21-9 Hawking radiation and black hole evaporation

With all the mass of a black hole hidden behind its event horizon and collapsed into a singularity, it may seem that there is no way of getting mass from the black hole back out into the universe. But in fact there is, as Stephen Hawking figured out in the 1970s. To understand how this is possible, we must look at the quantum mechanical behavior of matter at the microscopic scale of nuclei and electrons.

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The Heisenberg uncertainty principle is a basic tenet of quantum physics. This principle states that you cannot determine precisely both the position and the speed of a subatomic particle. Over extremely short distances or times, a certain amount of “fuzziness” is built into the nature of reality.

The Heisenberg uncertainty principle leads to the concept of virtual pairs: At every point in space, pairs of particles and antiparticles are constantly and spontaneously being created and destroyed. An antiparticle is quite like an ordinary particle except that it has an opposite electric charge and can annihilate an ordinary particle so that both particles disappear. In the case of virtual pairs, the process of creation and annihilation occurs over such incredibly brief time intervals that these virtual particles and antiparticles cannot be observed directly. With some added energy, a virtual particle can become a real and observable particle, and a black hole helps this to happen.

A fundamental uncertainty in physical knowledge makes it possible for black holes to emit particles and radiation into space

With virtual particle pairs everywhere, now let’s think about a black hole. Furthermore, think about the momentary creation of a virtual pair of an electron and a positron (the antiparticle of an electron) just outside the black hole’s event horizon (Figure 21-22). It may happen that one of the virtual particles falls into the black hole. Its partner is then deprived of a counterpart with which to annihilate and ends up becoming a real particle. However, some energy is required for a virtual particle to become a real particle. The energy to accomplish this conversion comes from the black hole’s mass according to E = mc2. This decreases the mass of the black hole by a tiny amount, and the newly created real particle is free to radiate away from the black hole. In this way, real particles can quantum mechanically “leak” out from a microscopic region just outside the event horizon of a black hole, carrying some of the hole’s mass with them. These particles would appear as a form of steady emission by a black hole and are called Hawking radiation.

Figure 21-22: Hawking Radiation and Evaporation of a Black Hole This illustration shows two pairs of virtual particles—an electron (e) and a positron (e+), and a pair of virtual photons (γ)—appearing just outside the event horizon of a black hole. If one member of the pair becomes real and escapes, it carries a little energy away from the black hole, the black hole decreases in mass and the event horizon shrinks. The real particles radiating away are referred to as Hawking radiation, and the process is described as black hole evaporation.

Hawking radiation might also have implications for the information loss implied by the no-hair theorem. Some scientists suggest that the detailed information about objects entering a black hole is not lost, but is actually preserved in slight quantum variations of the Hawking radiation. While that might answer an important question within theoretical physics, for all practical purposes, the information is unobservable through any foreseeable techniques.

The Temperature of a Black Hole

Hawking radiation lead to another remarkable discovery that black holes have a temperature. Recall that the warmer an object, the more radiation it emits (Section 5-3). Detailed calculations show that Hawking radiation has the same properties as the radiation that is emitted from objects due to their temperature: black holes emit blackbody radiation. The result is that black holes actually have a temperature, and the smaller a black hole’s mass, the higher its temperature.

As an example, a 1-trillion-ton (1015 kg) black hole would emit energy as if it were a blackbody with a temperature of nearly 109 K. That is hotter than the center of our Sun. However, the black holes that nature seems to produce are much larger and cooler. A 1-M (2 × 1030 kg) black hole would have a miniscule temperature around 10−7 K. This temperature is barely above absolute zero. In other words, stellar mass black holes (and larger) have such low temperatures that they would emit very little Hawking radiation.

The story is different for very low-mass black holes, such as the proposed primordial black holes we discussed in Section 21-5. As particles escape from a very small black hole, the mass of the black hole decreases significantly, making its temperature go up. As its temperature rises, still more particles escape, further decreasing the hole’s mass and forcing the temperature still higher. This runaway process of black hole evaporation finally causes the hole to vanish altogether! During its final seconds of evaporation, the hole gives up the last of its mass in a violent burst of energy equal to the detonation of a billion megaton hydrogen bombs!

A 1010-kg primordial black hole (comparable to the mass of Mount Everest) would take about 15 billion years to evaporate. This period is close to the present age of the universe. If primordial black holes were formed in the Big Bang, we would expect to see some of them today going through the explosive final stages of evaporation. In 2008, the Fermi Gamma-ray Space Telescope was launched on a 10-year mission with the capability to detect the nearest of these hypothesized bursts; so far, none have been found.

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By contrast, a 5-M black hole would take more than 1062 years to evaporate, and a supermassive black hole of 5 million solar masses would take more than 1080 years. These time spans are far longer than the age of the universe. We can safely predict that the black holes we have observed to date will remain as black holes for the foreseeable future.

So far, we have considered black holes in isolation. As we will see in Chapter 25, the universe contains numerous photons left over from the Big Bang (giving the universe a background temperature of 2.7 K). As a result, larger black holes that have cooler temperatures absorb more energy from their surroundings than they emit through Hawking radiation; these black holes would slowly grow! At the present universal temperature of 2.7 K, only black holes with masses less than that of the Moon (which would have a diameter about the width of a human hair) are hot enough to shrink by emitting more radiation than they absorb.

While Hawking radiation and black hole evaporation have not been observationally verified (yet), these predictions—based on established laws of physics—are being pursued. The Fermi Gamma-ray Space Telescope is already looking for evidence of evaporating black holes as noted above, and even particle accelerators have joined in the search. The Large Hadron Collider at CERN (which discovered the Higgs particle in 2012) has the energy to look for certain miniature black holes. They have not been detected, but if created by the collider, they would immediately evaporate by emitting observable Hawking radiation.

From supermassive black holes to stellar mass and primordial black holes, the physical parameters of black holes stretch across a wide range—from large, massive and cold to small, hot, and evaporating away with a burst. As new instruments are designed to detect these black holes, their exotic properties can be explored. As we will see in Chapter 24, supermassive black holes are already known to play a central role in powering objects called quasars, which are some of the brightest objects in the universe.

CONCEPT CHECK 21-16

Which object radiates more intensely, a supermassive black hole or a stellar mass black hole?

CONCEPT CHECK 21-17

Do black holes remain the same temperature forever?

CONCEPT CHECK 21-18

Suppose for a moment that a 1-kg black hole was detected. Is it likely that this miniature black hole was produced billions of years ago in the Big Bang or created more recently?