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

8 j j i i i D K D K p π − = (26) ij i j j i L D D β γ β β = + (27) L β denotes the Lie derivative with respect to the vector field β . ij K is the extrinsic curvature of the surface Σ given by ij i j K n α β α β γ γ = − ∇ where α ∇ is the four-dimensional covariant derivative. n β is the 1-form field normal to surface t=constant , and n n α α α β β β γ δ = + is the projector onto the t=constant hypersurfaces. ij ij K K γ = ij R is the Ricci tensor for the surface Σ and ij ij R R γ = is the Ricci scalar. The following variables are the decomposition of the stress-energy tensor T µν in terms of the 3+1 splitting. ij S is the spatial part of the stress-energy tensor. ij ij S S γ = is its trace. E is the energy density i p is the momentum density. Of course, the YEC version of the FLRW given above in equation (20), being a solution of the EFE, automatically satisfies the 3+1 equations. The initial condition, specified by our creation surface, was constructed from the implied embedding of the hypersurface in the FLRW cosmology, and it trivially satisfies the dynamic 3+1 equations. This 3-metric subsequently propagates in time in a way that maintains its curvature. This is expected since the momentum ij π of the metric was constrained from the embedding within the FLRW thus determining the extrinsic curvature ij K in equation (23) above and elsewhere. More interesting cases will result from specifying different values for ij K along an initial creation surface. CONCLUSION We have presented a consistent YEC cosmological model that satisfies the EFE and reproduces the observational consequences of both the FLRW space-time (“big bang”) and any modifications such as inhomogeneities. The model only differs from conventional solutions in that it uses an initial condition (“creation hypersurface”) that supports a young earth. There can be no unprejudiced objection to this solution. A prejudiced objection would rest only upon the assumption of requiring a naturalistic metaphysics requiring, in some sense, a synchronized (and simultaneous) explosion of all matter from a white hole by extrapolating a current value of the metric backward in a presumed preferred time to a putative initial singularity. Such an assumption is not dictated by GR. In fact, we have seen that GR allows for solutions with regions of differing “life times” and “non-simultaneous” (according to a conventional time coordinate) big bangs. This feature of “non-simultaneous” big bangs includes the external Schwarzschild solutions for collapsing stars and the class of general inhomogeneous L-T cosmologies. As we remarked, this flexibility in the theory allows us to choose an Dennis ◀ Young earth relativistic cosmology ▶ 2018 ICC 28 Figure 10. Null Cones in a Hyperbolic YEC Cosmology. The horizontal axis is the distance from the earth whose worldline is the time axis on the left. Solid lines indicate incoming light. Dashed lines are the outgoing light. Note that the global speed of incoming light approaches infinity as distance increases. Conversely the global speed of outgoing light decreases with distance. Since the model is a solution of the EFE, the local speed of light is constant in accordance with the principle of relativity. This graph is drawn at ‘epoch’ and used a value of a 0 b =1000 years for the “temporal radius” of the hyperbolic surfaces of simultaneity. Recall that the parameter b specifies the length of time in which an infinitely distant object crosses the particle horizon. This can be seen in the graph as the incoming light cone with the vertex at 1000 years is asymptotically horizontal to t = 0 as ρ approaches ∞.