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 Equation: G_{\mu\nu} + \Lambda g_{\mu\nu}
= \kappa T_{\mu\nu} 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 own 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 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 hole 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 particles. They sort of emerge from the electromagnetic
field in the broader region occupied by both of the 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 of a black hole that 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 Hawking radiation, 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 for 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. Before getting to comments, we’d
like to thank our supports on Patreon. And today’s special shoutout goes to Alex Kern who’s supporting us at the Quasar Level. Alex, as token of our appreciation, we asked our friends at Center for Computational Astrophysics to run a few Universe simulations and track the evolution of the entity known as Alex Kern. In one of those simulations you live 3000
years and become emperor of space, and in another you star in Interstellar instead of
Matthew McConaughey. But in all of the simulations you are incredibly generous, interesting, and much loved by all the other simulated entities. Just like in this one. Thank you for your support in this simulation. Our two recent episodes were all about simulating the universe. We talked about the ingenious method for simulating the insane amount of information in the quantum wavefunction with density functional theory,
and then went from the tiny to the enormous, exploring how we do simulations of everything from the sizes of planets to the size of the universe. Starting with the quantum, manonthedollar
asks - given the incredible amount of power required to simulate quantum interactions... do the ACTUAL interactions also require that
much effort from the universe? Well this is an excellent question - and the answer is that we have no idea. But Badly drawn Turtle has an interesting thought on the matter and I quote: "That a small part of the wavefunction can be used to "reconstruct"
the whole wavefunction, or at least the part of it that could be considered to correspond
with our reality, is an indicator that there's a much simpler underlying theory on the order
of complexity of that small part. It's not that the information of the wavefunction can be compressed below it's "true" informational volume, it's that it can be simplified down
from its false, overinflated informational volume." Agentdarkboote and Meisam pointed out an error - or at least, a missed detail. We said that in density function theory you
start with a make-believe system of non-interacting electrons. Agentdarkboote tells us that you do include
Coulomb and exchange interactions even in your initial guess, and that the remaining
part you have to approximate is the electron correlation. Thanks for the details guys - we went deep on this one and may have missed a few points. And speaking of corrections, for our episode
on astrophysical simulations, Mercurius314 spotted a serious blunder. We said that the room-sized computer used
to calculate the Apollo trajectories had the computing power of a smart phone. That's just not true. The Apollo mission computers such as the IBM 7090 ran around 100 kiloflops while the GPU of a modern smartphone is in the hundreds of gigaflops to teraflop range. So we were 5 orders of magnitude out. This is a case of me blithely repeating something I heard once without checking the math. Please don’t think that this is a habit. We check a lot of math on this show, but I guess sometimes something sneaks through. Still, not cool Matt. Don’t just say dumb stuff that you heard anywhere. That’s not what we do here. Inspired by the simulations we showed of the
inevitable collision of the Milky Way with the Andomeda Galaxy, Robert Herd asks the following: how can it be that in an expanding universe, where all the galaxies are rushing away from us, that we could be on such a collision course? Well the answer is sort of what you say in
your own question: the real universe is more chaotic than implied by simple expansion. But we understand that “chaos” very well. Distant galaxies appear to be moving away
because space on the largest scales is expanding evenly everywhere. But on small scales, local gravitational influences dominate. Imagine a bunch of magnets on a rubber sheet - stretch the sheet and the magnets move apart, unless they’re close together, then the
magnets will obviously form stars and galaxies. And speaking of the Milky Way-Andromeda collision, Roli Rivelino points out that way back in our 3-body problem video, they asked how we
can know that these galaxies will actually collide. And then thanks us for making this video just
to answer the question. Well, you’re welcome. For those who missed the answer - we know that the collision will happen because we simulated it. To be less glib, we simulated it a LOT - covering all reasonable unknown properties of the system. No matter what we put in for those unknown properties, the Milky Way & Andromeda still do collide in about 4 Billion years. Now Roli follows with another question: if we simulate a perfect universe containing beings that themselves are able to simulate a perfect
universe; wouldn't that be ultimate proof that we are in a simulation? Well I wouldn’t call that a proof - I’d
call it a demonstration of plausibility. After all, if you follow the chain all the
way up to the top layer - you have to have beings who simulated a universe containing beings who could simulate a universe, but they themselves were not simulated. Now couldn’t we be those top layer beings? Or maybe we’re the bottom layer, and every
level above is much more interesting. OR the simulations might run in a loop and
the top layer is simulated by the bottom. So we’d better get simulating or we’ll
break the cycle.
