How Does Gravity Escape a Black Hole? (Script) (Patreon)

Fact: in a black hole, all of the mass is concentrated at the singularity at the very center. Fact: every black hole singularity is surrounded by an event horizon. Nothing can escape from within the event horizon unless it can travel faster than light. Fact: gravity travels at the speed of light. So how does a black hole manage to communicate its gravitational force to the outside universe? How does gravity escape a black hole?

—-

In 1915 Einstein presented to the world the equations behind his general theory of relativity, which describe gravity not as a traditional force, but rather in terms of the curvature of the fabric of space and time. Einstein’s theory predicted the existence of the ultimate gravitational object: the black hole. These are objects of such extreme density that the fabric of space is dragged inwards at greater than the speed of light. According to Einstein’s theory, any object that reaches such a density has to collapse to a point-like singularity of infinite density surrounded by this boundary of no return - the event horizon.

General relativity made many other predictions. One of them is that gravity itself has a speed. Einstein built the equations of GR so they would be consistent with his special theory of relativity, which describes how lengths and times and other properties depend on how fast you are moving relative to the speed of light. Special relativity enshrined the speed of light as the absolute cosmic speed limit. It tells us that light speed is the maximum speed at which any causal influence can travel. It’s the maximum speed of information - the speed of causality.

Naturally enough, the “c” of the speed of light made its way into the equations of general relativity. When you use those equations to calculate the speed of various gravitational effects, they also turn out to be the speed of light. For example we have gravitational waves - ripples in spacetime caused by certain types of motion. They travel at the speed of light, and that’s been confirmed when gravitational waves from colliding neutron stars reach us at about the same time the corresponding electromagnetic radiation from the explosion. But this “speed of gravity” also tells us how quickly a regular gravitational field changes.

Imagine for a moment that the Sun just disappeared. Now you can’t just erase mass, but let’s pretend that you can for the sake of argument. It would take 8 minutes for us to notice the sudden darkness, and the Earth would continue to orbit the now-empty patch of space for the same time. It would take 8 minutes for the Sun’s deep indentation in the fabric of space to smooth itself - in the wake of some pretty crazy gravitational waves.

But here we have a problem. If gravity travels at the speed of light, and all of the mass of a black hole is hidden beneath the event horizon, how does its gravity get out to influence the surrounding universe? Shouldn’t a black hole’s event horizon protect the universe from its malicious influence?  To answer this we’re going to look at gravity in two completely different ways. First we’ll see what Einstein has to say on the matter, and then we’ll go deeper, into the speculative realm of quantum gravity.

Starting with good old fashioned general relativity. There’s no question here - a black hole’s gravity doesn’t care about the event horizon at all. In GR, the gravitational field - the curvature of spacetime - has an independent existence to the mass that causes it. For example, when Earth feels the pull of the Sun’s gravity - it’s not directly interacting with the Sun itself, it’s interacting only with the local part of the gravitational field.

Same for a black hole. The space around a black hole doesn’t need to know about the mass of the central singularity - it only needs to know what the space next to it is doing. There’s this old analogy of space as a sheet of rubber stretched by a heavy mass. It’s not that great an analogy in many ways, but here it’s actually useful. The rubber at any one point in the sheet doesn’t know about the massive object - it’s being stretched only by the pull of neighboring patches of rubber. And there’s another way to think about the action of gravity: instead of a stretching of spacetime, we can think about space as flowing towards the massive object. The “speed of space” is just the speed of a free-falling, or inertial observer. Falling from very far away, an observer and the patch of space that they occupy reach light speed at the event horizon of the black hole.

A close analogy to this picture of gravity is a river flowing towards a waterfall. The water is the fabric of space, and it accelerates towards the drop. At some point it exceeds the swimming speed of any possible fish - that’s the event horizon. Any fish that passes that point will be carried to the singularity - the fall itself. But let’s think about what pulls any patch of water. The water at the “event horizon” doesn’t know about the fall. It’s pulled along by the water a little ahead of it, which in turn is pulled by the next adjacent patch and so on.

Gravity works like the rubber sheet or the flowing river. One patch of space doesn’t need to see the ultimate source of the field - it only needs to see the next patch along. Depending on how you think about it, the curvature or the motion of each patch influences the next.

This explanation works for the black holes of general relativity. But we know that GR is not the final theory. It breaks down at very small distances and in very high gravitational fields. For example, at the black hole singularity. Many physicists believe that general relativity needs to be replaced by a theory of quantum gravity to explain the behavior of gravity in these circumstances. So can gravity escape from a “real” black holes of quantum gravity?

Now in quantum mechanics - or more specifically quantum field theory - forces are mediated by particles, not by the geometry of spacetime. For example the electromagnetic force is communicated between charged particles by transferring virtual photons - ephemeral excitations in the electromagnetic field. In theories of quantum gravity, the gravitational force should probably also have a mediating particle - usually called the graviton. OK, fine. But doesn’t that make things worse for black holes? If gravity is really communicated by a particle, how does that particle escape the event horizon?

Actually, even in this picture, the event horizon has no way to halt the force of gravity. There’s a bit of a misconception in how we think about virtual particles. They don’t really travel from one location to another, carrying force with them. Virtual particles aren’t localized like that. Let’s say two electrons approach each other. They interact by exchanging a virtual photon. Or more precisely, they exchange the sum of all possible virtual photons. But those photons don’t follow a well defined path between the interacting particle. They sort of emerge from the electromagnetic field in the broader region occupied by the force of the two electrons, and their summed effect leads to a repulsive force between the particles. So if gravity is really mediated by virtual gravitons, then those gravitons don’t emerge from the location of the singularity, and they don’t have to travel through the event horizon to do their work. The gravitational field around the black hole is already abuzz with virtual gravitons.

Now you might ask why those gravitons themselves don’t get swallowed by the black hole. That’s easy - these are virtual particles, and in quantum field theory, virtual particles are not restricted by the speed of light. They can travel at any speed. Interactions between particles result from the sum of all virtual particle interactions, possible and Impossible, and the speed of light limit actually emerges in a sort of statistical way. The overall interaction, along with any information that it communicates has to be sub-light-speed. But if we’re describing the gravitational field as being built up by virtual gravitons then the event horizon is no barrier at all. Unfortunately you still can’t send an SOS message from inside the black hole this way.

And this idea of sending information across an event horizon brings us to our last argument, and this one works whether we’re talking about the classical gravity of Einstein or some deeper theory of quantum gravity.  The cosmic speed limit is the speed limit of information. To experience the gravitational effect of a massive object, the information about the presence of that mass DOES have to be able to reach you. We have to be able to “see” that mass, at least in principle.

And it might surprise you to learn that you actually CAN see the mass of black hole. The present mass of a black hole is hidden below the event horizon, but we can see its past mass, and it’s the gravitational effect of the past mass that we actually feel. Think about a star collapsing into a black hole. As it approaches the surface that is to become the event horizon, it approaches light speed with respect to someone watching from a distance. According to relativity, that means its clock slows. It appears to freeze at the event horizon, and the light it emits becomes stretched out and sapped of energy. The star does appear to go black, but really the faintest signals of that collapsing star continue to make their way out into the universe over infinite time. That’s ignoring the whole black hole evaporation thing. So we can still “see” the mass of a black hole - it’s imprinted on the event horizon. Whether gravity is communicated by the curvature of spacetime or by virtual gravitons, we maintain a causal connection to the mass that generated that gravitational field.

And for those of you who love their Penrose diagrams, just think about the source of the gravitational field as always being in your past lightcone - and that has to be outside the black hole.

And this last argument also tells us how it can be that a black hole can possess electric charge. If a black hole swallows electric charge, the electromagnetic field around the black hole grows. How? Because when you look at a charged black hole you still have causal contact with all the charge that fell into it. You interact with the past charge, not the present. From the point of view of that charge, it’s inside the black hole, but from your point of view it’s frozen on the event horizon, but is happily exerting its influence on the surrounding universe.

This whole question is related to another very interesting one. In a black hole, where is the mass? A simplistic view says that it’s at the singularity - but that’s not the mass that you interact with. You interact with the local curvature of spacetime, which is produced by the past mass, which from your point of view is on the event horizon. In fact the whole idea of mass is poorly defined in general relativity in part because the gravitational field itself has energy, and so is a source of mass. To get a consistent definition of mass you need to integrate - add up - the contributions to infinite distance from the black hole. By that definition the mass of a black hole is everywhere - so it’s not surprising that it can escape the horizon.

To sum up - don’t mess around near black holes hoping that the event horizon will protect you from the black hole’s gravity. Many seemingly different pictures all point to the same result - the black hole will eat you right up, and even as you’re getting crushed into an infinitesimal point, you can rest assured that your own mass will continue to exert its gravitational influence on exterior regions of space time.