Ask Ethan: How does light escape from a black hole?

The most important feature of a black hole is that it has an event horizon: a region of space where the gravitational field is so strong that nothing, not even light, can escape from it. How, then, do we explain the matter and radiation that we both see being emitted from them, and also that we predict should come from them? That’s what Russell Sisson wants to know, as he asks:

“Everything you read about black holes indicates that ‘nothing, not even light, can escape them’. Then you read that there is Hawking radiation, which is ‘blackbody radiation that is predicted to be released by black holes’. Then there are relativistic jets that ‘shoot out of black holes at close to the speed of light’. Obviously, something does come out of black holes, right?”

Matter and radiation can definitely come toward us, originating from the black hole’s location. But does that really mean something escapes from a black hole? Let’s find out!

While distant host galaxies for quasars and active galactic nuclei can often be imaged in visible/infrared light, the jets themselves and the surrounding emission is best viewed in both the X-ray and the radio, as illustrated here for the galaxy Hercules A. It takes a black hole to power an engine such as this, but that doesn’t necessarily mean that this is matter/radiation escaping from inside the event horizon.

When we talk about a black hole, it’s important to recognize what we mean. If you put enough mass together in a small enough volume of space, the curvature of spacetime will become so large that a ray of light, no matter what direction it propagates in, will inevitably arrive back at the central singularity. The escape velocity — or the speed at which you’d need to move to overcome the black hole’s gravitational pull — is greater than the speed of light.

Since the speed of light is the ultimate cosmic speed limit, where all massive particles can only move slower than light and even massless ones can only move at the speed of light, that means that wherever the escape velocity exceeds the speed of light, nothing can escape from it. A consequence of this is that there’s a critical region, which physicists call an event horizon, where once you cross inside of it, you can never get out. Things that are inside the event horizon always hit the singularity; things that are outside can either escape or fall in, dependent on their properties.

Both inside and outside the event horizon of a Schwarzschild black hole, space flows like either a moving walkway or a waterfall, depending on how you want to visualize it. At the event horizon, even if you ran (or swam) at the speed of light, there would be no overcoming the flow of spacetime, which drags you into the singularity at the center. Outside the event horizon, though, other forces (like electromagnetism) can frequently overcome the pull of gravity, causing even infalling matter to escape.

There are, however, real particles and radiation that are emitted by, and originate from, a black hole. This is true on both the theoretical front, with Hawking radiation as an important example, as well as on the observational front, where relativistic jets, quasars, and active galaxies are seen all across the Universe. One spectacular example where theory and observation intersect is for an accretion disk: a large distribution of matter in orbit around a black hole.

Imagine you’re a particle outside of a black hole’s event horizon but gravitationally bound to it. The strong gravitational pull will cause you to move in an elliptical orbit, where your fastest speed corresponds to your closest approach to the black hole. So long as you don’t cross the event horizon, you shouldn’t ever fall in. Occasionally, if there are enough particles in orbit, you’ll interact with the other ones, experiencing inelastic collisions and friction. You’ll heat up, be compelled to move in a more circular orbit, and eventually emit radiation.

This radiation doesn’t come from inside the black hole but from the matter orbiting outside the event horizon.

An illustration of an active black hole, one that accretes matter and accelerates a portion of it outward in two perpendicular jets. The normal matter undergoing an acceleration like this describes how quasars and active galaxies work extremely well. Flows of matter inside the accretion disk can lead to flares in a black hole’s emissions. All known, well-measured black holes have enormous rotation rates, and the laws of physics, particularly the conservation of angular momentum, all but ensure that this is mandatory.

Sure, some of the matter will eventually lose enough energy that it will cross over to the inside of the event horizon, arriving at the singularity and increasing the mass of the black hole.

But there’s a lot going on in the vicinity of the black hole. There are charged particles of different signs and magnitudes traveling very rapidly: moving close to the speed of light. Charged objects in motion create magnetic fields, and that causes many of the ionized matter particles to be accelerated in a helix-shape, away from the plane of the accretion disk. These accelerating particles are the origin of relativistic jets, producing showers of particles and radiation when they collide with the material farther away from the black hole.

The galaxy Centaurus A is the closest example of an active galaxy to Earth, with its high-energy jets caused by electromagnetic acceleration around the central black hole. The extent of its jets are far smaller than the jets that Chandra has observed around Pictor A, which themselves are much smaller than the jets found in massive galaxy clusters. This picture, alone, illustrates temperatures ranging from ~10 K to as high as several millions of K, and relativistic jets that are even physically larger than the stellar extent of the galaxy itself.

Relativistic jets are a remarkable sight, and in some cases, are so brilliant that they actually appear in visible light.

The galaxy Centaurus A has a jet in both directions that becomes large, diffuse, and spectacular; the galaxy Messier 87 has a single, collimated jet that extends for over 5,000 light years. Both of these are caused by an active, supermassive black hole that’s many times larger than even the four-million-solar-mass monstrosity at the center of the Milky Way.

Streaming out from the center of M87 like a cosmic searchlight is one of nature’s most amazing phenomena: a black-hole-powered jet of subatomic particles traveling at nearly the speed of light. In this Hubble image, the blue jet contrasts with the yellow glow from the combined light of billions of unresolved stars and the point-like clusters of stars that make up this galaxy. The jet itself extends for more than 5,000 light-years in space, and is visible in even optical wavelengths.

For accretion disks and relativistic jets, these are phenomena that are observable around black holes, but nothing is coming from inside the black hole and getting out. Instead, it’s matter that’s around them being accelerated by a black hole’s intense gravity, where that matter becomes hot, ionized, and develops electric currents and magnetic fields within it, and that leads to forces that accelerate this energetic material back out from around a black hole, generating these jets.

For Hawking radiation, however, things get a little more complicated. In theory, you can imagine a black hole that was truly in the vacuum of space, with no matter, radiation, or other masses around it. If the black hole wasn’t there, all you’d have was the vacuum of flat, uncurved space governed by the fundamental laws of the Universe. But if you put the black hole there, you have curved space, an event horizon, and the laws of physics. And a consequence of that is that you get omnidirectional radiation with a blackbody spectrum to it: Hawking radiation.

The event horizon of a black hole is a spherical or spheroidal region from which nothing, not even light, can escape. But outside the event horizon, the black hole is predicted to emit radiation. Hawking’s 1974 work was the first to demonstrate this, and it was arguably his greatest scientific achievement. Although this treatment isn’t dependent on whether spacetime and gravity are quantum or not, treating gravity semiclassically has pathological consequences under a variety of circumstances.

The problem with conceptualizing Hawking radiation is the following: all of the radiation originates from outside the event horizon, but the only place to draw energy from is the mass inside the black hole itself.

For every quantum of energy (E) released in the form of Hawking radiation, the mass of the black hole (m) has to decrease by an equivalent amount.

How much is that?

By exactly the amount that Einstein’s most famous equation predicts: E = mc².

But how, then, can radiation from outside a black hole be caused by mass that’s inside a black hole, particularly if nothing can escape the event horizon?

The most common, and incorrect, explanation for how Hawking radiation arises is an analogy with particle-antiparticle pairs. If one member with negative energy falls into the black hole’s event horizon, while the other member with positive energy escapes, the black hole loses mass and outgoing radiation departs the black hole. This explanation has misinformed generations of physicists and came from Hawking himself. One of the errors inherent to this explanation is the notion that all of the Hawking radiation arises from the event horizon itself: it does not.

The most common explanation — given by Hawking himself — is also the most wrong. One of the ways people often visualize vacuum energy, or the energy inherent to space itself, is with particle-antiparticle pairs.

Empty space, because its zero-point energy is a positive value (rather than zero), can’t be treated as altogether empty; you need something to occupy it. If you decide to combine this fact with the Heisenberg uncertainty principle, you can conceptually arrive at a picture where matter-and-antimatter pairs pop into existence for a very brief amount of time, before annihilating away back into the nothingness of empty space. When one member is outside the event horizon but the other falls in, the “outside” one can escape, carrying energy away, while the “inside” one carries negative energy and decreases the mass of the black hole.

In Hawking’s most famous book, A Brief History of Time, he makes the analogy that space is filled with particle-antiparticle pairs and that one member can escape (carrying positive energy) while the other falls in (with negative energy), leading to black hole decay. This flawed analogy continues to confuse generations of physicists and laypersons alike.

First off, this visualization only applies not for real particles, but virtual ones. They are calculational tools only, not physically observable entities. Second, the Hawking radiation that leaves a black hole is almost exclusively photons, not matter or antimatter particles. And third, most of the Hawking radiation doesn’t come from the edge of the event horizon, but from a very large region surrounding the black hole. If you insisted on using the particle-antiparticle pairs explanation, even though you know it’s flawed, it’s better to try and view it as a series of four types of pairs:

• out-out pairs, where both members annihilate away outside the event horizon,
• out-in pairs, where a particle annihilates outside the event horizon but the antiparticle annihilates away inside the event horizon,
• in-out pairs, where a particle annihilates inside the event horizon but the antiparticle annihilates away outside the event horizon, and
• in-in pairs, where both members annihilate away inside the event horizon.

In this visualization, it’s the out-in and in-out pairs that virtually interact, producing photons that carry energy away. Where that missing energy comes from must be the curvature of space, and changing the spacetime curvature, in turn, decreases the mass of the central black hole.

It must be noted that it isn’t particles or antiparticles that are produced when black holes undergo Hawking radiation, but rather photons. One can calculate this using the tools of virtual particle-antiparticle pairs in curved space in the presence of an event horizon, but those virtual pairs should not be construed as being real particles, nor should all of the radiation be construed as arising from just barely outside the event horizon.

But the true explanation doesn’t lend itself very well to a visualization, and that troubles a lot of people. What you must calculate is how the quantum field theory of empty space behaves in the highly-curved region around a black hole.

Not necessarily right by the event horizon, mind you, but over a large, spherical region outside of it. Performing the quantum field theory calculation in curved space yields a surprising solution: that thermal, blackbody radiation is emitted in the space surrounding a black hole’s event horizon. And the smaller the event horizon is, the greater the curvature of space near the event horizon is, and thus the greater the rate of Hawking radiation.

In the far future, there will be no more matter around black holes, but instead their emitted energy will be dominated by Hawking radiation, which will cause the size of the event horizon to shrink. The transition from “growing” to “decaying” black holes will occur whenever the accretion rate drops below the mass loss rate due to Hawking radiation, an event estimated to occur some ~10^20 years in the future. How the information that went into making the black hole gets encoded into the outgoing radiation, or whether that’s even the case, has not yet been determined.

Under no circumstances, however, can we conclude that anything crosses the event horizon from inside to out. Hawking radiation comes from the space outside of the event horizon and propagates away from the black hole. The loss of energy lowers the mass of the central black hole, eventually leading to total evaporation. Hawking radiation is an incredibly slow process, where a black hole the mass of our Sun would take ~10⁶⁷ years to evaporate; the one at the Milky Way’s center would require ~10⁸⁷ years, and the most massive ones in the Universe could take up to ~10¹⁰³ years!

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Whenever a black hole decays, the last thing you see is a brilliant, energetic flash of radiation and high-energy particles.

As the Universe continues to age, the last sources of light will arise from the evaporation of black holes. While the least massive black holes will complete their evaporation after only 10^67 years or so, the most massive ones will persist for over a googol (10^100) years, making them the last cosmic objects to emit light, as far as we know.

These final decay steps, which won’t occur until long after the final star has burned out, are the last gasps of energy the Universe has to give off. In its own way, it’s the Universe itself trying, one final time, to create an energy imbalance and an opportunity for the creation of complex structures. When the last black hole decays, it will only be a swift cosmic burst: the Universe’s final attempt to say the same thing it loudly announced at the start of the hot Big Bang, “Let there be light!”

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Ethan Siegel is on vacation this week. Please enjoy this article from the Starts With A Bang archives!