Watsisname wrote:the photo guy, the better choice is escape velocity. For any black hole, the escape velocity at the event horizon is equal to the speed of light. In fact, if you set the escape velocity of an object to be equal to the speed of light, you'll end up with the formula for the size of a black hole:
Escape velocity is [math]
Set that equal to c, then solve for r, and we get [math]
which is exactly the formula for the size of the event horizon, or "Schwarzschild Radius", of a black hole. Actually, this is a coincidence. It used Newtonian gravity, where we really should be using general relativity, but it happens to give the right answer in this case.
The problem with using acceleration for this is that acceleration and velocity are incompatible. They have different units. So there is no sense in which an acceleration is faster or slower than light (or any other velocity that you choose). You just can't compare them.
For a black hole, you could with Newton's Laws calculate the acceleration due to gravity at its event horizon, and the answer will vary depending on the mass of the hole. For a larger black hole, you'll get a smaller acceleration due to gravity at its horizon. But, this is misleading. It implies you could hover at the horizon of a sufficiently massive black hole -- or even hover at any distance inside of the black hole if your thrusters are strong enough. That implication is wrong. It actually takes infinite acceleration to hover at the horizon, and no matter how large your acceleration is, you cannot hover inside the horizon. You get swept into the singularity.
Similarly, we should be careful about interpreting "escape velocity" at the event horizon. It might imply that a light ray emitted from there would just barely escape to infinity, like a rocket launched at the escape velocity from a planet. Or it may imply a light ray emitted from just inside the horizon would escape a little bit outside of it, and then fall back in. These implications are wrong. A ray of light emitted outward exactly at the horizon will simply be stuck there, as if it is climbing up a downward-moving escalator at the exact same speed that the escalator is moving. And a light ray emitted outward from just inside will be immediately pulled further inward, just like a fish trying (and failing) to swim up a waterfall.
Some might also think that you would be suddenly able to see the singularity (or whatever it is) deep inside the black hole, after you've fallen through the event horizon. But you'll never see it. Even when the singularity is mere inches in front of you (and assuming you haven't been torn apart by tidal forces yet), it is still invisible. That's because all light is being pulled into the singularity -- none is leaving from it.
The reason these intuitions fail are because there are based on Newtonian experience, whereas what's really happening involves a general relativistic treatment of the space-time. In a very real sense, a black hole in general relativity is a stronger attractor than anything in Newtonian gravity. The behavior of things near or inside black holes is less like the orbits of satellites around planets, and more like fish caught in a current about to go over a waterfall. Space itself is dragging things in, and inside the horizon it is completely overwhelming, while far away it is quite escapable.
Hopefully this "escalator" or "waterfall of space" analogy helps remove some of the mystery of black holes for you and answers your last questions. But if it is still confusing, feel free to ask more!
And the last thing I want to say is that the speed of light does not get violated in a black hole. Everything that falls in is moving at or less than the speed of light through the space. But the space itself is flowing into the singularity faster than light, like the river going over a waterfall. This might seem unsettling (and in fact this is a little bit of a simplification for how it really works -- the more correct explanation again requires general relativity and a description of space-time curvature), but the helpful answer is that special relativity places a limit on how fast things can move through space (speed of light), while general relativity allows the space itself to move, dragging things along with it, and the motion of space isn't limited by the speed of light.
Watsisname wrote:the photo guy, the better choice is escape velocity. For any black hole, the escape velocity at the event horizon is equal to the speed of light. In fact, if you set the escape velocity of an object to be equal to the speed of light, you'll end up with the formula for the size of a black hole:
Escape velocity is [math]
Set that equal to c, then solve for r, and we get [math]
which is exactly the formula for the size of the event horizon, or "Schwarzschild Radius", of a black hole. Actually, this is a coincidence. It used Newtonian gravity, where we really should be using general relativity, but it happens to give the right answer in this case.
The problem with using acceleration for this is that acceleration and velocity are incompatible. They have different units. So there is no sense in which an acceleration is faster or slower than light (or any other velocity that you choose). You just can't compare them.
For a black hole, you could with Newton's Laws calculate the acceleration due to gravity at its event horizon, and the answer will vary depending on the mass of the hole. For a larger black hole, you'll get a smaller acceleration due to gravity at its horizon. But, this is misleading. It implies you could hover at the horizon of a sufficiently massive black hole -- or even hover at any distance inside of the black hole if your thrusters are strong enough. That implication is wrong. It actually takes infinite acceleration to hover at the horizon, and no matter how large your acceleration is, you cannot hover inside the horizon. You get swept into the singularity.
Similarly, we should be careful about interpreting "escape velocity" at the event horizon. It might imply that a light ray emitted from there would just barely escape to infinity, like a rocket launched at the escape velocity from a planet. Or it may imply a light ray emitted from just inside the horizon would escape a little bit outside of it, and then fall back in. These implications are wrong. A ray of light emitted outward exactly at the horizon will simply be stuck there, as if it is climbing up a downward-moving escalator at the exact same speed that the escalator is moving. And a light ray emitted outward from just inside will be immediately pulled further inward, just like a fish trying (and failing) to swim up a waterfall.
Some might also think that you would be suddenly able to see the singularity (or whatever it is) deep inside the black hole, after you've fallen through the event horizon. But you'll never see it. Even when the singularity is mere inches in front of you (and assuming you haven't been torn apart by tidal forces yet), it is still invisible. That's because all light is being pulled into the singularity -- none is leaving from it.
The reason these intuitions fail are because there are based on Newtonian experience, whereas what's really happening involves a general relativistic treatment of the space-time. In a very real sense, a black hole in general relativity is a stronger attractor than anything in Newtonian gravity. The behavior of things near or inside black holes is less like the orbits of satellites around planets, and more like fish caught in a current about to go over a waterfall. Space itself is dragging things in, and inside the horizon it is completely overwhelming, while far away it is quite escapable.
Hopefully this "escalator" or "waterfall of space" analogy helps remove some of the mystery of black holes for you and answers your last questions. But if it is still confusing, feel free to ask more!
And the last thing I want to say is that the speed of light does not get violated in a black hole. Everything that falls in is moving at or less than the speed of light through the space. But the space itself is flowing into the singularity faster than light, like the river going over a waterfall. This might seem unsettling (and in fact this is a little bit of a simplification for how it really works -- the more correct explanation again requires general relativity and a description of space-time curvature), but the helpful answer is that special relativity places a limit on how fast things can move through space (speed of light), while general relativity allows the space itself to move, dragging things along with it, and the motion of space isn't limited by the speed of light.
A-L-E-X wrote:Source of the post The funny thing is that the universe does expand at faster than the speed of light (it's the basis for the Alcubierre drive).
Marko S. wrote:Source of the post And, can light travel to the infinity or??
the photo guy wrote:Marko S. wrote:Source of the post And, can light travel to the infinity or??
I would say no, because if it didn't I would imagine you would see stars from an infinite distance. but that doesn't happen, stars start to fade after a huge distance. so yes, light does weaken as it travels through the vacuum of space, or even any other place.
Marko S. wrote:Source of the post Thanks! So, gravitational waves are only caused if some objects are orbiting each other?
Marko S. wrote:Source of the post And, can light travel to the infinity or?? Is there fading to the light if it is traveling through vacuum? Can light weaken when it oscillates through space?
Marko S. wrote:Source of the post And what gravity is needed for light to orbit the planet or something else? Like, if want light to orbit Earth at 30.000 km away, how much gravity is required for that?
Gnargenox wrote:Source of the post Strange that the oscillations of mass actually do stretch space-time, creating an elastic like harmonization within our reality.
Watsisname wrote:Source of the post Then the mass contained within the Earth must be 1530 solar masses.
JackDole wrote:Watsisname wrote:Source of the post Then the mass contained within the Earth must be 1530 solar masses.
I assume it is a write error. When I apply your formula I get 1.52913392 solar masses. (Approximately 1.530)
JackDole wrote:Source of the post I assume it is a write error. When I apply your formula I get 1.52913392 solar masses. (Approximately 1.530)