I'm not a physicist so I'm sorry if this question is stupid from your point of view, but I believe it's not.

Let us make this thought experiment:

Take a black hole and put near it (but at a safety distance) a mass, for example a planet or a star and let it orbit around it, preventing it to fall inside the hole.

The points that were on the event horizon that face the mass now are attracted also by the little influence of this mass, so the radius of the event horizon should contract a little on the side of the mass, because the escape velocity of an ipothetic object on the old event horizon now is a little less of the speed of light, being helped by the gravitational force of the little mass. On the other hand the radius of the event horizon on the opposite side of the mass should increase a little.

Is that correct?

Now is it possible to imagine to increase the mass of the object until something that was originally inside the event horizon is revealed?

• The notion of escape velocity is not particularly useful in this case, and as nothing can be "stationary" inside the black hole event horizon, there could be nothing to reveal. Aug 14 '15 at 16:47
• Isn't the event horizon defined to be the locus of points where the escape velocity from the mass of the black hole is equal to the speed of light? Aug 14 '15 at 16:59
• Technically speaking, points are not influenced by gravity. When you say "points...are attracted...", what you really want to talk about is the value of the gravitational field at those points. Aug 14 '15 at 17:49

The first part of the argumentation is basically right: external objects influence the gravitational field so that the event horizon of the black hole in the middle will no longer be "exactly spherical and isotropic" when additional objects' gravity distorts the field.

Well, the reality is that even the spacetime refuses to be spherically symmetric in the presence of objects around the black hole that break the spherical symmetry. The spacetime itself is curved, not spherically symmetric, so we couldn't even define what it would mean for the event horizon to "remain" spherically symmetric.

However, the second part of the argumentation isn't right. These additional objects can't retroactively redefine the event horizon and "pull" some points from the black hole interior.

The reason is that the black hole interior – whose boundary is, by definition, the event horizon – has a clear and totally unambiguous definition. The point $P$ in spacetime is said to be in the black hole interior if there exists no future-directed time-like trajectory starting at $P$ that ends in the asymptotic Minkowski region at infinity, the "scri plus". (In plain English: if no massive particle has any chance to escape from this point to the safe exterior.)

With additional objects distorting the gravitational field, we are effectively given a new spacetime (including its future shape) and we have to solve the exercise of dividing the spacetime into the black hole interior and the black hole exterior again – the results from a different spacetime, one without the stars and the extra curvature they caused, is not useful anymore.

When we run the exercise again, from scratch, we will have a clear separation of the spacetime into the interior and the exterior again, and the boundary in between these two parts is the event horizon. There can't be any sense in which one spacetime point was "previously" inside but it is outside "later" when the star is added.

Again, the separation only makes sense for spacetime points, not for "points of 3D space". The spacetime points are defined by their location as well as the timing – there is no "before" and "after" for them. And for the spacetime points, there exists an unambiguous procedure or definition that decides whether the spacetime point is inside or outside. This procedure or definition depends on the shape of the whole spacetime (including and especially in the future). But the shape of the whole spacetime must be considered to be well-defined and fixed for the notion to be well-defined. One can't talk about "two different spacetime shapes" at the same moment.

In other words, one might say that an oscillating star in the vicinity of the black hole will make the event horizon oscillate as well. But there will still exist a hypersurface given by an equation $f(x,y,z,t)=0$ – where the function $f$ may depend on $t$ and not just on $x,y,z$ – which will define the event horizon, the boundary between the interior and the exterior. From points in the interior, one can't get out; from those in the exterior, one is out and can stay there.

• Thank you! That's sufficiently clear (even if I have no idea of the mathematical aspects of the general relativity) :-) Aug 14 '15 at 17:07