Non-exact Solutions In General Relativity
   HOME

TheInfoList



Click Here for Items Related To - Non-exact Solutions In General Relativity
OR:
Non-exact Solutions In General Relativity on:   [Wikipedia]   [Google]   [Amazon]

Non-exact solutions in general relativity are
solutions Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Soluti ...
of Albert Einstein's field equations of general relativity which hold only approximately. These solutions are typically found by treating the gravitational field, g, as a background space-time, \gamma, (which is usually an exact solution) plus some small perturbation, h. Then one is able to solve the
Einstein field equations In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the form ...
as a
series Series may refer to: People with the name * Caroline Series (born 1951), English mathematician, daughter of George Series * George Series (1920–1995), English physicist Arts, entertainment, and media Music * Series, the ordered sets used in ...
in h, dropping higher order terms for simplicity. A common example of this method results in the
linearised Einstein field equations In the theory of general relativity, linearized gravity is the application of perturbation theory to the metric tensor that describes the geometry of spacetime. As a consequence, linearized gravity is an effective method for modeling the effects ...
. In this case we expand the full space-time metric about the flat
Minkowski metric In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of Three-dimensional space, three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two Event (rel ...
, \eta_: ::g_ = \eta_ + h_ +\mathcal(h^2), and dropping all terms which are of second or higher order in h.


See also

*
Exact solutions in general relativity In general relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though the starting point for that derivation may be an idealized case like a perfectly spherical sh ...
*
Linearized gravity In the theory of general relativity, linearized gravity is the application of perturbation theory to the metric tensor that describes the geometry of spacetime. As a consequence, linearized gravity is an effective method for modeling the effects ...
*
Post-Newtonian expansion In general relativity, the post-Newtonian expansions (PN expansions) are used for finding an approximate solution of the Einstein field equations for the metric tensor. The approximations are expanded in small parameters which express orders of ...
*
Parameterized post-Newtonian formalism In physics, precisely in the study of the theory of general relativity and many alternatives to it, the post-Newtonian formalism is a calculational tool that expresses Einstein's (nonlinear) equations of gravity in terms of the lowest-order devi ...
*
Numerical relativity Numerical relativity is one of the branches of general relativity that uses numerical methods and algorithms to solve and analyze problems. To this end, supercomputers are often employed to study black holes, gravitational waves, neutron stars and ...


References

General relativity {{Relativity-stub