General Relativity in the Planck Vacuum Theory

Constants of motion for vacuum general relativity

The 3+1 Hamiltonian Einstein equations, reduced by imposing two commuting spacelike Killing vector fields, may be written as the equations of the SL(2, R) principal chiral model with certain ‘source’ terms. Using this formulation, we give a procedure for generating an infinite number of non-local constants of motion for this sector of the Einstein equations. The constants of motion arise as exp...

On the general relativity theory

In Appendix III of the fifth edition of his book Space, Time, Matter [15] henceforth cited as W (which has not been translated into English), Hermann Weyl derived for the first time, motivated by cosmological considerations, the general frequency shift formula for sources and observers moving arbitrarily in a general spacetime. In his discussion of cosmology (W, 39) he argued for a non-stationa...

Electrodynamics in the General Relativity Theory.

The restricted relativity theory resulted mathematically in the introduction of pseudo-euclidean four-dimensional space and the welding together of the electric and magnetic force vectors into the electromagnetic tensor. Einstein's general relativity theory led to the assumption that the fourdimensional space mentioned above is a curved space and the curvature was made to account for the gravit...

Vacuum in quantum liquids and in general relativity

Quantum liquids, in which an effective Lorentzian metric and thus some kind of gravity gradually arise in the low-energy corner, are the objects where the problems related to the quantum vacuum can be investigated in detail. In particular, they provide the possible solution of the cosmological constant problem: why the vacuum energy is by 120 orders of magnitude smaller than the estimation from...

Einstein’s General Theory of Relativity