Christodoulou originally encountered this gravitational-wave effect as a mathematical formula derived from the

Einstein equations describing gravitational fields located far from their sources.

In order for Maxwell's equations to satisfy Einstein's equations, it is shown that: (1) a free electromagnetic field along the trajectory of an orbiting body must be present, by means of purely magnetic "standing" waves; (2) electromagnetic fields don't satisfy the

Einstein equations in a region of orbiting space bodies if there is no distribution of another substance (e.

The difficulty lies in trying to get some kind of physical information out of the

Einstein equations," says astrophysicist David W.

The correct linearization proves that the

Einstein equations are completely compatible with weak waves of the metric.

The second group joins studies around a search for such solutions to the

Einstein equations for gravitational fields, which, proceeding from physical considerations, could describe gravitational radiations.

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.

Objective: Breakthroughs in numerical relativity in 2005 gave us unprecedented access to the strong-field regime of general relativity, making possible solutions of the full nonlinear

Einstein equations for the merger of two black holes.

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.

This possibility cannot be accommodated in the cosmological Concordance Model based on the

Einstein equations with a cosmological constant in the framework of general relativity (GR).

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.

Local and global existence theorems for the

Einstein equations.