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The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic radius associated with any quantity of mass.
In the Schwarzschild coordinates, the Schwarzschild radius = is the radial coordinate of the event horizon = =. In the Kruskal–Szekeres coordinates the event horizon is given by =. Note that the metric is perfectly well defined and non-singular at the event horizon.
The Schwarzschild black hole is characterized by a surrounding spherical boundary, called the event horizon, which is situated at the Schwarzschild radius (), often called the radius of a black hole. The boundary is not a physical surface, and a person who fell through the event horizon (before being torn apart by tidal forces) would not notice ...
The Schwarzschild radius of an object is proportional to its mass. Theoretically, any amount of matter will become a black hole if compressed into a space that fits within its corresponding Schwarzschild radius. For the mass of the Sun, this radius is approximately 3 kilometers (1.9 miles); for Earth, it is
The equatorial (maximal) radius of an ergosphere is the Schwarzschild radius, the radius of a non-rotating black hole. The polar (minimal) radius is also the polar (minimal) radius of the event horizon which can be as little as half the Schwarzschild radius for a maximally rotating black hole. [2]
The equation of motion for the particle derived above = + + can be rewritten using the definition of the Schwarzschild radius r s as = [] + + (+) which is equivalent to a particle moving in a one-dimensional effective potential = + (+) The first two terms are well-known classical energies, the first being the attractive Newtonian gravitational ...
Schwarzschild solution in Schwarzschild coordinates, with two space dimensions suppressed, leaving just the time t and the distance from the center r. In red the incoming null geodesics. In blue outcoming null geodesics. In green the null light cones on which borders light moves, while massive objects move inside the cones.
For example, the Schwarzschild radius of a nonrotating uncharged black hole with mass m becomes r = 2m. For this reason, many books and papers on relativistic physics use geometric units. An alternative system of geometrized units is often used in particle physics and cosmology, in which 8πG = 1 instead.