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The Schwarzschild radius (sometimes inappropriately referred to as the gravitational radius[1]) is a characteristic radius associated with every mass. The term is used in physics and astronomy, especially in the theory of gravitation, general relativity. It was found in 1916 by Karl Schwarzschild and results from his discovery of an exact solution for the gravitational field outside a static, spherically symmetric star (see Schwarzschild metric, which is a solution of the Einstein field equations). The Schwarzschild radius is proportional to the mass. The Sun has a Schwarzschild radius of approximately 3 km, the Earth's being approximately 9 mm. RADIUS (Remote Authentication Dial In User Service) is an AAA (authentication, authorization and accounting) protocol for applications such as network access or IP mobility. ...
Mass is a property of a physical object that quantifies the amount of matter it contains. ...
A Superconductor demonstrating the Meissner Effect. ...
Astronomy (Greek: αστÏονομία = άστÏον + νόμος, astronomia = astron + nomos, literally, law of the stars) is the science of celestial objects and phenomena that originate outside the Earths atmosphere, such as stars, planets, comets, aurora, galaxies, and the cosmic background radiation. ...
In physics, gravitation or gravity is the tendency of objects with mass to accelerate toward each other. ...
It has been suggested that Einsteins theory of gravitation be merged into this article or section. ...
1916 (MCMXVI) is a leap year starting on Saturday (link will take you to calendar) // Events January-February January 1 - The Royal Army Medical Corps first successful blood transfusion using blood that had been stored and cooled. ...
Karl Schwarzschild (October 9, 1873 - May 11, 1916) was a noted German Jewish physicist and astronomer, father of astrophysicist Martin Schwarzschild. ...
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It has been suggested that Deriving the Schwarzschild solution be merged into this article or section. ...
In physics, the Einstein field equation or Einstein equation is a differential equation in Einsteins theory of general relativity. ...
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Earth is the third planet in the solar system. ...
An object smaller than its Schwarzschild radius is called a black hole. The surface at the Schwarzschild radius acts as an event horizon in a static body. (A rotating black hole operates slightly differently.) Neither light nor particles can escape through this surface from the region inside, hence the name "black hole". The Schwarzschild radius of the Supermassive black hole at our Galactic Center is approximately 7.8 million km. The Schwarzschild radius of a sphere with a uniform density equal to the critical density is equal to the radius of the visible universe. A black hole is a concentration of mass great enough that the force of gravity prevents anything past its event horizon from escaping it except through quantum tunnelling behaviour (known as Hawking Radiation). ...
Event Horizon is a 1997 science fiction and horror film. ...
It has been suggested that this article or section be merged into Kerr metric. ...
Top: artists conception of a supermassive black hole drawing material from a nearby star. ...
The Galactic Center is the rotational center of the Milky Way galaxy. ...
In cosmology, the Big Crunch is a hypothesis that states the universe will stop expanding and start to collapse upon itself; a counterpart to the Big Bang. ...
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Connie Willis's hard science fiction short story "The Schwarzschild Radius" offers both an accessible and accurate explanation of the phenomenon which makes it surprisingly applicable to not-so-scientific pursuits. Connie Willis at Worldcon 2005 in Glasgow Constance Elaine Trimmer Willis (born December 31, 1945) is an American science fiction writer. ...
Hard science fiction, or hard SF, is a subgenre of science fiction characterized by an interest in scientific detail or accuracy. ...
It is coincidental that Schwarzschild also means "black shield", which is befitting for the idea of a black hole.
Formula for the Schwarzschild radius
The Schwarzschild radius is proportional to the mass, with a proportionality constant involving the gravitational constant and the speed of light. The formula for the Schwarzschild radius can be found by setting the escape velocity to the speed of light, and is According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...
In physics, for a given gravitational field and a given position, the escape velocity is the minimum speed an object without propulsion, at that position, needs to have to move away indefinitely from the source of the field, as opposed to falling back or staying in an orbit within a...
 where - rs is the Schwarzschild radius
- G is the gravitational constant, that is 6.67 × 10-11 N m2 / kg2;
- m is the mass of the gravitating object; and
- c² is the speed of light squared, that is (299,792,458 m/s)² = 8.98755 × 1016 m²/s².
The proportionality constant, 2G / c2, can be approximated as 1.48 × 10-27 m / kg. According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...
Cherenkov effect in a swimming pool nuclear reactor. ...
This means that the equation can be approximately written as
 with rs in meters and m in kilograms.
Note that although the result is correct, general relativity must be used to truly derive the Schwarzschild radius. It is only a coincidence that Newtonian physics produces the same result. It has been suggested that Einsteins theory of gravitation be merged into this article or section. ...
Classical mechanics is a model of the physics of forces acting upon bodies. ...
Classification by Schwarzschild radius
Supermassive black hole If one accumulates matter of normal density (say 1000 kg/m³, such as water, which also happens to be about the same as the average density of the Sun) up to about 300,000 times the mass of the Sun, such an accumulation will fall inside its own Schwarzschild radius and thus it would be a supermassive black hole of 300,000 solar masses (Supermassive black holes up to a few billion solar masses are thought to exist). The supermassive black hole in the center of our galaxy (2.5 million solar masses) constitutes observationally the most convincing evidence for the existence of black holes in general. It is thought that large black holes like these don't form directly in one collapse of a cluster of stars. Instead they may start as a stellar-sized black hole and grow larger by the accretion of matter and other black holes. The larger the mass of a galaxy, the larger is the mass of the supermassive black hole in its center. Top: artists conception of a supermassive black hole drawing material from a nearby star. ...
Stellar black hole If one accumulates matter at nuclear density (the density of the nucleus of an atom, about 1018 kg/m³; neutron stars also reach this density), such an accumulation would fall within its own Schwarzschild radius at about 3 solar masses and thus would be a stellar black hole. Nuclear density is the density of the nucleus of an atom, about 10^18 kg/m³; neutron stars reach this density. ...
Kilogram per cubic metre is the SI measure of density and is represented as kg/m³, where kg stands for kilogram and m³ stands for cubic metre. ...
Neutron stars are one of the few possible endpoints of stellar evolution. ...
A stellar black hole is a black hole formed by the gravitational collapse of a massive star (3 or more solar masses) at the end of its lifetime. ...
Primordial black hole Conversely, a small mass has an extremely small Schwarzschild radius. A mass as big as Mount Everest has a Schwarzschild radius smaller than a nanometre. Its average density at that size would be so high that no known mechanism could form such extremely compact objects. Such black holes might possibly be formed in an early stage of the evolution of the universe, just after the Big Bang, when densities were extremely high. Therefore these hypothetical baby black holes are called primordial black holes. A nanometre (American spelling: nanometer, symbol: nm) is 1. ...
According to the Big Bang theory, the universe emerged from an extremely dense and hot state (bottom). ...
A primordial black hole is a hypothetical type of black hole that is formed not by the gravitational collapse of a star but by the extreme densities of matter present during early universe. ...
See also Classification of black holes by type: A black hole is a concentration of mass great enough that the force of gravity prevents anything past its event horizon from escaping it except through quantum tunnelling behaviour (known as Hawking Radiation). ...
A classification of black holes by mass: A Schwarzschild black hole or static black hole is a black hole fully defined by its only parameter, the mass M. In general black holes could have in addition angular momentum (rotating black holes) and electric charge (see charged black holes). ...
It has been suggested that this article or section be merged into Kerr metric. ...
A charged black hole is a black hole that possesses electric charge. ...
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