Escape from a black hole with another black hole?

[CosmicVoyager]

Greetings,

The event horizon of a black hole is supposedly a point of no return. But can't the presence of another gravitational source decrease the event horizon? If you are between two sources of gravity isn't it easier to move away from either one?

If immediately after a particle crosses the event horizon of a black hole, another more massive black hole were to near-miss it with the event horizons overlapping, couldn't the event horizon be moved back so the the particle is outside and get pulled into the other black hole? Or, if the speed and trajectories were just right, free the particle from both?

Thanks

 

[Nabeshin]

The event horizon is defined to be the surface beyond which no outgoing light rays will propagate to infinity. It is determined by a complete knowledge of the four-dimensional spacetime: that is, to compute the event horizon you actually need to know the entire future evolution of the system! Since it is defined to be this surface, no situation you concoct will allow a light ray, or any other particle, to propagate away to infinity from within this boundary.

 

[CosmicVoyager]

The event horizon is defined to be the surface beyond which no outgoing light rays will propagate to infinity. It is determined by a complete knowledge of the four-dimensional spacetime: that is, to compute the event horizon you actually need to know the entire future evolution of the system! Since it is defined to be this surface, no situation you concoct will allow a light ray, or any other particle, to propagate away to infinity from within this boundary.

So there is no equation for calculating the event horizon since it would have to incorporate the entire evolution of the system?

Well, what about the same scenario for the Schwarzschild radius? That is supposed to be a point of no return (for a non-rotating spherical body), and it has a simple equation that does not consider anything beside the body.
http://en.wikipedia.org/wiki/Schwarzschild_radius

 

[Dmitry67]

That solution is exact only if you assume that there is nothing outside the Black hole. Exactly what Nabeshin explained in his post.

 

[CosmicVoyager]

That solution is exact only if you assume that there is nothing outside the Black hole. Exactly what Nabeshin explained in his post.

So anyplace, such as the wikipedia article, that gives the equation for the schwartzchild radius and does not say it is only true if you assume that there is nothing outside the black hole, is incorrect.

Based I that, I am now guessing that there is an equation for the event horizon which would also be incorrect if that stipulation is not made. If a book says it is calculated by a given equation, that book would be incorrect because there are scenarios something could escape.

 

[Nabeshin]

When you have a solution such as a schwarzschild or kerr black hole, what you have is a solution in vacuum -- that is, the only gravitational source that exists is a delta function source. As soon as you start to talk about matter falling into the hole, this solution is no longer correct! Now, we can analyze the motion of such matter if we assume that its mass is negligible compared to that of the hole -- in which case it will just follow geodesics without distorting the spacetime at all. It is in this regime that we typically discuss things falling past the event horizon.

When the spacetime is not given by such a simple one-body situation, then indeed there is no formula for the event horizon. In some situations, such as two black holes orbiting each other when they are quite far away, you can probably use perturbation theory to see how the event horizons around each hole deviate from the normal horizons. But for anything more extreme, you need to know the entire evolution of the spacetime (when you can write down the metric explicitly, as in the schwarzschild case, you DO know the entire evolution!).

Does that clear it up?

 

[CosmicVoyager]

When you have a solution such as a schwarzschild or kerr black hole, what you have is a solution in vacuum -- that is, the only gravitational source that exists is a delta function source. As soon as you start to talk about matter falling into the hole, this solution is no longer correct! Now, we can analyze the motion of such matter if we assume that its mass is negligible compared to that of the hole -- in which case it will just follow geodesics without distorting the spacetime at all. It is in this regime that we typically discuss things falling past the event horizon.

When the spacetime is not given by such a simple one-body situation, then indeed there is no formula for the event horizon. In some situations, such as two black holes orbiting each other when they are quite far away, you can probably use perturbation theory to see how the event horizons around each hole deviate from the normal horizons. But for anything more extreme, you need to know the entire evolution of the spacetime (when you can write down the metric explicitly, as in the schwarzschild case, you DO know the entire evolution!).

Does that clear it up?

I understood perfectly. The point of my last post is to say that what I originally posted is correct, which is that if a text says the event horizon is a point of no return and gives the standard equation without stipulations, then it is false.

 

[Nabeshin]

if a text says the event horizon is a point of no return and gives the standard equation without stipulations, then it is false.

Well I wouldn't say it's false, but there is a tacit assumption that the matter has negligible mass compared with the hole.

 

[Chronos]

I may be missing something obvious, but, a black hole's event horizon cannot contract relative to its center of mass under any circumstances I can imagine.

 

[CosmicVoyager]

I may be missing something obvious, but, a black hole's event horizon cannot contract relative to its center of mass under any circumstances I can imagine.

Hi :-)

The event horizon is the distance at which nothing can escape the gravitational pull of the black hole, right?

If you have something outside pulling on things in the opposite direction, doesn't that mena things need to be closer to the black hole to get pulled in?

It's like if you had another planet next to the earth. Wouldn't the escape velocity of the Earth in the area between the two planets be less?

 

[IsometricPion]

If you have something outside pulling on things in the opposite direction, doesn't that mena things need to be closer to the black hole to get pulled in?

The escape velocity of a set of stationary masses can be easily computed in Newtonian gravity. The potential energies of each massive object can simply be added to obtain the total potential energy of an object. \frac{-GM_{1}m}{\sqrt{x^{2}+y^{2}+z^{2}}}-\frac{GM_{2}m}{\sqrt{(x-\alpha{})^{2}+y^{2}+z^{2}}} where G is the universal gravitational constant, M_{1} is the mass of the object at the origin, M_{2} is the mass of the second massive object at a distance of \alpha from the origin along the x-axis, m is the mass and x,y,z are the coordinates of the object for which one wishes to calculate the escape velocity. Since the potentials add to each other, adding additional masses to a system always increases the escape velocity from any given point in that system (since the kinetic energy required to escape must be greater than or equal to the total initial potential energy), including the point halfway between the masses (x=\frac{\alpha}{2},y=z=0). General relativity only serves to increase the gravitational attraction (though this is significant only within a few radii of the event horizon). This result can be made somewhat more intuitive by realizing that while the addition of another mass may decrease the force on an object at a given point, in order to escape the object will have to go through regions with higher gravity than if only one mass were present. Therefore, it seems like a reasonable inference that the surface area of the event horizons of two black holes near each other would be larger than their areas when they are far apart.

 

[CosmicVoyager]

The escape velocity of a set of stationary masses can be easily computed in Newtonian gravity. The potential energies of each massive object can simply be added to obtain the total potential energy of an object. \frac{-GM_{1}m}{\sqrt{x^{2}+y^{2}+z^{2}}}-\frac{GM_{2}m}{\sqrt{(x-\alpha{})^{2}+y^{2}+z^{2}}} where G is the universal gravitational constant, M_{1} is the mass of the object at the origin, M_{2} is the mass of the second massive object at a distance of \alpha from the origin along the x-axis, m is the mass and x,y,z are the coordinates of the object for which one wishes to calculate the escape velocity. Since the potentials add to each other, adding additional masses to a system always increases the escape velocity from any given point in that system (since the kinetic energy required to escape must be greater than or equal to the total initial potential energy), including the point halfway between the masses (x=\frac{\alpha}{2},y=z=0). General relativity only serves to increase the gravitational attraction (though this is significant only within a few radii of the event horizon). This result can be made somewhat more intuitive by realizing that while the addition of another mass may decrease the force on an object at a given point, in order to escape the object will have to go through regions with higher gravity than if only one mass were present. Therefore, it seems like a reasonable inference that the surface area of the event horizons of two black holes near each other would be larger than their areas when they are far apart.

I am referring to the event horizon as defined by the equation that does not take anything outside into account. The question was answered prior to Chronos' post. Repeating what I have said previously, it is usually stated that the event horizon is a point beyond which a particle cannot escape the objects gravitational pull, *and* the equation given does not take into account anything outside the black hole. It is not for a multiple body system.

 

[jobigoud]

Repeating what I have said previously, it is usually stated that the event horizon is a point beyond which a particle cannot escape the objects gravitational pull, *and* the equation given does not take into account anything outside the black hole. It is not for a multiple body system.

I'm no cosmology expert, and I find the question interesting, however I think your logic is wrong here.

We have the statement : "if nothing else is taken into account outside the Black Hole (A), then nothing can escape the event horizon (B)."
You use this to infer that under different circonstances (not A), then something could escape (not B). Although it might be true (I don't know), you cannot infer it from this discussion alone, and thus the matter is not resolved.

PS: This is called http://en.wikipedia.org/wiki/Denying_the_antecedent" .

 

[Nabeshin]

I may be missing something obvious, but, a black hole's event horizon cannot contract relative to its center of mass under any circumstances I can imagine.

It's certainly true that the area of the event horizon cannot decrease. However, the horizon can oscillate, which should allow points which were previously inside the horizon to come into causal contact with the rest of the universe. Of course, these are just mathematical points and any real observer which was at one time inside the horizon will forever remain inside the horizon.

 

[Jonathan Scott]

Greetings,

The event horizon of a black hole is supposedly a point of no return. But can't the presence of another gravitational source decrease the event horizon? If you are between two sources of gravity isn't it easier to move away from either one?

If immediately after a particle crosses the event horizon of a black hole, another more massive black hole were to near-miss it with the event horizons overlapping, couldn't the event horizon be moved back so the the particle is outside and get pulled into the other black hole? Or, if the speed and trajectories were just right, free the particle from both?

Thanks

If you are near to two sources, you are in a deeper potential than if you are near to either one alone, and hence less able to get away overall. The fact that the local field is decreased between the sources is not relevant to getting away.

If one event horizon comes near another, they will cause each other to expand because the combined potential given by the product of the factors is deeper, although exact solutions are not known.

If event horizons touch, you're not going to get them apart again. They combine into a larger event horizon.

 

[Feullieton]

Allright. If nothing then can escape black hole, how come it is still considered part of our universe. My thought is like this: if not even light with its speed (of light in vacuum) can't get pass event horizon of black hole, how come gravity is still influencing objects outside it's horizon range? If this influence persists, then it can be said that gravity exceeds speed of light in vacuum - the same light than can not escape black hole that is.

Or is there still some meta space-time which is not curved, preserving universal speed of light in vacuum to be still greater than possible black hole influence propagation?

 

[CosmicVoyager]

Allright. If nothing then can escape black hole, how come it is still considered part of our universe. My thought is like this: if not even light with its speed (of light in vacuum) can't get pass event horizon of black hole, how come gravity is still influencing objects outside it's horizon range? If this influence persists, then it can be said that gravity exceeds speed of light in vacuum - the same light than can not escape black hole that is.

Or is there still some meta space-time which is not curved, preserving universal speed of light in vacuum to be still greater than possible black hole influence propagation?

The light inside is still traveling at c. It just curves back in. The escape velocity is greater than c.

 

[Dmitry67]

1 Allright. If nothing then can escape black hole, how come it is still considered part of our universe.

2 how come gravity is still influencing objects outside it's horizon range? If this influence persists, then it can be said that gravity exceeds speed of light in vacuum - the same light than can not escape black hole that is.

1. Because you can go there. So it is in a part of your future lightcone.

2. Only CHANGES in G field propagate with c, Gravity itself does not have 'speed'. The same is true for electrical charge: if Black hole is charged (because the collapsed body as charged) then the whole black hole become charged itself, but no movement of charged particles after the collapse can influence EM field outside the black hole.