Singularity-free interpretation

Sastry, S., Debenedetti, P., Sciortino, F., and Stanley, H.E. 1996. Singularity-free interpretation of the thermodynamics of supercooled water. Phys. Rev. E53, 6144-6154. 

We then calculated the Arrhenius activation energy (P) from the low-T slope of log T versus l/T and extrapolated the temperature T P) at which t reaches a fixed macroscopic time ta > tc, with Tg, P) smaller than the crossover temperature. For Ta = 10 Monte Carlo (MC) steps > 100 s, Ea(P) and Tg (P) decrease upon increasing P in both scenarios, providing no distinction between the two interpretations. Instead, there is a dramatic difference in the -dependence of the quantity E / k T in the two scenarios, increasing for the LL critical point and approximately constant for the singularity free. 

As long as L(t) is not singular one is free to apply any transformation of y using the familiar rules of calculus in particular one may transform (4.5) into the quasilinear equation (4.3). In the latter the limit rc — 0 gives no problem and the result is (4.4). Transforming back to the original variables gives (4.8), as we found before. Hence, whenever the delta function stands for a sharp, but not infinitely sharp peak the Stratonovich interpretation is appropriate. The Ito interpretation cannot even be formulated unless tc is strictly zero. 

Although the Godel solution is free of singularities the need to accommodate black holes in the cosmic model requires an interpretation of the Schwarzschild singularity which occurs with infinite curvature of space-time. A new interpretation is rather obvious. Such a high degree of curvature must clearly rupture the interface between adjacent sides of the postulated cosmic double cover. Rather than disappear into a singularity, the matter,... 

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