Search results for "geodesics"

Geons in Palatini Theories of Gravity

2017

An explicit implementation of geons in the context of gravitational theories extending general relativity is discussed in detail. Such extensions are formulated in the Palatini approach, where metric and affine connection are regarded as independent entities. This formulation is inspired on the macroscopic description of the physics of crystalline structures with defects in the context of solid-state physics, whose study can provide valuable lessons for going beyond GR. We discuss several theories for the gravitational field including additional contributions of the Ricci tensor in four and higher dimensions. As opposed to the standard metric approach, the Palatini formulation generates gho…

Lens Effect and CMB Anisotropies: Simulations

2003

Cosmological structures deviate the photons of the Cosmic Microwave Background (CMB). The resulting deviations can be calculated moving photons in the gravitational field of realistic lens distributions obtained from numerical simulations. The main goal of this paper is answering the following question: Which types of numerical simulations are appropriate to study angular CMB deformations caused by lensing?

Distance of matter inside an Einstein-Strauss vacuole

2008

Lorentzian Comments on Stokes Parameters

2003

The popular Stokes statements about polarized light are interpreted in a Minkowskian language using a Lorentzian representation for the Stokes parameters and the degree of polarization. The evolution equations for Stokes parameters on a curved space-time are obtained using the parallel transport of the polarization vector along a null geodesic. The interest of these equations in Astrophysics and Relativistic Cosmology is outlined.

THE 1-HARMONIC FLOW WITH VALUES IN A HYPEROCTANT OF THE N-SPHERE

2014

We prove the existence of solutions to the 1-harmonic flow — that is, the formal gradient flow of the total variation of a vector field with respect to the [math] -distance — from a domain of [math] into a hyperoctant of the [math] -dimensional unit sphere, [math] , under homogeneous Neumann boundary conditions. In particular, we characterize the lower-order term appearing in the Euler–Lagrange formulation in terms of the “geodesic representative” of a BV-director field on its jump set. Such characterization relies on a lower semicontinuity argument which leads to a nontrivial and nonconvex minimization problem: to find a shortest path between two points on [math] with respect to a metric w…

Sub-Riemannian geometry: one-parameter deformation of the Martinet flat case

1998

Black Holes, Geons, and Singularities in Metric-Affine Gravity

2016

Uno de los problemas abiertos en la descripción de la gravedad es la existencia de singularidades. Las geometrías singulares se caracterizan por geodésicas incompletas, lo que físicamente se corresponde con observadores que desaparecen del espacio-tiempo, o que aparecen de la nada. Múltiples extensiones de la Relatividad General tratan de resolver este problema de algún modo. Por ello, en esta tesis estudio modificaciones al Lagrangiano de Relatividad General, tales como gravedad cuadrática y gravedad de Born-Infeld, en el formalismo Métrico-Afín. En este formalismo, la conexión (de la cual se derivan los tensores de curvatura) se considera independiente de la métrica, y permitimos que sea …

Existence of optimal transport maps in very strict CD(K,∞) -spaces

2018

We introduce a more restrictive version of the strict CD(K,∞) -condition, the so-called very strict CD(K,∞) -condition, and show the existence of optimal maps in very strict CD(K,∞) -spaces despite the possible lack of uniqueness of optimal plans. peerReviewed