The Present Invalid Nature of Humphreys' White Hole Cosmology
Robert A. Herrmann Mathematics Department U. S. Naval Academy 572C Holloway Rd Annapolis, MD 21402-5002 USA June 1996. Revised 1 OCT 2017.)
Even if the below technical problem is eliminated, I personally cannot accept this model for Biblical reasons.
"Darkness was upon the face of (*) the deep . . . spirit of God moved upon the face of [A] the waters (1.2) . . . firmament in the midst of [B] the waters and let it divide [C] the waters from [D] the waters . . . (1.6). . . God made the firmament and divided [E] the waters which were under the firmament from [F] the waters which were above the firmament (1.7). . . Let [G] the waters under the heaven be gathered together unto one place, and let the dry land appear; and it was so. (1.9) And God called the dry land Earth; and the gathering together of [G] the waters called he Seas; and God saw that it was good." (1:10)
I accept that the word "waters" in Genesis 1:2 and in 1:6 refers to the same physical material [A]. The verses are too close together for this to be otherwise. It is this material that is divided. Humphreys uses the term "deep" (*) as somehow different from the term "waters" that appears in the same verse and in different configurations throughout these verses. For the meaning, when first presented and that must be retained, the term "deep" is used only to convey a necessary aspect of the waters, the waters prior to their separation as stated in the same verse. Verse [B] begins the necessary characterizations for this term. God uses the firmament to divide these "waters" into two pieces [C] and [D]. Then from Genesis 1:9 the portion of the waters [G] referred to as "under the heaven" is further characterized as the Seas and the "dry land" appears. The physical material started as waters and remains waters in different configurations throughout these processes. This is the "straightforward " interpretation. Since the land is dry, I consider this as one of the sudden appearances that occur throughout creation-week.
The most significant Biblical error is that this Humphreys' model does not yield an enteral Sun, Moon and star universe as is Biblically required for the day-four through the Fall of Man period. Originally Morris and ICR accepted this Eden period. I also accept that this is a valid description. The Bible not only requires this Eden period but strongly implies that after the Fall we can have no knowledge as to how to achieve eternal physical life.
A Technical Error
It appears that Humphreys' (1994) model may fail to achieve the goals claimed, at the least, in one instance. Indeed, a direct contradiction is obtained. In this note, the cosmological constant "Λ" is briefly investigated. First, the present day cosmological constant Λ is estimated to be no larger than Humphreys uses the approximating Schwarzschild configuration, the vacuum solution, and the classical Schwarzschild surface (i.e. event horizon) throughout his discussions, especially relative to the geometry exterior to such surfaces. He states, "I suggest that the event horizon reached earth early in the morning of the fourth day." (Humphreys, 1994, p. 126) The earth here is a type of "water-world" that has stayed "coherently together." (Humphreys, 1994, p. 124) The event horizon also remains approximately in that position the entire "fourth day." Using this extreme approximation for matter behavior, Humphreys states relative to the spherical event horizon surfaceOutside the sphere, the metric has to be the same as the Schwarzschild metric, eq. (13). (1994, p. 114)
Humphreys mentions (1994, p. 120) that the Klein metric that implies his results would actually need to be altered to include the cosmological constant. However, this would also be the case for the Schwarzschild exterior metric as well since Λ is a constant. Such a modification is known; it is the "modified Schwarzschild metric." (Herrmann, 1993, p. 80) Assuming that the earth has its present mass, consider the modified Schwarzschild solution where the significant expression is
.[Note: Although it is not necessary for this analysis, the Λ in this expression is written as Λ/c^2 in Herrmann (1994).]
The location of the event horizon is obtained by setting this expression to zero. For the earth, a simple calculation, using as the radius of earth and .889 cm as the value for yields Based upon Humphreys' Schwarzschild exterior geometry, this value appears, at the least, to be required during the entire day four and, probably, through day six so that the event horizon (Schwarzschild surface) remains approximately at the earth's surface. But, Humphreys states that Λ is set at a large value on day two of his creation model in order to produce a "rapid, inflationary expansion of space". (1994, p. 124) As shown in the paper by Moles (1991), as cited by Humphreys, the above value for Λ does not appear to be the large value Humphreys is suggesting for his expansion model.
More significantly, however, if this calculated Λ and the estimated mass of the universe are inserted into this expression and this is the value of Λ prior to the collapse of the event horizon as required by Humphreys' model, then the event horizon about the bounded universe would not exist. Indeed, the solution of the cubic equation yields a negative and two complex values for r. The same type of result is obtained even if we reduce considerably the estimated mass of the universe. Further, any increase in such a mass or an increase in Λ will always lead to this same conclusion. You only get a positive event horizon for this metric and the given mass of the universe if Λ is slightly less than 10^(-53.6). Thus, assuming that there is an event horizon at the earth's surface that is produced by the collapse of an event horizon at the outer boundary yields, for this metric, a cosmological constant that when applied to the entire universe does not yield the required event horizon at the outer boundary. Event horizons are produced for simple variations for the parameters used for this metric but they appear contradictory if they are considered as constants over the entire cosmos. (Including a term for "charge," in the above, will not significantly affect these results.)
This all signifies that, prior to accepting this model as viable, an additional analysis is required for the exterior geometry and its relation to the cosmological constant using the proper metrics that describe the gravitational fields. More attention should be given to the cosmological constant, its relation to solutions to the Hilbert-Einstein equations, and how under such a circumstance an appropriate Λ produces the required expansion and satisfies, at the least, the two necessary event horizon requirements. If time-dilation can be achieved without the cosmological constant for the earth being the one calculated or the exterior metric is not the modified Schwarzschild, then this might correct this problem. Of course, one can also postulate that the cosmological constant is set at different values under specific circumstances. Or one can simply reject all such non-Biblical models and accept the Biblically verified and Complete GGU-model produced Eden Model.
Note All calculations, using MAPLE V, can be found in this maple worksheet.
ReferencesHerrmann, R. A. 1994. Einstein Corrected
Humphreys, D. R. 1994. Starlight and Time. Master Books. Colorado Springs, Colorado.
Moles, M. 1991. Physically permitted cosmological models with nonzero cosmological constant. The Astrophysical Journal 382 (December 1):369-376.
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