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.

Only a few months later, Karl Schwarzschild found a solution to Einstein field equations, which describes the gravitational field of a point mass and a spherical mass.

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.

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.

Finkelstein's solution extended the Schwarzschild solution for the future of observers falling into a black hole.

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

* Gravitational redshift does not assume the Schwarzschild metric solution to Einstein's field equation – in which the variable cannot represent the mass of any rotating or charged body.

But as early as 1916, the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the so-called Schwarzschild metric.

The best-known exact solutions, and also those most interesting from a physics point of view, are the Schwarzschild solution, the Reissner – Nordström solution and the Kerr metric, each corresponding to a certain type of black hole in an otherwise empty universe, and the Friedmann – Lemaître – Robertson – Walker and de Sitter universes, each describing an expanding cosmos.

As one examines suitable model spacetimes ( either the exterior Schwarzschild solution or, for more than a single mass, the post-Newtonian expansion ), several effects of gravity on light propagation emerge.

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.

One type of non-traversable wormhole metric is the Schwarzschild solution ( see the first diagram ):

* The Schwarzschild solution, which describes spacetime surrounding a spherically symmetric non-rotating uncharged massive object.

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.

An example is the Schwarzschild solution that describes a non-rotating, uncharged black hole.

* 1918 — Friedrich Kottler gets Schwarzschild solution without Einstein vacuum field equations

* 1923 — George David Birkhoff proves that the Schwarzschild spacetime geometry is the unique spherically symmetric solution of the Einstein vacuum field equations

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.

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

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.

The observer originates from the right, and another universe becomes visible in the center of the wormhole ’ s shadow once the horizon is crossed, the observer seeing light that has fallen into the black hole interior region from the other universe ; however, this other universe is unreachable in the case of a Schwarzschild wormhole, as the bridge always collapses before the observer has time to cross it, and everything that has fallen through the event horizon of either universe is inevitably crushed in the singularity.

The motion through a Schwarzschild wormhole connecting two universes is possible in only one direction.

Timelike and null geodesics in the gravitational field of a Schwarzschild wormhole are complete because the expansion scalar in the Raychaudhuri equation has a discontinuity at the event horizon, and because an Einstein – Rosen bridge is represented by the Kruskal diagram in which the two antipodal future event horizons are identified.

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.

* A Disruptor of Order in Aligned Systems is the device that allows Heechee to unseal the Schwarzschild barrier in black holes and allow ships to traverse the boundaries ( referred to jokingly by humans as a " can opener ").

He is also the father of astrophysicist Martin Schwarzschild.

* Schwarzschild ( disambiguation ), items named after Karl Schwarzschild

The Schwarzschild radius was named after the German astronomer Karl Schwarzschild who calculated this exact solution for the theory of general relativity in 1915.

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.

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.

* 1873 – Karl Schwarzschild, German physicist and astronomer ( d. 1916 )

Karl Schwarzschild discovered that the color of a star, and hence its temperature, could be determined by comparing the visual magnitude against the photographic magnitude.

* May 11 – Karl Schwarzschild, German physicist ( b. 1873 )

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

* 1916 — Karl Schwarzschild solves the Einstein vacuum field equations for uncharged spherically-symmetric non-rotating systems

* 1906 — Karl Schwarzschild explains solar limb darkening

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

* Martin Schwarzschild, son of Karl Schwarzschild, and renowned astronomer

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