Related papers: The geodesic rule for higher codimensional global …

Global topological defects produce nonzero stress-energy throughout spacetime, and as a result can have observable gravitational influence on surrounding matter. Gravitational effects of global strings are used to place bounds on their…

Topological defects, in particular cosmic strings, give rise to an interesting mechanism for generating the primordial perturbations in the early Universe which are required to explain the present structure. An overview of the cosmic string…

We construct convex bodies that can be "captured by nets." More precisely, for each dimension $n \geq 2$, we construct a family of Riemannian $n$-spheres, each with a stable geodesic net, which is a stable 1-dimensional integral varifold.…

We give a finitary criterion for the convergence of measures on non-elementary geometrically finite hyperbolic orbifolds to the unique measure of maximal entropy. We give an entropy criterion controlling escape of mass to the cusps of the…

Geodesic deviation is the most basic manifestation of the influence of gravitational fields on matter. We investigate geodesic deviation within the framework of Regge calculus, and compare the results with the continuous formulation of…

A real projective orbifold has a radial end if a neighborhood of the end is foliated by projective geodesics that develop into geodesics ending at a common point. It has a totally geodesic end if the end can be completed to have the totally…

We construct a generally-covariant formulation of non-equilibrium thermodynamics in General Relativity. We find covariant entropic forces arising from gradients of the entropy density, and a corresponding non-conservation of the energy…

We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists if…

Directional media, such as nematic liquid crystals and ferromagnets, are characterized by their topologically stabilized defects in directional order. In nematics, boundary conditions and surface-treated inclusions often create complex…

We derive the 2-component Camassa-Holm equation and corresponding N=1 super generalization as geodesic flows with respect to the $H^1$ metric on the extended Bott-Virasoro and superconformal groups, respectively.

We consider a geodesic flow on a compact manifold endowed with a Riemannian (or Finsler, or Lorentz) metric satisfying some generic, explicit conditions. We couple the geodesic flow with a time-dependent potential, driven by an external…

The existence of chaotic behavior for the geodesics of the test particles orbiting compact objects is a subject of much current research. Some years ago, Gu\'eron and Letelier [Phys. Rev. E \textbf{66}, 046611 (2002)] reported the existence…

Growth processes in many living organisms create thin, soft materials with an intrinsically hyperbolic geometry. These objects support novel types of mesoscopic defects - discontinuity lines for the second derivative and branch points -…

The Sharpened Distance Conjecture and Tower Scalar Weak Gravity Conjecture are closely related but distinct conjectures, neither one implying the other. Motivated by examples, I propose that both are consequences of two new conjectures: 1.…

We study the problem of rigidity of closures of totally geodesic plane immersions in geometrically finite manifolds containing rank $1$ cusps. We show that the key notion of K-thick recurrence of horocycles fails generically in this…

The geodesic deviation equation, describing the relative accelerations of nearby particles, and the Raychaudhury equation, giving the evolution of the kinematical quantities associated with deformations (expansion, shear and rotation) are…

Using a Newtonian approximation, we developed a quantitative criterion for the collapse of a spherical distribution of matter under an isolated texture field. In particular, we found that the evolution of an overdense region is strongly…

Displacement and velocity memory effects in the exact, vacuum, plane gravitational wave line element have been studied recently by looking at the behaviour of pairs of geodesics or via geodesic deviation. Instead, one may investigate the…

We consider planar directed last-passage percolation on the square lattice with general i.i.d. weights and study the geometry of the full set of semi-infinite geodesics in a typical realization of the random environment. The structure of…

We study the junction condition relating the pressure to the heat flux at the boundary of a shearing and expanding spherically symmetric radiating star when the fluid particles are travelling in geodesic motion. The Lie symmetry generators…