Black Holes

In general relativity, a black hole is a region of space in which the gravity well is so deep that gravitational time dilation halts time completely. This forms an event horizon, a one-way surface into which objects can fall, but out of which nothing can appear. It is called "black" because it absorbs all the light that hits it, reflecting nothing, just like a perfect black body in thermodynamics.Thermodynamics of Black Holes,P.C.W Davies, Rep. Prog. Phys Vol. 41(1978), pp.1313-1355. Quantum analysis of black holes shows them to possess a temperature and Hawking radiation.

Despite its invisible interior, a black hole can be observed through its interaction with other matter. A black hole can be inferred by tracking the movement of a group of stars that orbit a region in space which looks empty. Alternatively, one can see gas falling into a relatively small black hole, from a companion star. This gas spirals inward, heating up to very high temperatures and emitting large amounts of radiation that can be detected from earthbound and earth-orbiting telescopes. Such observations have resulted in the scientific consensus that, barring a breakdown in our understanding of nature, black holes exist in our universe.

In general relativity, an event horizon is a boundary in spacetime, most often an area surrounding a black hole, beyond which events cannot affect an outside observer. Light emitted from beyond the horizon can never reach the observer, and any object that approaches the horizon from the observer's side appears to slow down and never quite pass through the horizon, with its image becoming more and more redshifted as time elapses. The traveling object, however, experiences no strange effects and does, in fact, pass through the horizon in a finite amount of proper time.

More specific types of horizon include the related but distinct absolute and apparent horizons found around a black hole. Still other distinct notions include the Cauchy and Killing horizon; the photon spheres and ergospheres of the Reissner-Nordström solution; particle and cosmological horizons relevant to cosmology; and isolated and dynamical horizons important in current black hole research.

A photon sphere is a spherical region of space where gravity is strong enough that photons are forced to travel in orbits. The formula to find the radius for a circular photon orbit is: r=3GM/c2. Because of this equation photon spheres can only exist in the space surrounding an extremely compact object, such as a black hole.

As photons travel near the event horizon of a black hole they can escape being pulled in by the gravity of a black hole by traveling at a nearly vertical direction known as an exit cone. A photon on the boundary of this cone will not completely escape the gravity of the black hole. Instead it orbits the black hole. These orbits are not stable.

The photon sphere is located further from the center of a black hole than the event horizon and ergosphere. Within a photon sphere it is possible to imagine a photon that starts at the back of your head and orbits around a black hole only then be seen by your eyes.

For non-rotating black holes, the photon sphere is a sphere of radius 3/2 Rs, where Rs denotes the Schwarzschild radius (the radius of the event horizon) - see below for a derivation of this result. No unaccelerated orbit with a semi-major axis less than this distance is possible, but within the photon sphere, a constant acceleration will allow a spacecraft or probe to hover above the event horizon.

A rotating black hole has two photon spheres. As a black hole rotates it drags space with it. The photon sphere that is closer to the black hole is moving in the same direction as the rotation, whereas the photon sphere further away is moving against it. The greater the angular velocity of the rotation of a black hole the greater distance between the two photon spheres. Because the black hole has an axis of rotation this only holds true if approaching the black hole in the direction of the equator. If approaching at a different angle, such as one from the poles of the black hole to the equator, there is only one photon sphere. This is because approaching at this angle the possibility of traveling with or against the rotation does not exist.