Quantum mechanics tells us that we can't know exactly where a particle is located. In particular, it could be located at any position within its DeBroglie wavelength. If the DeBroglie wavelength of a particle is larger than the size of the event horizon, then there is no reason to think that it is actually inside of the black hole. Quantum mechanics tells us that due to the wave nature of particles, mass that has fallen into the black hole can potentially get out. This concept is called quantum tunneling and leads to the process of Hawking radiation. Stephen Hawking calculated the probabilities for particles escaping from a black hole. Hawking showed that the number of particles with various energies that escape from a black hole corresponds to exactly the same emission as black body radiation. So, Hawking proved that black holes are actually black body emitters. Very cold blackbody emitters, but still this was rather surprising result. So, if an object is hot and emits as a black-body this means that it has a temperature. We learned earlier in this course that a hot object's temperature is inversely related to the peak wavelength through Wien's law. The peak wavelength is the wavelength where the most particles or photons are emitted. Wien's Law is temperature of a hot object is Wien's constant w, divided by the peak wavelength. We know if the peak wavelength is red, corresponding to 700 nanometers, the temperature of the object is 4100 Kelvin. If the wavelength is longer in the infrared or radio parts of the electromagnetic spectrum, then the temperature will be cooler. So what would be the temperature of a black hole? We already know the event horizon radius of a one solar mass black hole is three kilometers. A hot object whose peak wavelength is this large has a very small temperature, which we saw in the last section is 60 nano Kelvin. A lower mass black hole will have a smaller event horizon. So, the emitted Hawking radiation will have a smaller peak wavelength. Smaller peak wavelength means higher temperature. This leads to the inverse relationship between black hole mass and temperature. Where does the energy for this radiation come from? The energy is coming from the mass of the black hole. The process of Hawking radiation slowly converts the mass of the black hole into energy by allowing the mass to leak out of the black hole. The Hawking radiation that the black hole emits is black-body radiation which has no dependence on the composition of the material that originally fell into the black hole. The emitted Hawking radiation depends only on the black hole's mass and angular momentum. So, it preserves the no-hair property of black holes. This is another aspect of the black hole information paradox. The emitted radiation doesn't convey any of the information that had previously been captured by the black hole. Hawking radiation is a quantum mechanical process that allows mass to slowly leak out of the black hole's event horizon into the region outside. If a black hole loses mass, we know that its event horizon must shrink. Shrinking the event horizon means that the temperature will increase. Since higher temperature, hot objects are also brighter, this means that the rate that mass is lost will increase. So, as black holes lose mass and become smaller, they also radiate faster. This could get messy. The result that Hawking radiation causes a black hole to lose mass is called, Black Hole Evaporation. If you were to extrapolate down to zero mass, the equations would predict infinite brightness and temperature. This extrapolation is most likely not correct and requires a quantum theory of gravity to predict the outcome correctly. One possibility is that all of the information that was lost inside the black hole is finally released in the moments before the Hawking radiation process is finished. The process of black hole evaporation takes a long time for the black holes that we see in nature, but is rapid for black holes with tiny mass. For instance, a black hole like Cygnus X-1 would take 10 to the power of 68 years. That's an enormous amount of time, longer than the present age of the universe by a factor of an octodecillion which is a one followed by 57 zeroes. Since Cygnus X-1 won't evaporate anytime soon, the Hawking radiation plays no important role in its lifespan. In addition, Cygnus X-1 is accreting mass from its companion. So, it is gaining mass at a much faster rate than the black hole evaporation rate. The X-rays emitted by the accretion disk are enormously bright in comparison to the Hawking radiation making it impossible to detect the faint signal from the black hole's evaporation. At present, Hawking radiation has never been detected from any black hole. This is due to the very long wavelength associated with it and the very low temperature and energy associated with astrophysical black holes. In order to detect Hawking radiation, we need to hunt for a special set of circumstances. First of all, it would be best to look for an isolated black hole that is not accreting matter from a companion star. Secondly, the mass should be very small so that the temperature is high enough that we could detect it. How small should the mass be? If we could find a black hole with the mass the same as our moon, then the Hawking radiation would be 1.6 Kelvin which would be difficult but possible to measure. Any black hole with a mass smaller than our moon would be hotter and easier to detect. If we want to see the whole evaporation process, it would be convenient if the time for the evaporation to take place would be less than the present age of the universe which is 13.8 billion years. A black hole with a much smaller mass, such as a trillion kilograms or smaller, would take less than 13.8 billion years to evaporate. That might sound like a large mass but a trillion kilograms is approximately just the mass of a large mountain here on Earth. That may still sound like a large mass, but to astrophysicists that's tiny. Unfortunately, we don't know about any mechanisms for creating mountain mass black holes from astrophysical objects like stars or planets or asteroids. One possibility is that very small black holes, called primordial black holes, could have been created in the Big Bang. However, no evidence for Hawking radiation from these conjectured primordial black holes has ever been seen. If you are really interested in detecting Hawking radiation, you'll have to artificially create your own black hole by smashing protons and antiprotons together at incredible speed. Making your own black hole sounds kind of silly. Wouldn't it be dangerous to create a black hole on Earth? Well, we just learned that small black holes evaporate quickly by emitting Hawking radiation, so if it's a really tiny one, it won't last long enough to capture matter from the Earth. It is theoretically possible to create one using a particle accelerator such as the Large Hadron Collider, also known as the LHC, located in Geneva, Switzerland. The LHC accelerates protons and antiprotons in opposite directions along a circular path. When the particles are moving fast enough, the proton and anti-proton beams are crossed and allowed to smash into each other. If the proton and antiproton get closer together than the Schwarzschild radius for two protons, they could form a tiny black hole before they get a chance to annihilate each other. The tiny black holes formed in the LHC would evaporate very quickly in much less than a second and we could then observe the energy released. Scientists are looking for the signature of the energy released from Hawking radiation, but so far no evidence for black holes created in the LHC has been found. We should remember that the Earth's atmosphere is bombarded by natural high energy particle called cosmic rays that possibly originate from the jets of supermassive black holes in faraway galaxies. Some of these cosmic rays could interact with atoms in the Earth's atmosphere and create a tiny black hole. No evidence for this process has ever been seen. This tells us that either tiny black holes are difficult to create, or when they are created the radiation that they emit is difficult to detect. Some people expressed concern about the possible harm to the Earth if a tiny black hole were created in the LHC. However, the very short lifetime due to hawking radiation would make these tiny black holes harmless. In addition, in the five billion years of the Earth's history, no cosmic ray collision, which could be more energetic than the LHC, has ever created a black hole that has harmed the Earth. We also had not seen any other planets or stars harmed by interactions with tiny black holes. So, there is no evidence of risk. Physicists who study these tiny black holes are confident that their existence does not endanger life on Earth
