April 13, 2013 at 16:59 (Edit)
Well what if the are no GW. Does that mean that GR needs to be modified?
Can GR be changed with “new geometry” are still match currents results??
Nonobservation of GW is not a reason to modify GR. It is rather opposite, because GR (Einstein’s equations) does not have a wave solution, and non-existence (GW were not observed) of such a phenomenon in nature is confirmed by many experiments during the last half of century.
Einstein’s GR is a system of nonlinear equations, and it is a well-known mathematical fact that not all nonlinear equations can be solved starting from some linear approximation. In case of GR, unsuitability of a linear approximation, that has a wave solution, was demonstrated long time ago – the non-renormalizability of GR (where the first approximation is exactly one with a wave solution). So, already in 80s it was proven that, at least, a linear approximation, which corresponds to the wave solution of Einstein’s equation, is not appropriate, and either different linear approximation must be used or there is no linear approximation at all that can lead to a solution of GR equations. Arguments in support of the latter scenario can be given. Perhaps one additional argument for people familiar with the Hamiltonian formulation of GR is: the Hamiltonians of full GR and so-called spin-2 model (a linear approximation) are fundamentally different and there is no continuous transition from one into another.
We would also like to add that Einstein’s name was and continues to be used as one of major arguments for existence of GW in his GR (especially in “scientific” writings for general public). This is just wrong, because during almost four decades after 1916 his opinions changed. He did not die in 1916 (either physically or scientifically). Einstein’s understanding of GR was evolving, including his views on GW, quantization, a role of non-linearity (again, ahead of his time), general covariance, etc.