## Black Holes

The fact that light is bent by a gravitational field brings up the following thought experiment. Imagine adding mass to a body. As the mass increases, so does the gravitational pull and objects require more energy to reach escape velocity. When the mass is sufficiently high enough that the velocity needed to escape is greater than the speed of light we say that a black hole has been created.

Another way of defining a black hole is that for a given mass, there is a radius where if all the mass is compressed within this radius the curvature of spacetime becomes infinite and the object is surrounded by an event horizon. This radius is called the Schwarzschild radius and varies with the mass of the object (large mass objects have large Schwarzschild radii, small mass objects have small Schwarzschild radii).

Schwarzschild radius is the radius below which the gravitational attraction between the particles of a body must cause it to undergo irreversible gravitational collapse. This phenomenon is thought to be the final fate of the more massive stars.

The gravitational radius (R) of an object of mass M is given by the following formula, in which 'G' is the universal gravitational constant and 'c' is the speed of light: R = 2GM/c2 . For a mass as small as a human being, the gravitational radius is in the order of 10-23 cm, much smaller than the nucleus of an atom; for a typical star such as the Sun, it is about 3 km (2 miles).

The Schwarzschild radius marks the point where the event horizon forms, below this radius no light escapes. The visual image of a black hole is one of a dark spot in space with no radiation being emitted. Any radiation falling on the black hole is not reflected but rather absorbed, and starlight from behind the black hole is lensed.

A black hole can come in any size. Stellar mass black holes are thought to form from supernova events, and have radii of 5 km. Galactic black hole in the cores of most galaxies, millions of solar masses and the radius of a solar system, are built up over time by cannibalizing stars. Mini black holes formed in the early Universe (due to tremendous pressures) down to masses of asteroids with radii the size of a grain of sand.

## Hawking Radiation

Hawking, an English theoretical physicist, was one of the first to consider the details of the behavior of a black hole whose Schwarzschild radius was on the level of an atom. These black holes are not necessarily low mass, for example, it requires 1 billion tons of matter to make a black hole the size of a proton. But their small size means that their behavior is a mix of quantum mechanics rather than relativity.

Before black holes were discovered it was know that the collision of two photons can cause pair production. This is a direct example of converting energy into mass (unlike fission or fusion which turns mass into energy). Pair production is one of the primary methods of forming matter in the early Universe.

Note that pair production is symmetric in that a matter and antimatter particle are produced (an electron and an anti-electron (positron) in the above example).

Hawking showed that the strong gravitational gradients (tides) near black holes can also lead to pair production. In this case, the gravitational energy of the black hole is converted into particles.

If the matter/anti-matter particle pair is produced below the event horizon, then particles remain trapped within the black hole. But, if the pair is produced above the event horizon, it is possible for one member to fall back into the black hole, the other to escape into space. Thus, the black hole can lose mass by a quantum mechanical process of pair production outside of the event horizon.

The rate of pair production is stronger when the curvature of spacetime is high. Small black holes have high curvature, so the rate of pair production is inversely proportional to the mass of the black hole (this means its faster for smaller black holes). Thus, Hawking was able to show that the mini or primordial black holes expected to form in the early Universe have since disintegrated, resolving the dilemma of where all such mini-black holes are today.