The first approach involves the use of Gauss's law for gravitation [nabla] x [??] = -4[pi]G[[rho].sub.matter] and the (t, t) component of Einstein's field equations
for a perfect fluid (where [T.sub.tt] = -[[rho].sub.matter][c.sup.2]): [G.sub.tt] = 8[pi]G[[rho].sub.matter]/[c.sup.2].
Another way to achieve this result is to reveal the solutions of Einstein's field equations
by incorporating some kinematical assumptions, which are in consistency with the observed kinematics of the universe.
A 2D sections of the 4D spacetime of Einstein spaces are geometrically one of the geometries of spacetime which satisfies the standard Einstein's field equations
in absence of energy-momentum.
and Herlt, E., Exact Solutions of Einstein's Field Equations
, Cambridge University Press, Cambridge, (2003).
Thus in Einstein's theory gravitation is associated with the geometry of space-time (described by the metric g) and is coupled to the nongravitational fields which, apart from the condition of Einstein's field equations
, have an independent existence.
The programme met with some initial success, allowing a rederivation of Einstein's field equations
based on field equations for what a spin-2 graviton field should be like.
Investigation of the nature of singularities in gravitational collapse solution of Einstein's field equations
in different systems is of particular interest in general relativity.
Exact Solutions of Einstein's Field Equations
. Cambridge University Press, 1979, p.101.
Thus our algorithm has produced a new (not conformally flat) solution to the Einstein's field equations
. This has been generated from a seed conformally flat model.
Villas da Rocha, "Type II fluid solutions to Einstein's field equations
in N-dimensional spherical spacetimes, " International Journal of Modern Physics D, vol.
The year 2015 also marks the 100th anniversary of Einstein's geometric theory of space-time and gravitation, the General Theory of Relativity, since the final formulation of the generally covariant Einstein's field equations
of gravitation in the last quarter of 1915 (during a very tragic and difficult time of World War I).