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Hilbert starts his paper by citing Einstein: "The vast problems posed by Einstein as well as his ingeniously conceived methods of solution, and the far-reaching ideas and formation of novel concepts by means of which Mie constructs his electrodynamics, have opened new paths for the investigation into the foundations of physics." [5]
The strictest version of the problem was solved in 2023, after an initial discovery in 2022. The einstein problem can be seen as a natural extension of the second part of Hilbert's eighteenth problem, which asks for a single polyhedron that tiles Euclidean 3-space, but such that no tessellation by this polyhedron is isohedral. [3]
p. 172: "Although Poincaré's principle of relativity is stated in a manner similar to Einstein's, the difference in content is sharp. The critical difference is that Poincaré's principle admits the existence of the ether, and so considers the velocity of light to be exactly c only when it is measured in coordinate systems at rest in the ether.
David Hilbert. Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and ...
The Cauchy problem (sometimes called the initial value problem) is the attempt at finding a solution to a differential equation given initial conditions. In the context of general relativity , it means the problem of finding solutions to Einstein's field equations — a system of hyperbolic partial differential equations — given some initial ...
The Einstein–Hilbert action in general relativity is the action that yields the Einstein field equations through the stationary-action principle. With the (− + + +) metric signature , the gravitational part of the action is given as [ 1 ]
In mathematics, Hilbert's fourth problem in the 1900 list of Hilbert's problems is a foundational question in geometry.In one statement derived from the original, it was to find — up to an isomorphism — all geometries that have an axiomatic system of the classical geometry (Euclidean, hyperbolic and elliptic), with those axioms of congruence that involve the concept of the angle dropped ...
The differences between Einstein–Cartan theory and general relativity (formulated either in terms of the Einstein–Hilbert action on Riemannian geometry or the Palatini action on Riemann–Cartan geometry) rest solely on what happens to the geometry inside matter sources. That is: "torsion does not propagate".