The Proceedings of the Eighth International Conference on Creationism (2018)

surface as a horizontal line rather than as a hyperboloid embedded in the FLRW manifold. That instantaneous surface is, of course, a curved manifold. As discussed above GR places no temporal constraints on whether any spacelike surfaces are excluded. In fact, relativity forbids that man can operationally determine what is the current “now” surface. This is the case because we can only observe the universe along the past null cone. We can use equation (21) to compute the particle horizon which gives the observable universe at a given time. For an incoming light ray emitted from 0 ρ at the creation time 0 0 τ = and arriving at the earth ( 0 ρ = ) at time τ the solution for the horizon 0 ρ is: 0 log 1 b τ ρ   = − −    This shows that the entire universe is observable after the passage of time b . In particular, we note that in this model the light from distant objects arrives at the young earth. Further that all observable physics will be in line with the equations of GR and the implications of the FLRW metric (or any modifications of that solution for inhomogeneities) since the solution is in fact a section of the FLRW manifold. All tensorial equations and invariant quantities are the same. In particular, the predictions of red-shifts are identical to those of the FLRW cosmology. 12. Postscript. FutureAvenues of Research. The 3+1 Formalism. I had initially intended toanalyze theentireclassofYECcosmologies by utilizing the 3+1 formulation of EFE. Unfortunately, due to time constraints, I have not been able to pursue that approach to the depth and rigor required for publication, at this time. I propose that possible future research in YEC cosmologies might benefit from using the 3+1 formulation of the EFE in which a spacelike initial surface (3-metric ij γ and metric 3-momentum ij π ) is integrated forward in time by way of a Hamiltonian approach. The 3+1 formulation directly corresponds to the presentist philosophy of time, and the initial data, namely. To analyze the time development of solutions to EFE, the 3+1 formalism decomposes space-time into a foliation of spatial hypersurfaces indexed by time t. Each hypersurface t Σ can thus be interpreted as a surface of “now;”with the time coordinate t denoting the actual cosmic time. In this way the 3+1 formalism conceptually reflects the presentist view of time. The 3-dimensional metric ij γ and its momentum ij π can be specified on an initial creation spatial hypersurface and its temporal development examined. Details of the 3+1 formalism can be found in detail in Gourgoulhon (2012). The metric is written in terms of the intrinsic metric ij γ of the Dennis ◀ Young earth relativistic cosmology ▶ 2018 ICC 26 Time Large Look back time Earth Space Small Look back time Initial space-like creation surface Light ray from remote location Figure 8. A solution to the light travel time problem based on a hyperbolic initial creation surface given by a function ( ) C t t r = in terms of the FLRW cosmic time coordinate. Due to the curvature of the surface the look-back time at the earth increases with distance. The creation surface occurs simultaneously at the beginning of day one, even though the “look-back time” (relative to the FLRW extrapolated “cosmic time”) for distant events is very large. The look-back time will be a smooth function of distance in the detailed model.