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hyunxu
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I hear people say that even light cannot escape from black hole.So how big is this black hole?Why gravitational pull is very high? Does it have any escape velocity like Earth have?
hyunxu said:I hear people say that even light cannot escape from black hole.So how big is this black hole?Why gravitational pull is very high? Does it have any escape velocity like Earth have?
For a spherically symmetric, massive body such as a star, or planet, the escape velocity for that body, at a given distance, is calculated by the formula[3]
v e = 2 G M r , {\displaystyle v_{e}={\sqrt {\frac {2GM}{r}}},}
where G is the universal gravitational constant (G ≈ 6.67×10−11 m3·kg−1·s−2), M the mass of the body to be escaped from, and r the distance from the center of mass of the body to the object
In principle, black holes can be any size. The ones that are formed from stars, though, don't form unless the star is above a certain mass because only big enough stars can compress their core enough to overcome internal pressure and collapse into a black hole. So there's a minimum size limit for black holes formed this way.hyunxu said:So how big is this black hole?
Because all of its mass is concentrated in a small volume (there are several criticisms one could make of that answer, but it'll do). At the moment, you are feeling a 1g pull from the Earth. Some of its mass is very close to you, but some of it is over 12,000km away - so the pull from those bits is quite weak. It turns out to average out to the same pull as if all of the mass of the Earth were at a point in the centre of the Earth. But if you (somehow) compressed the Earth into a black hole, then all of the mass would actually be in a very small volume around the centre of the Earth and you could get very close to all of the mass, and it would all pull on you very strongly.hyunxu said:Why gravitational pull is very high?
No (contrary to the previous answer). At the "surface" of a black hole, which is called the event horizon (it's not a surface in any physical sense, but is the point of no return, where you can no longer escape no matter how powerful your rocket is) it is simply impossible to move away from the black hole without moving faster than light, which is impossible. This is a different concept from the escape velocity, which is the speed you need to be going at to get to infinite distance without using your engines any more. That is meaningless for a black hole because you cannot move away even slightly, let alone to infinite distance.hyunxu said:Does it have any escape velocity like Earth have?
Ibix said:Escape velocity does make sense as a concept from points above the event horizon, but the formula provided by @stefan r is incorrect
Is that correct? The only reference I can find online that actually derives it (https://link.springer.com/article/10.1134/S102833581506004X) arrives at that result for the weak-field solution (equation 14). Frustratingly, the last two pages where they appear to be deriving the full solution are paywalled.PeterDonis said:Actually, the formula ##v_e = \sqrt{2M / r}## is exactly correct for the Schwarzschild metric in GR, for any point above the horizon.
hyunxu said:I hear people say that even light cannot escape from black hole.So how big is this black hole?Why gravitational pull is very high? Does it have any escape velocity like Earth have?
Ibix said:His equations 7.47 & 7.48, using ##\lambda=\tau##, setting L=0 for radial motion, ##\epsilon=-1## for a massive particle, and E=1 for it to come to rest at infinity
D'oh! Careless reading of the text following 7.39. Correcting that, I now get ##dr/d\tau=\sqrt{2M/r}## since the halves now cancel and the Newtonian potential term has the opposite sign. I do indeed need to multiply by ##\sqrt{-g_{rr}}## to convert dr into something physically meaningful, but I also need to multiply by ##\sqrt{g_{tt}}## to convert from the escaping object's proper time to a hovering observer's proper time, and it happens that ##-g_{rr}g_{tt}=1##.PeterDonis said:It should be ##\epsilon = 1## for a massive particle; see equation 7.39 and the text just following. Try it that way and you should get the result I gave.
Ibix said:Even noting that I think I actually want to know ##\sqrt{g_{rr}(dr/d\tau)^2}##
hyunxu said:I hear people say that even light cannot escape from black hole.So how big is this black hole?Why gravitational pull is very high? Does it have any escape velocity like Earth have?
This part is not correct, or, at least, is potentially misleading. The proper acceleration needed to hover at the event horizon is infinite, whatever the mass of the black hole.stefan r said:If a black hole's event horizon was 4.6 x 1015 m radius then gravity at the event horizon would be 9.8 m/s2.
Ibix said:This part is not correct. The proper acceleration needed to hover at the event horizon is infinite, whatever the mass of the black hole.
stefan r said:You can stand on Earth because the forces from the floor balance the force of gravity. There is nothing to stand on at the event horizon.
stefan r said:Falling would briefly have the same acceleration rate.
PeterDonis said:No, free-falling means zero proper acceleration.
There is no size of black hole, that's why it is a singularity in mathematical terms.hyunxu said:I hear people say that even light cannot escape from black hole.So how big is this black hole?Why gravitational pull is very high? Does it have any escape velocity like Earth have?
stefan r said:When I jump out of an airplane or jump off a diving board I get the impression that I am free falling and also appear to be accelerating.
As Peter says, this formulation of gravitational acceleration doesn't have an unambiguous definition in general relativity. If you are in a closed box, no experiment will tell you the acceleration due to gravity that you are undergoing - if you are in free fall you cannot tell if you are seconds from impact on the ground or are far out in deep space. This leads us (well, Einstein) to the conclusion that gravitational acceleration is a fictitious acceleration, similar to the centrifugal acceleration that appears in rotating reference frames. What its value is depends on the frame you pick. So "the acceleration rate of an observer crossing the event horizon" - in this sense - can take any value you like.stefan r said:You can stand on Earth because the forces from the floor balance the force of gravity. There is nothing to stand on at the event horizon. Falling would briefly have the same acceleration rate.
This isn't correct. Black holes of a wide variety of sizes, including very small, are likely...though tthere are more common sizes.stefan r said:An Earth mass black hole is unlikely.
Some people tried to address this, but not succinctly/directly enough:If a black hole's event horizon was 4.6 x 1015 m radius then gravity at the event horizon would be 9.8 m/s2.
As you get closer and closer to the event horizon the escape velocity approaches c, yes. But I think it's worth repeating that there isn't really an escape velocity from the event horizon because you can't escape. An object may hover at the event horizon if it was created there and moves at c. But nothing can reach infinity.russ_watters said:A black hole is defined by the event horizon, which has an escape velocity of "C"
russ_watters said:...
The error is you are mixing together an earth-mass black hole and an earth-radius black hole. A black hole of Earth's mass is only 2 cm in diameter. An Earth radius black hole has a mass much larger than any single star.
Saturn's surface gravity is 10.55 m/s2 but escape velocity is 35.5 km/s. "Escape velocity c" is not the same as "infinite surface gravity". The singularity probably does have infinite "surface" gravity.russ_watters said:...Some people tried to address this, but not succinctly/directly enough:
A black hole (and its size) is defined by the event horizon, which has an escape velocity of C and infinite "surface" g. So saying g=9.8 isn't correct/is a contradiction.
You need to define what you mean by infinite surface gravity before you can tell us what values it takes on. Gravity is not a force.stefan r said:"Escape velocity c" is not the same as "infinite surface gravity".
This claim is even more problematic.The singularity probably does have infinite "surface" gravity.
Well, as we keep saying, nothing has an escape velocity of c. Escape velocity doesn't make sense at or below the event horizon because you cannot escape. I don't think it's clear what "surface gravity" would mean in a general relativistic context. The closest analogy to the Newtonian concept is the proper acceleration needed to remain at constant altitude. So, with the caveats that the escape velocity doesn't really mean "escape" and that "surface gravity" is to be interpreted as the proper acceleration needed to stay at a height then both "escape velocity c" and "infinite surface gravity" are synonyms for "at the event horizon". All three are the same.stefan r said:"Escape velocity c" is not the same as "infinite surface gravity".
I'm pretty certain that isn't a coherent concept. The singularity isn't a place - it's a time in the future of anyone crossing the event horizon. Does next Friday have a surface gravity? (Edit: although Mondays do suck...)stefan r said:The singularity probably does have infinite "surface" gravity.
Assuming you're pointing the lamp straight up, they go straight up. Otherwise they follow curving paths that may continue to infinity or may curve back down into the black hole - it depends on the angle. They'll be either red- or blue-shifted when detected, depending on whether the detector is at a higher or lower altitude. Other Doppler effects may occur depending on the states of motion of the emitter and receiver.stefan r said:If you are a few meters above the event horizon (4.6 x 1015 +10 m ) and you turn on a light what happens to the photons?
You don't really specify what experiment you are doing here. I think you're shining a light upwards and detecting it at a point higher in the gravitational field. In that case, the receiver will measure a longer wavelength, yes. As you say, the effect is not extreme in the Earth's gravity. Please note, however, that the effect does not depend on the gravitational acceleration - it cannot, since that isn't well defined. Gravitational redshift depends on the difference in gravitational potential between the receiver and emitter. So I think this bit:stefan r said:On Earth the 9.8 m/s2 gravity has a small but greater than 0 effect on the wavelength of light. The photon would be longer if measured on the moon for example.
...is wrong.stefan r said:Near this event horizon gravity has the same effect on the photon. However, the gravity would still be 4.9 m/s2 at 1.4 times the radius from the hole. The gravity would be stretching the photon's wavelength for a very long time-distance (1.9 x 1015m) . So from a long distance the red shift is very large
That's not a good way to look at it. Better to say that a clock hovering near a black hole runs slower than a clock hovering far away. It's more precise, and avoids complications about "whose time do you mean?".stefan r said:Time also stretches.
Depends what you mean by a reasonable timescale, who's doing the measuring, and where home is. But yes, since clocks near a black hole run slowly, a distant observer will regard the astronaut as taking a long time to send a message - part and parcel of the redshift.stefan r said:The astronaut turning on a light would not get a message home on a reasonable time scale.
Correct, assuming the astronauts aren't so far apart that tidal effects become apparent. Ditto your hand - near a small black hole tidal effects will spaghettify you.stefan r said:However, two astronauts shining flashlights at each other would see something much like two skydivers shining flash lights at each other. If you were holding the light in front of you it would not look red shifted even if your hand crossed the event horizon first.
stefan r said:I would not consider myself an expert on gravity.
stefan r said:The singularity probably does have infinite "surface" gravity.
stefan r said:If you are a few meters above the event horizon (4.6 x 1015 +10 m ) and you turn on a light what happens to the photons?
stefan r said:Time also stretches.
Then I don't know what error caused you to say what I quoted. Regardless, it was wrong.stefan r said:I certainly did not make that error.
This is true; surface gravit[ational acceleration, or g] and escape velocity are not the same thing. But at the event horizon of a black hole, infinite g and escape velocity of c coincide. For other objects, the relationship depends on the mass and radius of the object, which can vary with respect to each other. For a black hole, each mass has only one radius (you can't have black holes of the same mass with different radii).Saturn's surface gravity is 10.55 m/s2 but escape velocity is 35.5 km/s. "Escape velocity c" is not the same as "infinite surface gravity".
Others have pointed out this doesn't make sense, but I'll assume you meant "event horizon", not "singularity". In that case, unlike your previously quoted statement, it is true.The singularity probably does have infinite "surface" gravity.
Since nothing can reach infinity, I don't see "you can't escape" and "escape velocity of c" as contradicting each other because you can't reach c. The main difference I see between that and other examples of escape velocity is there isn't even any ballistic trajectory that takes you away from the event horizon at all because no matter how fast you are going, you are stationary with respect to c.Ibix said:As you get closer and closer to the event horizon the escape velocity approaches c, yes. But I think it's worth repeating that there isn't really an escape velocity from the event horizon because you can't escape. An object may hover at the event horizon if it was created there and moves at c. But nothing can reach infinity.
No.Monsterboy said:I have a question, a single black hole finds itself between three other black holes who are more massive and are equidistant from it and from each other, can the three black holes rip the central black hole apart ?
Martin0001 said:No.
However such a system would be very unstable. How would you keep 3 larger BH apart?
Monsterboy said:They won't be apart for long, I wanted to know the effect on the central black hole before all of them combine.
No hair theorem is increasingly questioned. It implies information loss and undermines one of sacrest cows of QM, unitarity principle.stefan r said:Before the combination the black hole's event horizon has a radius. After the combination the event horizon has a larger radius. To say that "ripped the event horizon outward" would be a strange way to look at it.
Rotating black holes have a ring singularity. If 3 black holes merge they should become another rotating black hole. I have know idea which part of the new ring came from each black hole. Could that be your question?
There is a no hair theorem. The effect is that it does not matter how the black hole got its mass, momentum, and spin. They are all identical to someone on the outside. That would not need to mean that there was no ripping going on. It just cannot be observed.
Monsterboy said:a single black hole finds itself between three other black holes who are more massive and are equidistant from it and from each other, can the three black holes rip the central black hole apart ?
A black hole's gravitational pull is a phenomenon in which the intense gravitational force of a black hole pulls in and traps any nearby matter, including light. This pull is so strong that it can prevent even light from escaping, giving black holes their characteristic dark appearance.
The strength of a black hole's gravitational pull depends on its mass. The more massive the black hole, the stronger its gravitational pull. For example, the supermassive black hole at the center of our galaxy has a gravitational pull that is millions of times stronger than our Sun's.
Once an object crosses the event horizon of a black hole, it is impossible for it to escape the gravitational pull. This includes light, which is why black holes are invisible and appear as dark regions in space. However, some particles may escape through quantum processes, but this is still a topic of ongoing research.
According to Einstein's theory of general relativity, a black hole's intense gravitational pull causes time to slow down. This is due to the warping of spacetime near the black hole, which creates a strong gravitational gradient. As a result, time passes more slowly near a black hole compared to a distant observer.
Yes, a black hole's gravitational pull can affect objects that are far away. This is because gravity is a long-range force, and its effects can be felt even at great distances. For example, the gravitational pull of the supermassive black hole at the center of our galaxy affects the orbits of stars and gas clouds that are light-years away.