If we think of a black hole as an event horizon caused by a massive object then we need to think about two black holes in proximity.
We tend to think about the event horizon as a closed spherical surface but we could think of it in another way. We could think about the gravitational acceleration at each point in space. In the case of a static spherical distribution of matter this would lead us to a spherical surface that is the event horizon.
But in a black hole merger, think of the gravitational acceleration at the point mid way between the merging black holes of equal mass. The gravitational acceleration must be in balance here so there can be no event horizon here.
So I am guessing that during a merger the event horizon will be two spherical hemispheres on opposite sides of the system.
This suggests that during a merger we have the possibility of observing the mass which is causing the event horizon.
Richard
The event horizon isn't a surface in space, but in spacetime. More precisely, it's a light-like surface in spacetime. It's distinct from the space-like surface of a collapsing object, that doesn't turn light-like at the end of collapse.
That's why the answer is No.
Stam Nicolis Except that the position of an event horizon is defined by the Schwarzschild radius R=2GM/c^2.
This is a position in space with no reference to time in the equation.
Richard
The event horizon or Horizon is that part of space outside which no effect of the event inside impacts the observer.
The event horizon of a black hole is different as nothing ever escapes the event horizon, or in other words, a person outside can never know what is happening inside the event horizon of a black hole. So, to observe a black hole, we need to enter the event horizon, which is no good as nothing escapes from it. The person or device will hit the surface, and the gravitational force of the black hole will crush it into millimeter cubes.
As you suggest, there will be no net gravitational acceleration at the center of the black hole as forces are in opposite directions and will cancel each other.
The problem is the same again-even if the person or the device does observe something-the information will never leave the event horizon.
At this point, the body will be at a stable equilibrium in the y-axis (according to the diagram), i.e. body will try to retain its position if disturbed from its location. And even if net forces on the body at center will be zero, if it tries to escape and moves from the point, gravitation forces will not be remain zero and bring it back to the previous location or worse, crush to one the black holes.
So, even if the observation can be the made during the black merger, it will serve no good to us.
Once more: The Schwarzschild radius defines a surface, not whether it’s space-like or light-like. The statement that that surface is an event horizon means that it’s light-like, if one looks at the metric: The light cones tip over at the Schwarzschild radius. This statement refers to spacetime, of course. It doesn’t make sense in space. For a collapsing star, a radius less than the Schwzrschild radius is, just, a radius less than that of the Sun for the Sun. The black holes that are observed in the universe are, just, collapsing stars.
Let’s take a very specific example of a static spherical distribution of matter with an event horizon at the surface of the sphere.
For example if we had a neutron star of 3.4 solar masses, the radius of the star and the event horizon would be around 10km.
So we would expect an event horizon to form in this case with a radius of 10km.
Now we imagine a second identical distribution of matter is placed so that the two spheres are next to each other. At the point mid way between the centres of the two spherical distributions a ray of light could travel freely in any direction because the net gravitational force is zero. So there can be no event horizon here.
The question then arises as to whether the event horizons of the individual black holes merge in such a way that it remains a closed surface before and after the merger. At some points in space the gravitational forces would be acting in opposite or nearly opposite directions and tend to cancel.
In principle, I see nothing wrong with the idea that in a non-symmetrical or non-static distribution of matter that the event horizon could be partially open, depending on the gravitational conditions at each point in space.
Richard
Event horizons are defined by inertial observers in asymptotically flat space-time. A light ray that is not attracted to either black hole center can run some length before it is attracted by both, and it may or may not be able to reach the asymptotically flat space-time.
I think that the study of the global structure of event horizons is quite complex. It demands heavy mathematical tools. Naturally, important work in this regard was carried out by Hawking and Penrose in the 60's.
Jose Gaite I think I understand your first paragraph to say that it is possible that an event horizon could be open in some places but it requires a much more detailed analysis using the Einstein equations of General Relativity?
I think there are other situations where we might find the event horizon to be not a completely closed sphere. The example I am thinking of comes from the observation of rotating black holes. These formed from the merger of two black holes or neutron stars which accounts for the rotation.
What is observed is that the jets emerging from rotating black holes are very similar to the jets emerging from rotating neutron stars. This suggests to me two things. 1. that the interior of a black hole contains a neutron star and 2. That it is possible for the frame dragging associated with a rotating neutron star to result in the event horizon being open at the axis of rotation.
This is again a complex problem which might be difficult to analyse using the Einstein equations but it does seem that some work has been done in this area in connection with modelling the gravitational waves from a neutron star or black hole merger.
Richard
Dear Richard Lewis ,
I did not mean that an event horizon could be open in some places. I think that two BHs have two separate event horizons that deform, pinch and merge, becoming one, namely, one BH. The zone between the BHs is not included in the event horizon before the merge. Even afterwards, a photon there can surely travel some distance along the middle line before being pulled back.
At any rate, one needs General Relativity to deal with this strong gravity problem. However, it is not maneageable with analytical or even numerical methods. Hawking and Penrose were cleverer and employed more abstract means, in particular topological methods.