Ad
related to: metric tensor functions calculator with solutionwalmart.com has been visited by 1M+ users in the past month
Search results
Results from the WOW.Com Content Network
In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study.The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past.
A metric tensor field g on M assigns to each point p of M a metric tensor g p in the tangent space at p in a way that varies smoothly with p. More precisely, given any open subset U of manifold M and any (smooth) vector fields X and Y on U , the real function g ( X , Y ) ( p ) = g p ( X p , Y p ) {\displaystyle g(X,Y)(p)=g_{p}(X_{p},Y_{p})} is ...
The metric tensor is a central object in general relativity that describes the local geometry of spacetime (as a result of solving the Einstein field equations). Using the weak-field approximation, the metric tensor can also be thought of as representing the 'gravitational potential'. The metric tensor is often just called 'the metric'.
In general relativity, post-Newtonian expansions (PN expansions) are used for finding an approximate solution of Einstein field equations for the metric tensor. The approximations are expanded in small parameters that express orders of deviations from Newton's law of universal gravitation. This allows approximations to Einstein's equations to ...
But if one requires an exact solution or a solution describing strong fields, the evolution of both the metric and the stress–energy tensor must be solved for at once. To obtain solutions, the relevant equations are the above quoted EFE (in either form) plus the continuity equation (to determine the evolution of the stress–energy tensor):
Tensor [4] is a tensor package written for the Mathematica system. It provides many functions relevant for General Relativity calculations in general Riemann–Cartan geometries. Ricci [5] is a system for Mathematica 2.x and later for doing basic tensor analysis, available for free.
In mathematics, the Poincaré metric, named after Henri Poincaré, is the metric tensor describing a two-dimensional surface of constant negative curvature. It is the natural metric commonly used in a variety of calculations in hyperbolic geometry or Riemann surfaces .
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon.The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find.
Ad
related to: metric tensor functions calculator with solutionwalmart.com has been visited by 1M+ users in the past month