Hawking radiation

• 1. Introduction

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  Hawking radiation is a faint glow that should seep out of black holes, the one kind of object that was supposed to give nothing back. Physicist Stephen Hawking developed the model behind it in 1974. Earlier models had assumed that once light crossed a black hole's event horizon, it was trapped for good. Hawking's model said otherwise, and its consequences reach into the question of what a black hole even is. The predicted glow is so weak that it sits many orders of magnitude below what the best telescopes can detect. So how can a trap leak? What becomes of a black hole that keeps losing energy? And why has nobody caught the glow yet?

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• 2. Zero Entropy, Then Not

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  Einstein's 1915 theory of general relativity gave physics its modern black holes. Evidence that such objects truly exist began to mount about half a century later.

  A black hole forms when enough matter or energy is squeezed into a small enough volume that the escape velocity exceeds the speed of light. Because nothing outruns light, nothing inside a certain distance can get out, and that distance grows with the black hole's mass. The boundary is the event horizon. An outside observer cannot see, learn of, or be touched by anything that happens within it. General relativity offers a second picture, in which space itself pours inward faster than light, even though nothing can move through space that quickly. Whatever crosses the boundary falls into a singularity, a point of zero size and infinite curvature. What remains behind is warped, empty spacetime. The simplest version, neither spinning nor electrically charged, is described by only its mass and its horizon.

  Early researchers such as Karl Schwarzschild and John Wheeler modelled these objects as having zero entropy. Entropy is a measure of disorder, so a black hole was treated as perfectly simple.

  Then, in 1971, the Soviet scientists Yakov Zeldovich and Alexei Starobinsky proposed that rotating black holes ought to create and emit particles. They reasoned by analogy with spinning metal spheres in electromagnetism. The process is now called Zeldovich amplification. A year later, Jacob Bekenstein developed a theory in which a black hole has an entropy proportional to its surface area. Hawking at first argued against it, because he still saw black holes as simple objects with no entropy. In 1973 he met Zeldovich in Moscow. Afterwards he fused the two ideas, using a blend of quantum field theory and general relativity. That meeting in Moscow set up the calculation that followed.

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• 3. Pairs at the Horizon

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  Hawking's paper showed that, in theory, a black hole radiates particles as if it were a blackbody, a perfect emitter of thermal glow. Each escaping particle carries energy away, so the black hole is drained. The effect carries Bekenstein's name alongside Hawking's, because Bekenstein's entropy work implied that a black hole must also have a temperature. Since the original publication, many other physicists have confirmed the result mathematically by different routes.

  The simplest picture starts with the vacuum, which is never truly empty. A fluctuation in the electromagnetic field can produce a pair of photons, one outside the horizon and one inside. The horizon lets one member of the pair escape in each direction.

  A second picture rests on the Unruh effect. An observer hovering near the horizon must keep accelerating to avoid falling in. Such an accelerating observer sees a thermal bath of particles that pop out of the local acceleration horizon, turn around, and fall back. For the whole arrangement to stay consistent with distant space, the bath must have a finite temperature far away. That means some particles are not reabsorbed and become outgoing radiation. Worked through for a nonrotating black hole, the temperature at a great distance comes out inversely proportional to the black hole's mass. A typical quantum of this radiation has a wavelength similar to the size of the black hole itself.

  The spectrum is not perfectly black. Quantities called greybody factors, which depend on frequency and angular momentum, describe how a real black hole's emission departs from a pure blackbody. For a charged black hole, they can also depend on the charge of the particles being emitted.

  Temperature then hands over the black hole's entropy almost for free. Adding heat raises the mass, and integrating that relationship shows the entropy is proportional to the horizon's surface area. This entropy also acts as a bound on the information that any sphere of spacetime can hold. The form of the result strongly suggests that a theory of gravity might be encoded on a bounding surface.

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• 4. Cold Giants, Hot Dwarfs

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  A black hole with the mass of the Sun would need about 2.14 times ten to the 67th years to evaporate. That is vastly longer than the present age of the universe. By dimensional analysis, an evaporating black hole's lifespan scales with the cube of its initial mass, so heavier black holes last staggeringly longer.

  Mass also sets the temperature, and heavy means cold. The smallest predicted stellar black hole, at about 3 solar masses, would sit near 10 to the power -7 kelvin. Space itself is filled with the cosmic microwave background at 2.7 kelvin, which is warmer. So no stellar black hole can evaporate; each is colder than its surroundings. Even the largest monsters, which may grow to perhaps 10 to the power 14 solar masses as superclusters of galaxies collapse, would take up to 2 times 10 to the power 106 years.

  Small black holes behave very differently. Unlike most objects, a black hole grows hotter as it radiates away mass, and the rise in temperature is exponential. Micro black holes therefore emit far more per unit of mass and dissipate faster. If tiny black holes exist, as the hypothesis of primordial black holes allows, they would lose mass at an accelerating pace. The most likely end is a violent burst of gamma rays. Describing that last moment fully requires a model of quantum gravity, since the mass approaches 1 Planck mass and the radius approaches two Planck lengths.

  Evaporation does have one tidy benefit. It shows how black holes exchange heat with the rest of the universe, giving black hole thermodynamics a more consistent footing.

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• 5. Primordial Survivors

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  Only a black hole lighter than 0.8 percent of the Earth's mass could be dissipating today. That rules out any black hole made by a collapsing star. Only primordial black holes, formed in the early universe, could have been created with so little mass.

  Hawking estimated that any black hole born in the early universe with a mass below roughly 10 to the power 12 kilograms would have evaporated completely by now.

  In 1976, Don Page sharpened the estimate. He calculated the radiated power and the time to evaporation for a nonrotating, uncharged Schwarzschild black hole of a given mass. The task is awkward because a black hole of finite size is not a perfect blackbody. Its absorption cross section falls in a complicated, spin-dependent way as frequency drops, especially when the wavelength becomes comparable to the horizon's size. Page concluded that primordial black holes could survive to the present only if they began above a certain mass.

  Page's numbers carried a flaw that was invisible in 1976. He assumed neutrinos have no mass and that only two flavors exist. Modern physics counts three flavors, all with nonzero masses, so his lifetimes no longer match. A 2008 calculation used the particle content of the Standard Model and the WMAP measurement of the universe's age to produce an updated mass bound.

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• 6. The Lost Information

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  The prediction that a black hole can disappear raised a puzzle known as the black hole information paradox. In the simplest models of evaporation, the Hawking radiation is random and has no relation to what originally fell in. When the black hole dissipates, the information content it appeared to hold seems to vanish with it.

  Physicists have proposed several ways out. One suggestion is that the radiation is subtly perturbed so that it does contain the missing information. Another is that evaporation leaves behind some kind of remnant particle that stores it. A third accepts that information really can be lost under these conditions. A full answer would likely need the same quantum gravity that the final burst demands.

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• 7. Doubts at the Horizon

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  Follow a single outgoing photon of Hawking radiation backward in time, and its wavelength shrinks without limit as it nears the horizon. This is the trans-Planckian problem. Near the horizon, time appears to stop as measured from far away, so a photon with finite frequency today must once have had infinite frequency. Hawking handled this by using a black hole that forms at a finite time. Then every outgoing photon traces back to a microscopic point at the moment of formation. The relevant modes start with wavelengths far below the Planck length, where the laws of physics are unknown, so some found the original calculation unconvincing. Today the problem is mostly considered a mathematical artifact of horizon calculations. Alternative pictures of the radiation also exist that address it, and the Unruh effect's temperature is not controversial.

  A different worry concerns gravity at tiny scales. The formulas hold only if gravity behaves normally all the way down to the Planck scale. For masses below the Planck mass, they give lifetimes shorter than the Planck time, which is usually read as a sign that the Planck mass is the lowest possible black hole mass. In models with large extra dimensions, 10 or 11 in number, the Planck constants can differ radically. The lifetime formulas change accordingly, as worked out by Cheung in 2002 and Carr in 2005. In that picture the low-energy scale could be as small as a few TeV.

  Parikh and Wilczek, and separately Padmanabhan and Srinivasan, described the effect as tunneling through the horizon. Comparing the tunneling probability with a Boltzmann distribution gives the same temperature as Hawking's derivation. Because the method is local, it also works for various horizons, including mildly dynamical ones.

  Loop quantum gravity gives a more complicated verdict. Its study of the horizon's quantum geometry does not reproduce the Bekenstein-Hawking entropy unless a free parameter is tuned to cancel various constants. Still, it yields quantum corrections. Fluctuations in the horizon area would produce deviations at discrete, sharply peaked frequencies on top of the Hawking spectrum. Those would be visible if X-rays from evaporating primordial black holes were ever observed.

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• 8. Looking for the Glow

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  In June 2008, NASA launched the Fermi space telescope, which searches for the terminal gamma-ray flashes expected from evaporating primordial black holes. As of January 2024, none had been detected.

  In 2023, the neutrino detector KM3NeT recorded a 120 PeV event labeled KM3-230213A. One proposed explanation is the evaporation of a primordial black hole. A broad range of measurements at KM3NeT and IceCube are consistent with such evaporation, if primordial black holes make up a significant fraction of dark matter.

  Particle colliders offer another route. If speculative large extra dimension theories are right, CERN's Large Hadron Collider might create micro black holes and watch them evaporate. No such micro black hole has been observed there.

  The real effect is too small to observe directly under achievable conditions. So physicists have turned to analogy. In sonic black holes, sound perturbations play the part of light, and the flow of an approximately perfect fluid plays the part of gravity. Observations of Hawking radiation have been reported in sonic black holes made with Bose-Einstein condensates.

  In September 2010, an experimental setup created a laboratory white hole event horizon. The experimenters claimed it radiated an optical analog of Hawking radiation. The results remain unverified and debatable, and whether they confirm the effect is still in doubt.

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