamma as an exercise for the reader.
kineticenergy / mass = (totalenergy - mass) / mass
so
kineticenergy / mass = (totalcenergy / mass) - 1
so
kineticenergy / mass = gamma - 1
so
gamma = the kinetic energy/mass ratio, which approaches infinity when a falling object approaches event horizon, plus one
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How much would G2's escape have been influenced by the fact that it is not just gas; but has a very large star at its centre?
What effect would the star's presence have on the field dilation?
What actual evidence is there of a central star?