This solution had a peculiar behaviour at what is now called the Schwarzschild radius, where it became singular, meaning that some of the terms in the Einstein equations became infinite.

In 1924, Arthur Eddington showed that the singularity disappeared after a change of coordinates ( see Eddington – Finkelstein coordinates ), although it took until 1933 for Georges Lemaître to realize that this meant the singularity at the Schwarzschild radius was an unphysical coordinate singularity.

Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped.

Because of this property, the collapsed stars were called " frozen stars ," because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius.

with the Schwarzschild radius

When the photon is emitted at a distance equal to the Schwarzschild radius, the redshift will be infinitely large.

In the Newtonian limit, i. e. when is sufficiently large compared to the Schwarzschild radius, the redshift can be approximated by a binomial expansion to become

The mass of a very large star or black hole may be identified with its Schwarzschild radius ().

Some terms associated with gravitational mass and its effects are the Gaussian gravitational constant, the standard gravitational parameter and the Schwarzschild radius.

In natural units, the mass of the depicted star is 1 and its radius 4, or twice its Schwarzschild radius.

Its size is 10 – 10, 000 times the Schwarzschild radius of the black hole.

Whether objects heavier than the Planck mass ( about the weight of a large bacterium ) have a de Broglie wavelength is theoretically unclear and experimentally unreachable ; above the Planck mass a particle's Compton wavelength would be smaller than the Planck length and its own Schwarzschild radius, a scale at which current theories of physics may break down or need to be replaced by more general ones.

For radial distances from the center which are much greater than the Schwarzschild radius, the accelerations predicted by the Schwarzschild solution are practically identical to those predicted by Newton's theory of gravity.

Another type of singularity predicted by general relativity is inside a black hole: any star collapsing beyond a certain point ( the Schwarzschild radius ) would form a black hole, inside which a singularity ( covered by an event horizon ) would be formed, as all the matter would flow into a certain point ( or a circular line, if the black hole is rotating ).

* 1958 — David Finkelstein theorises that the Schwarzschild radius of a black holes is a causality barrier: an event horizon

The boundary of this region is called the event horizon and has an effective radius called the Schwarzschild radius, which is about for Cygnus X-1.

If a spacecraft gets close to the Schwarzschild radius of a black hole ( the ultimate gravity well ), space becomes so curved that slingshot orbits require more energy to escape than the energy that could be added by the black hole's motion.

The Schwarzschild solution, which makes use of Schwarzschild coordinates and the Schwarzschild metric, leads to the well-known Schwarzschild radius, which is the size of the event horizon of a non-rotating black hole.

Schwarzschild's second paper, which gives what is now known as the " Inner Schwarzschild solution " ( in German: " innere Schwarzschild-Lösung "), is valid within a sphere of homogeneous and isotropic distributed molecules within a shell of radius r = R.

The first modern solution of general relativity that would characterize a black hole was found by Karl Schwarzschild in 1916, although its interpretation as a region of space from which nothing can escape was not fully appreciated for another four decades.

The first type of wormhole solution discovered was the Schwarzschild wormhole which would be present in the Schwarzschild metric describing an eternal black hole, but it was found that this type of wormhole would collapse too quickly for anything to cross from one end to the other.

Before the stability problems of Schwarzschild wormholes were apparent, it was proposed that quasars were white holes forming the ends of wormholes of this type.

Karl Schwarzschild (/' shvarts shĭld /) ( October 9, 1873 – May 11, 1916 ) was a German physicist.

Schwarzschild was born in Frankfurt am Main to Jewish parents.

From 1912, Schwarzschild was a member of the Prussian Academy of Sciences.

Schwarzschild, in contrast, chose a more elegant " polar-like " coordinate system and was able to produce an exact solution which he first set down in a letter to Einstein of 22 December 1915, written while Schwarzschild was serving in the war stationed on the Russian front.

In the early years of general relativity there was a lot of confusion about the nature of the singularities found in the Schwarzschild and other solutions of the Einstein field equations.

In 1950, John Synge produced a paper that showed the maximal analytic extension of the Schwarzschild metric, again showing that the singularity at r = r < sub > s </ sub > was a coordinate artifact.

However due to the obscurity of the journals in which the papers of Lemaître and Synge were published their conclusions went unnoticed, with many of the major players in the field including Einstein believing that singularity at the Schwarzschild radius was physical.

The modification in the coordinate system was the first to reveal clearly that the Schwarzschild radius is a mere coordinate singularity ( with however, profound global significance: it represents the event horizon of a black hole ).

The Kerr metric is a generalization of the Schwarzschild metric, which was discovered by Karl Schwarzschild in 1916 and which describes the geometry of spacetime around an uncharged, spherically-symmetric, and non-rotating body.

The highest honour for astronomical research in Germany, the Karl Schwarzschild Medal of the German Astronomical Society ( AG ), was awarded to the astrophysicist Reinhard Genzel, director at the MPE.

* Schwarzschild ( disambiguation ), items named after Karl Schwarzschild

In Einstein's theory of general relativity, the Schwarzschild solution ( or the Schwarzschild vacuum ), named after Karl Schwarzschild, describes the gravitational field outside a spherical, uncharged, non-rotating mass such as a ( non-rotating ) star, planet, or black hole.

The Schwarzschild solution is named in honor of Karl Schwarzschild, who found the exact solution in 1916, a little more than a month after the publication of Einstein's theory of general relativity.

In general relativity Eddington – Finkelstein coordinates, named for Arthur Stanley Eddington and David Finkelstein, are a pair of coordinate systems for a Schwarzschild geometry which are adapted to radial null geodesics ( i. e. the worldlines of photons moving directly towards or away from the central mass ).

The Schwarzschild metric is named in honour of its discoverer Karl Schwarzschild, who found the solution in 1915, only about a month after the publication of Einstein's theory of general relativity.

A Planck particle, named after physicist Max Planck, is a hypothetical particle defined as a tiny black hole whose Compton wavelength is equal to its Schwarzschild radius.

In general relativity Kruskal – Szekeres coordinates, named for Martin Kruskal and George Szekeres, are a coordinate system for the Schwarzschild geometry for a black hole.

A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution for the point mass and wrote more extensively about its properties.

These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916.

* 1915 – Karl Schwarzschild publishes the Schwarzschild metric about a month after Einstein published his general theory of relativity.

The solutions of Einstein's field equation for the gravitational field of an electrically charged point mass ( with zero angular momentum ) in empty space was obtained in 1918 by Hans Reissner and Gunnar Nordström, not long after Karl Schwarzschild found the Schwarzschild metric as a solution for a point mass without electric charge and angular momentum.

It is hypothesized that shortly after the big bang the Universe was dense enough for any given region of space to fit within its own Schwarzschild radius.

Named after Karl Schwarzschild:

The Schwarzschild solution was found by Karl Schwarzschild shortly after Einstein published his field equations.

However, in 1957 ( two years after Einstein's death in 1955 ), Martin Kruskal published a proof that black holes are called for by the Schwarzschild Solution.