These are only two blog posts, so it is likely you haven't followed the whole derivation?

Either way, since they are actually good questions, I will take time to answer.

A couple of simple questions

I have probably missed something, but where did your bivector gravity equation come from on the first line?

What are you hoping to show, ie can your theory reproduce the predictions of general relativity ?.

The paper doesnt have introductions or summaries which might give the reader a clue where you are headed, other than in the title.

∇μDν=∂μ⋅Dkνγkγ0−(Γμ×Dkν)γkγ1γ2γ3

The bivector arises from three arguments, I reinterpret the following equations:

1) [math]\nabla = \partial + \Gamma[/math]

2) [math]\mathbf{J} = \mathbf{S} + \mathbf{J}[/math]

and

3) [math]\Box = \partial + \Gamma[/math]

The first equation is a correction derivative, basically the basis for Einstein's connections which treats [math]+\Gamma[/math] as a correction term. The third equation is also the same, except we show mathematically in the blog, the four dimensional operator adds some new rules, such as the first term on the RHS being associated to time derivatives.

As for your question, it reproduces general relativity, absolutely fine... in fact, arguably better than Einstein's approach, because the bivector approach would have suggested that torsion was not an ad hoc assumption but something fundamental to Poincare symmetry.

**Edited by Dubbelosix, 04 March 2019 - 12:32 PM.**