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

the Lichnerowicz junction conditions (Synge 1971, p.39ff): , , G f G f β β α β α β + − = The subscripts + and − indicating evaluation to the “right” and “left” of the two regions to be joined. The differential of f is the normal to the hypersurface ( ) 0 f x = .] As mentioned above, an example of straightforward cutting and stitching of solutions is the collapse of an interior homogeneous dust cloud (which is diffeomorphic to a subset of the FLRW cosmology) joined to an exterior vacuum Schwarzschild metric (which is diffeomorphic to a subset of the Kruskal-Szekeres maximal extension of the Schwarzschild solution). See Misner et. al. (1973, pp. 851-3) for the joining in Schwarzschild coordinates. See Novikov (1963), Frolov and Novikov (1998) for the joining in Novikov coordinates which we follow here. The mathematical details of matching the solutions is given in Appendix B. The matching consists of specifying 0 C (continuous) functions ( ) M r and ( ) E r in equations (4) - (6) above. The results are illustrated in Figure 5 and Figure 6. Figure 5 depicts an embedding diagram of a spatial section of this “bar bell” cosmology at the time of maximum expansion. [Note: the diagram is not a depiction of a potential well. Instead it displays a two-dimensional surface that is the / 2 θ π = section of the spatial S 3 manifold. Each circumference in the diagram is a slice of the two-dimensional sphere, S 2 .] Note the cosmology is closed. It has both a “north” and a “south” pole at the top and bottom of the figure. The spherical sections at the poles are locally homogeneous FLRW regions. The waist in the middle is a section of the Schwarzschild vacuum solution; it is a “void” in the cosmology in which the invariant mass density is zero. This model cosmology exhibits the possible features of general closed inhomogeneous cosmologies. In Figure 6 we have displayed the temporal evolution of the bar bell cosmology showing the “non-simultaneous big bangs.” The “big bang” in the denser “south pole” region occurred later than the “big bang” in the “north pole” region. Also, regions of the Schwarzschild waist come into existence at different times. This solution can be interpreted as two exploding white holes, expanding to a maximum expansion and then collapsing into a black hole. With the cycloidal parametrization above, both FLRW regions have synchronized clocks reading t=0 at maximum expansion. The chronology enigma that presents itself is that the “initial” time of each white hole explosion is not necessarily the same (i.e. “simultaneous”). A similar consideration applies to the time of the final collapse to the black hole. Further the total life time of each region is different as the lifetimes of each region are proportional to the mass and inversely proportional to the total energy within each region. As a result, at least one of the events, big bang or big crunch, must be non-simultaneous. The point to be emphasized is that it is not required by GR that any of the singularities be “simultaneous.” 10. AYEC Cosmology Hiding in Plain Sight If we look at the general solution to the inhomogeneous cosmology, given in equation (8). above, we notice a rather remarkable feature of the general solution. That feature is the presence of the arbitrary function of integration, ( ) B t r called there as the “time to the Big Bang.” It is this function that allows us to shift the regions in Dennis ◀ Young earth relativistic cosmology ▶ 2018 ICC 23 Figure 4. Conceptual diagram of two FLRW regions connected via a vacuum neck. The “Big Bangs” and the “Big Crunches” are non- simultaneous. Nothing inGR requires that these two regions are necessarily synchronized. Each region can be shifted vertically in time to construct cosmologies with different creation times in the two regions. This model will be analyzed and constructed with exact mathematical solutions of the EFE along with continuous joining conditions in later sections. Figure 5. Embedding diagramof the inhomogeneous “bar bell” cosmology. The solution consists of two semi-closed homogeneous FLRW regions which are subsets of the full FLRW cosmological model and a vacuum Schwarzschild region. The FLRW region at the “north pole” (top of the figure) has a smaller matter density at maximal expansion than the FLRW region at the “south pole.” The two FLRW regions are connected by an equatorial waist in which the density is zero. The waist is an “Einstein- Rosen” bridge and is a subset of the Schwarzschild solution. This diagram is an example of stitching together three solutions of the EFE. The surface of the “bar bell” reflects the geometry of the 2-dimensional cross section of the full space-time at a fixed time and / 2 θ π = . The coordinates in the figure are ( ) , r ϕ ( r is measured vertically, and ϕ is axial angle). The independent parameters for this diagram are 1 3 / 4 α π = and the maximum radii of the FLRW regions are 1 2 (0) (0) / 2 a a = .