In 1985 Goode and Wainwright devised the concept of an isotropic singularity. Since that time, numerous authors have explored the interesting consequences, in mathematical cosmology, of assuming the existence of this type of singularity. In this paper, we collate all examples of cosmological models which are known to admit an isotropic singularity, and make a number of observations regarding th...

Global visibility of naked singularities is analyzed here for a class of spherically symmetric spacetimes, extending previous studies limited to inhomogeneous dust cloud collapse to more physical valid situations in which pressures are non-vanishing. Existence of nonradial geodesics escaping from the singularity is shown, and the observability of the singularity from far-away observers is discu...

Global stability of the spherically symmetric nonisentropic compressible Euler equations with positive density around global-in-time background affine solutions is shown in presence free vacuum boundaries. Vacuum achieved despite a non-vanishing by considering negatively unbounded entropy, and we use novel weighted energy method, whereby exponential entropy will act as changing weight to handle...

Let $f(\mathbf z,\bar{\mathbf z})$ be a convenient Newton non-degenerate mixed polynomial with strongly polar non-negative weighted homogeneous face functions. We consider regular simplicial cone subdivision $\Sigma^*$ which is admissible for $f$ and take the toric modification $\hat{\pi} : X \to \mathbb{C}^n$ associated $\Sigma^*$. show that resolves topologically singularity of hypersurface g...

Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a γ-law equation of state. There are, however, some general properties of cosmological models which admit an Isotropic Singularity, irrespective of the matter source. In particular, we show ...

Fundamental theories of quantum gravity such as supergravity include a four form field strength which contributes to the cosmological constant. The inclusion of such a field into our theory of open inflation [1] solves the problem of the most likely universe being too empty. It also allows an anthropic solution to the cosmological constant problem in which cosmological constant gives a small bu...