In general relativity, a black hole is a region of space in which the gravitational field is so powerful that nothing, including light, can escape its pull. The black hole has a one-way surface, called an event horizon, into which objects can fall, but out of which nothing can come. It is called "black" because it absorbs all the light that hits it, reflecting nothing, just like a perfect blackbody in thermodynamics. Quantum analysis of black holes shows them to possess a temperature and radiate like black bodies.

Despite its invisible interior, a black hole can reveal its presence through 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 temperature and emitting large amounts of radiation that can be detected from earthbound and earth-orbiting telescopes. Such observations have resulted in the general scientific consensus that, barring a breakdown in our understanding of nature, black holes do exist in our universe.

Introduction and terminology

A black hole is often defined as an object whose escape velocity exceeds the speed of light. This picture is qualitatively wrong, but provides a way of understanding the order of magnitude for the black hole radius.

The escape velocity is the speed at which an object needs to travel so as to just manage to get infinitely far away from a source of gravity before stopping. On the Earth, the escape velocity is equal to 11 km/s, so no matter what the object is, a rocket or a baseball, it must go at least 11 km/s to avoid falling back to the Earth's surface eventually. To calculate the escape velocity in Newtonian mechanics, consider a heavy object of mass M centered at the origin. A second object with mass m starting at distance r from the origin with speed v, trying to escape to infinity, needs to have just enough kinetic energy to make up for the negative gravitational potential energy, with nothing left over:

$\{mv^2\backslash over\; 2\}\; -\; \{GMm\backslash over\; r\}\; =\; 0$

That way, as it gets closer to $\backslash scriptstyle\; r=\backslash infty$ it has less and less kinetic energy, finally ending up at infinity with no speed.

This relation gives the critical escape velocity v in terms of M and r. But it also says that for each value of v and M, there is a critical value of r so that a particle with speed v is just able to escape:

$r\; =\; \{2GM\backslash over\; v^2\}$

When the velocity is equal to the speed of light, this gives the radius of a hypothetical Newtonian dark star, a Newtonian body from which a particle moving at the speed of light cannot escape. In the most commonly used convention for the value of the radius of a black hole, the radius of the event horizon is equal to this Newtonian value.