## Modified General Relativity and the Klein-Gordon Equation in Curved Spacetime

**Authors:** Gary Nash

From the existence of a line element field $(A^{\beta},-A^{\beta}) $ on a four-dimensional time oriented Lorentzian manifold with metric, the Klein-Gordon equation in curved spacetime, $ \nabla_{\mu}\nabla^{\mu}\Psi=k^{2}\Psi $, can be constructed from one of the pair of regular vectors in the line element field, its covariant derivative and associated spinor-tensor; and scalar product for spins 1,1/2 and 0, respectively. The left side of the asymmetric wave equation can then be symmetrized. The symmetric part, $ \tilde{\varPsi}_{\alpha\beta}$, is the Lie derivative of the metric, which links the Klein-Gordon equation to modified general relativity for spins 1,1/2 and 0. Modified general relativity is intrinsically hidden in the Klein-Gordon equation for spins 2 and 3/2. Massless gravitons do not exist as force mediators of gravity in a four-dimensional time oriented Lorentzian spacetime. The diffeomorphism group Diff(M) is not restricted to the Lorentz group. $ \tilde{\varPsi}_{\alpha\beta}$ can instantaneously transmit information to, and quantum properties from, its antisymmetric partner $ K_{\alpha\beta} $ along $ A^{\beta} $. This establishes the concept of entanglement.

**Comments:** 10 Pages.

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### Submission history

[v1] 2019-04-28 12:53:54

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