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# Black hole

Black holes are objects so dense that not even light can escape their gravity. They are believed to form from the gravitational collapse of astronomical objects containing two or more solar masses. Astronomical observations suggest that the center of most galaxies, including our own Milky Way, contain supermassive black holes containing millions to billions of solar masses.

The core of the galaxy M87, where there is evidence for a supermassive black hole. Image taken by the Hubble space telescope.

Black holes are predictions of Einstein's theory of general relativity. In particular, they occur in the Schwarzschild metric[?], one of the earliest and simplest solutions to Einstein's equations, found by Karl Schwarzschild in 1915. This solution describes the curvature of spacetime in the vicinity of a static and spherically symmetric object.

According to Schwarzschild's solution, a gravitating object will collapse into a black hole if its radius is smaller than a characteristic distance, known as the Schwarzschild radius. Below this radius, spacetime is so strongly curved that any light ray emitted in this region, regardless of the direction in which it is emitted, will travel towards the center of the system. Because relativity forbids anything from travelling faster than light, anything below the Schwarzschild radius - including the constituent particles of the gravitating object - will collapse into the center. A gravitational singularity, a region of theoretically infinite density, forms at this point. Because not even light can escape from within the Schwarzschild radius, a classical black hole would truly appear black.

The Schwarzschild radius is given by

$r_s = {2GM \over c^2}$

where G is the gravitational constant, M is the mass of the object, and c is the speed of light. For an object with the mass of the Earth, the Schwarzschild radius is a mere 9 millimeters.

Since the mean radius of the Earth is around 6371 kilometers, the Earth would have to be compressed to a ludicrous 4 × 1026 times its current density for it to collapse into a black hole. For an object with the mass of the Sun, the Schwarzschild radius is approximately three kilometers, much smaller than the Sun's current radius of about 700,000 kilometers. It is also significantly smaller than the radius to which the Sun will ultimately shrink after exhausting its nuclear fuel, which is several thousand kilometers. More massive stars can collapse into black holes at the end of their lifetimes (see the section on "Black Hole Formation" below.)

More general black holes are also predicted by other solutions to Einstein's equations, such as the Kerr metric[?] for a rotating black hole, which possesses a ring singularity, and the Reissner-Nordstrøm metric[?] for charged black holes. The generalization of the Schwarzschild radius is known as the event horizon.

Theoretical Consequences Black holes demonstrate some counter-intuitive properties of general relativity. Consider a hapless astronaut falling radially towards the center of a Schwarzschild black hole. The closer she comes to the event horizon, the longer the photons she emits take to escape to infinity. A distant observer will see her descent slowing as she approaches the event horizon, which she never appears to reach. However, in her own frame of reference, the astronaut crosses the event horizon and reaches the singularity in a finite amount of time.

Black holes produce other interesting results when applied in unison with other physical theories. A commonly stated proposition is that "black holes have no hair", meaning they have no observable external characteristics that can be used to determine what they are like inside. Black holes have only three measurable characteristics: mass, angular momentum, and electric charge, and can be completely specified by these three parameters.

The entropy of black holes is a fascinating subject, and an area of active research. In 1971, Hawking showed that the total event horizon area of any collection of classical black holes can never decrease. This sounds remarkably similar to the Second Law of Thermodynamics, with area playing the role of entropy. Therefore, Bekenstein[?] proposed that the entropy of a black hole really is proportionate to its horizon area. In 1975, Hawking applied quantum field theory to a semi-classical curved spacetime and discovered that black holes can emit thermal radiation, known as Hawking radiation. This allowed him to calculate the entropy, which indeed was proportionate to the area, validating Bekenstein's hypothesis. It was later discovered that black holes are maximum-entropy objects, meaning that the maximum entropy of a region of space is the entropy of the largest black hole that can fit into it. This led to the proposal of the holographic principle.

Observational Evidence There is now a great deal of observational evidence for the existence of two types of black holes:

This evidence comes not from seeing the black holes directly, but by observing the behavior of stars and other material near them.
A third proposed type of black hole, primordial black holes, have not been observed.

In the case of a stellar size black hole, matter can be drawn in from a companion star, producing an accretion disk and large amounts of X-rays.

Galaxy-mass black holes with 10 to 100 billion solar masses were found in Active Galactic Nuclei (AGN), using radio and X-ray astronomy. It is now believed that such supermassive black holes exist in the center of most galaxies, including our own Milky Way. Sagittarius A* is now agreed to be the most plausible candidate for the location of a supermassive black hole at the center of the Milky Way galaxy.

Black holes are also the leading candidates for energetic astronomical objects such as quasars and gamma ray bursts.

Black Hole Formation Black holes are created by the gravitational collapse of supermassive stars. When a star exhausts its nuclear fuel, the equilibrium between gravitation and radiation pressure is disturbed, and it collapses. If the mass of the star is greater than about 3 times the mass of the sun, the collapse cannot be stopped, and a black hole is created. (See stellar evolution.)

Instead of collapsing on themselves, black holes might also be created by compression of matter by extreme external pressure. Such black holes are called primordial black holes. The enormous pressures necessary for creating primordial black holes are thought to have existed in the very early stages of the universe. These black holes can have masses smaller than that of the sun.