A $$1+5$$ 1 + 5 -dimensional gravitational-wave solution: curvature singularity and spacetime singularity

Dimensional dependence of naked singularity formation in spherical gravitational collapse

The complete spectrum of the endstates naked singularities, or blackholes of gravitational collapse is analyzed for a wide class of N -dimensional spacetimes in spherical symmetry, which includes and generalizes the dust solutions and the case of vanishing radial stresses. The final fate of the collapse is shown to be fully determined by the local behavior of a single scalar function and by the...

Singularity-free gravitational collapse and asymptotic safety

Singularity Resolution and Gravitational Chern-Simons terms

We show that gravitational Chern-Simons corrections, associated with the sigma-model anomaly on the M5-brane world-volume, can resolve the singularity of the M2-brane solution with Ricci-flat, special holonomy transverse space. We explicitly find smooth solutions in the cases when the transverse space is a manifold of Spin(7) holonomy and SU(4) holonomy. We comment on the consequences of these ...

Singularity Behavior of the Mean Curvature Flow

It was proved that a blow-up solution to the mean curvature flow with positive mean curvature is an ancient convex solution, that is a convex solution which exists for time t from −∞. In this paper we study the geometry of ancient convex solutions. Our main results are contained in Theorems 1-3 below. Theorem 1 asserts that after normalization, the solution converges to a sphere or cylinder as ...

The complex singularity of a Stokes wave

Two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth can be described by a conformal map of the fluid domain into the complex lower half-plane. Stokes wave is the fully nonlinear gravity wave propagating with the constant velocity. The increase of the scaled wave height H/λ from the linear limit H/λ = 0 to the critical value Hmax/λ marks the tran...