The resemblance between the equation for a characteristic hypersurface through which wavefronts of light rays pass and optical metrics of general relativity has long been known. Discontinuities in the hypersurface are...The resemblance between the equation for a characteristic hypersurface through which wavefronts of light rays pass and optical metrics of general relativity has long been known. Discontinuities in the hypersurface are due to refraction involving Snell’s law, as opposed to discontinuities in time that would involve the Doppler effect. The presence of a static gravitational potential in the metric coefficients is accounted by an index of refraction that is entirely dependent on the space coordinates. The two-time Einstein metric must be reinterpreted as a two-space scale metric because of the two different speeds of light. It is shown that the Schwarzschild metric is incompatible with the laws of classical physics. Gravitational waves are identified with the transverse-trans-verse plane wave solutions to Einstein’s equations in vacuum, which propagate at the speed of light. Yet, when energy loss is evaluated, his equations acquire, surprisingly, a source term. Poynting’s vector, which is not a true vector, is defined in terms of the pseudo-gravitational tensor, and hence energy is neither localizable nor conserved. The solutions to the equations of motion are geodesics and, by definition, do not radiate. A finite speed of propagation implies that gravitational waves should aberrate, like their electromagnetic wave counterparts, and if they do not aberrate they cannot radiate.展开更多
文摘The resemblance between the equation for a characteristic hypersurface through which wavefronts of light rays pass and optical metrics of general relativity has long been known. Discontinuities in the hypersurface are due to refraction involving Snell’s law, as opposed to discontinuities in time that would involve the Doppler effect. The presence of a static gravitational potential in the metric coefficients is accounted by an index of refraction that is entirely dependent on the space coordinates. The two-time Einstein metric must be reinterpreted as a two-space scale metric because of the two different speeds of light. It is shown that the Schwarzschild metric is incompatible with the laws of classical physics. Gravitational waves are identified with the transverse-trans-verse plane wave solutions to Einstein’s equations in vacuum, which propagate at the speed of light. Yet, when energy loss is evaluated, his equations acquire, surprisingly, a source term. Poynting’s vector, which is not a true vector, is defined in terms of the pseudo-gravitational tensor, and hence energy is neither localizable nor conserved. The solutions to the equations of motion are geodesics and, by definition, do not radiate. A finite speed of propagation implies that gravitational waves should aberrate, like their electromagnetic wave counterparts, and if they do not aberrate they cannot radiate.
