Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-05-07
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Scientific paper
The Hodge-de Rham Laplacean is an extension to forms of the wave equation. A frame is a quartuple of 1-forms. The Hodge-de Rham Laplacean is modified to model it on the frame itself (not on the standard frame $dx$). This modified Laplacean is invariant. The basic equation is: The modified Laplacean operating on the frame is equal to a source term times the frame. Kaniel and Itin (Il Nuovo Cimento vol 113B,N3,1998) analyzed the equation for steady state and spherically symmetric frame (General Relativity). They computed a closed solution for which the derived metric is Rosen's. This closed solution is intrinsically different than Schwarzschild solution. Yet it passes the three classical experimental tests to the same accuracy. The same basic equation is,also, the alternative to Schroedinger equation, where the source term is the electromagnetic potential. The same quantization as in Schroedinger equation is attained. The suggested system is hyperbolic, in contrast to the time dependent Schroedinger equation which is parabolic. For time dependent frames the equation is quite complicated. Thus, the linearized equation is explicitly solved .
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