Relativity and Cosmology


General Relativity and Dark Energy Are Hidden in the Klein-Gordon Equation in Curved Spacetime

Authors: Gary Nash

The Klein-Gordon equation in curved spacetime can be symmetrized into symmetric and antisymmetric rank 2 tensors for bosons with spins 0,1,2 (spinor-tensors for fermions with spins $1/2,3/2$). A modified Einstein equation of general relativity is obtained from the symmetric part of the Klein-Gordon equation by using the principle of least action, a decomposition of symmetric tensors on a time oriented Lorentzian manifold, and a fundamental postulate of general relativity. The decomposition introduces a new symmetric tensor which describes the energy-momentum of the gravitational field, completes Einstein's equation and addresses the energy localization problem. The positive part of the trace of the new tensor with respect to the metric, describes dark energy. The tensors that constitute the modified Einstein equation add to zero. General relativity and dark energy are hidden in the Klein-Gordon equation and the formalism of quantum field theory, for each spin. The metric as a field variable describing gravitons vanishes from the massless spin-2 Klein-Gordon equation in the long-range to particle regimes of spacetime. Unlike the other three known fundamental forces in nature, no particle exchange is required to explain the effective force of gravity in those regimes. The cosmological constant must vanish and is dynamically replaced by the trace of the new tensor. A cyclic universe which developed after the Big Bang is described. The dark energy density provides a natural explanation of why the vacuum energy density is so small, and why it dominates the present epoch of the universe.

Comments: 22 Pages.

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Submission history

[v1] 2017-09-18 09:35:00
[v2] 2018-06-26 13:05:09
[v3] 2018-07-04 08:44:19

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