The

Einstein equations of general relativity have been tentatively modified in the spirit of Mach's principle, multiplying a new cosmological coefficient by the ratio of total retarding gravitational potential of matter in the universe to [c.

The present proposal focusses on two aspects of the evolution problem for the

Einstein equations which has been initiated by the pioneering work of Y.

In fact, due to its peculiar formulation, it leads to view the usual

Einstein equations as merely initial conditions following the Cauchy problem.

Dr Bruni said: "Much more work will be needed in future to fully comprehend the importance of the differences between simulations based on

Einstein equations and those making simplifying assumptions.

In November 1915 Albert Einstein presented to the Prussian Academy of Sciences in Berlin four papers on general relativity, the so-called

Einstein equations which were he said 'the most valuable theory of his life' and 'of incomparable beauty' describing the evolution of the Universe, black holes, the behaviour of orbiting neutron stars, gravitational lensing, and why clocks run slower on the surface of the Earth than in space and the possibility of time travel.

Despite the diversity of energy-momentum complexes, there are a wide range of solutions to the

Einstein equations for which they exhibit identical results.

The method works as follows: a solution of the vacuum

Einstein equations is taken, such that there is a discontinuity in the derivatives of the metric tensor on the plane of the disk, and the energy-momentum tensor is obtained from the

Einstein equations.

of California-Davis) show that the

Einstein equations for a spherically symmetric spacetime in Standard Schwazschild Coordinates close to form a system of three ordinary differential equations for a family of self-similar expansion waves, and that embedded as a single point in this family is the critical (k = 0) Friedmann universe associated with the pure radiation phase of the Standard Model of Cosmology.

The

Einstein equations, brilliant as they are, reveal a universe that is 90 percent hidden from our eyes.

Soon after him, the Dutch De Sitter, the Russian Friedmann and the Belgian, Lemaitre introduced non-static universes as solutions for the

Einstein equations of relativity.

The

Einstein equations of evolution--A Geometric approach "Journ.

For example, we understand general relativity much better by studying the properties of black hole solutions to the

Einstein equations than we would if we restricted attention to the tiny differences between the predictions of Newtonian gravity and general relativity for, say, planetary orbits.