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] allows an anthropic solution to the cosmological constant problem in which cosmological constant gives a small but non-negligible contribution to the density of today's universe. We inc...

Mass of singularity is defined, and its relation to whether the singularity is spacelike, timelike or null is discussed for spherically symmetric spacetimes. It is shown that if the mass of singularity is positive (negative) the singularity is non-timelike (non-spacelike). The connection between the sign of the mass and the force on a particle is also discussed.

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] allows an anthropic solution to the cosmological constant problem in which cosmological constant gives a small but non-negligible contribution to the density of today's universe. We inc...

Gravitational collapse is one of the most fruitful subjects in gravitational physics. It is well known that singularity formation is inevitable in complete gravitational collapse. It was conjectured that such a singularity should be hidden by horizons if it is formed from generic initial data with physically reasonable matter fields. Many possible counterexamples to this conjecture have been pr...

Hallin and Ley (2012) investigate and fully characterize the Fisher singularity phenomenon in univariate and multivariate families of skew-symmetric distributions. This paper proposes a refined analysis of the (univariate) Fisher degeneracy problem, showing that it can be more or less severe, inducing n (“simple singularity”), n (“double singularity”), or n (“triple singularity”) consistency ra...

We study the behavior of geodesies passing through a point singularity of a Riemannian manifold. In particular, we show that if the curvature does not blow up too rapidly near the singularity, then the singularity is at worst an orbifold singularity. The idea is to construct the exponential map centered at a singularity. Since there is no tangent space at the singularity, a surrogate is needed....

We prove that there are stationary solutions to the 2D incompressible free boundary Euler equations with two fluids, possibly a small gravity constant, feature splash singularity. More precisely, in we construct interface is $$\mathcal {C}^{2,\alpha }$$ smooth curve intersects itself at one point, and vorticity density on of class {C}^\alpha $$ . The proof consists perturbing Crapper’s family f...

In this paper, a weighted and shifted Grünwald-Letnikov difference (WSGD) Legendre spectral method is proposed to solve the two-dimensional nonlinear time fractional mobile/immobile advection-dispersion equation. We introduce correction deal with singularity in time, stability convergence analysis are proven. numerical implementation, fast applied based on globally uniform approximation of trap...