Does General Relativity Entail Eternalism?

Recently, a scientist by the name of Gustavo E. Romero wrote a paper where he gives an argument from General Relativity in favor of eternalism. The paper, called On the ontology of spacetime, offers a simple argument for eternalism based on the existence of gravitational waves:

P1. There are gravitational waves.
P2. Gravitational waves have non-zero Weyl curvature.
P3. Non-zero Weyl curvature is only possible in 4 or more dimensions.
P4. Presentism is incompatible with a 4 dimensional world.
Then, presentism is false.

A little less than a year ago gravitational waves were empirically verified by two teams of scientists in two independent tests in the US. So premise 1 is true. (At the time Romero wrote his paper, gravitational waves had not yet been confirmed; now they have.) The rest of the argument is a bit technical, but Romero writes:

Premises P2 and P3 are necessarily true. Gravitational waves propagate in empty space, where the Einstein’s field equations are reduced to: 

Rab = 0. 

This expression means that the 10 coefficients of the Ricci tensor are identically null. But the full Riemann tensor3 has 20 independent coefficients since is a rank 4 tensor. The remaining 10 components are expressed by the Weyl tensor. Then, since the gravitational waves are disturbances in the curvature, the Weyl tensor must be non-zero in their presence. If the dimensionality of the world were 3, as proposed by the presentists, the Riemann tensor would have only 6 independent components, and since in 3 dimensions the Einstein’s equations in vacuum are reduced to 6, the Weyl tensor must vanish. Only in 4 or more dimensions gravity can propagate through empty spacetime (see Hobson et al. 2006, p.184, and Romero and Vila 2014, p. 19). 

It's an interesting argument using General Relativity, instead of Special Relativity—which is most often used, to make an argument for eternalism. Some have argued that General Relativity argues against eternalism, and this would seem to challenge that view. It further adds to the case that physics supports eternalism and negates presentism, and I think we should take the findings from science to inform our worldviews seriously.

Happy Labor Day weekend!