In the mathematical field of Lorentzian geometry, a Cauchy surface is a certain kind of submanifold of a Lorentzian manifold. In the application of Lorentzian geometry to the physics of general relativity, a Cauchy surface is usually interpreted as defining an "instant of time". In the mathematics of general relativity, Cauchy surfaces provide boundary conditions for the causal structure in which the Einstein equations can be solved (using, for example, the ADM formalism.)
They are named for French mathematician Augustin-Louis Cauchy (1789-1857) due to their relevance for the Cauchy problem of general relativity.
In the mathematical field of Lorentzian geometry, a Cauchysurface is a certain kind of submanifold of a Lorentzian manifold. In the application of Lorentzian...
Augustin-Louis Cauchy. For a partial differential equation defined on Rn+1 and a smooth manifold S ⊂ Rn+1 of dimension n (S is called the Cauchysurface), the...
continuum mechanics, the Cauchy stress tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress...
relativity states complete knowledge of the universe on a spacelike Cauchysurface can be used to calculate the complete state of the rest of spacetime...
three-dimensional Cauchysurface, and furthermore that any two Cauchysurfaces for M are diffeomorphic. In particular, M is diffeomorphic to the product of a Cauchy surface...
in general relativity can be posed as an initial value problem on a Cauchysurface. There is a hierarchy of causality conditions, each one of which is...
disjoint from I + [ S ] {\displaystyle I^{+}[S]} . A Cauchysurface is a closed achronal set whose Cauchy development is M {\displaystyle M} . A metric is...
everywhere on a spacelike three-dimensional hypersurface, called the Cauchysurface). Failure of the cosmic censorship hypothesis leads to the failure of...
In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem (a particular boundary value problem of the theory...
mathematics, the Crofton formula, named after Morgan Crofton (1826–1915), (also Cauchy-Crofton formula) is a classic result of integral geometry relating the length...
developed by Colin Maclaurin and Augustin-Louis Cauchy and is sometimes known as the Maclaurin–Cauchy test. Consider an integer N and a non-negative function...
The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any...
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with...
In mathematics, the Cauchy condensation test, named after Augustin-Louis Cauchy, is a standard convergence test for infinite series. For a non-increasing...
the right and left Cauchy–Green deformation tensors. In 1839, George Green introduced a deformation tensor known as the right Cauchy–Green deformation...
of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have...
the derivatives of the Gauss map. If the projected Gauss map obeys the Cauchy–Riemann equations then either the trace vanishes or every point of M is...
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