12 research outputs found
Einstein equations in the null quasi-spherical gauge III: numerical algorithms
We describe numerical techniques used in the construction of our 4th order
evolution for the full Einstein equations, and assess the accuracy of
representative solutions. The code is based on a null gauge with a
quasi-spherical radial coordinate, and simulates the interaction of a single
black hole with gravitational radiation. Techniques used include spherical
harmonic representations, convolution spline interpolation and filtering, and
an RK4 "method of lines" evolution. For sample initial data of "intermediate"
size (gravitational field with 19% of the black hole mass), the code is
accurate to 1 part in 10^5, until null time z=55 when the coordinate condition
breaks down.Comment: Latex, 38 pages, 29 figures (360Kb compressed
Vortices in Superfluid Films on Curved Surfaces
We present a systematic study of how vortices in superfluid films interact
with the spatially varying Gaussian curvature of the underlying substrate. The
Gaussian curvature acts as a source for a geometric potential that attracts
(repels) vortices towards regions of negative (positive) Gaussian curvature
independently of the sign of their topological charge. Various experimental
tests involving rotating superfluid films and vortex pinning are first
discussed for films coating gently curved substrates that can be treated in
perturbation theory from flatness. An estimate of the experimental regimes of
interest is obtained by comparing the strength of the geometrical forces to the
vortex pinning induced by the varying thickness of the film which is in turn
caused by capillary effects and gravity. We then present a non-perturbative
technique based on conformal mappings that leads an exact solution for the
geometric potential as well as the geometric correction to the interaction
between vortices. The conformal mapping approach is illustrated by means of
explicit calculations of the geometric effects encountered in the study of some
strongly curved surfaces and by deriving universal bounds on their strength.Comment: 50 pages, 38 figure
Extended Theories of Gravity
Extended Theories of Gravity can be considered a new paradigm to cure
shortcomings of General Relativity at infrared and ultraviolet scales. They are
an approach that, by preserving the undoubtedly positive results of Einstein's
Theory, is aimed to address conceptual and experimental problems recently
emerged in Astrophysics, Cosmology and High Energy Physics. In particular, the
goal is to encompass, in a self-consistent scheme, problems like Inflation,
Dark Energy, Dark Matter, Large Scale Structure and, first of all, to give at
least an effective description of Quantum Gravity. We review the basic
principles that any gravitational theory has to follow. The geometrical
interpretation is discussed in a broad perspective in order to highlight the
basic assumptions of General Relativity and its possible extensions in the
general framework of gauge theories. Principles of such modifications are
presented, focusing on specific classes of theories like f (R)-gravity and
scalar-tensor gravity in the metric and Palatini approaches. The special role
of torsion is also discussed. The conceptual features of these theories are
fully explored and attention is payed to the issues of dynamical and conformal
equivalence between them considering also the initial value problem. A number
of viability criteria are presented considering the post-Newtonian and the
post-Minkowskian limits. In particular, we discuss the problems of neutrino
oscillations and gravitational waves in Extended Gravity. Finally, future
perspectives of Extended Gravity are considered with possibility to go beyond a
trial and error approach.Comment: 184 pages, 3 figures, survey to appear in Physics Report
Combining cauchy and characteristic codes IV: the characteristic field equations in axial symmetry
This paper is part of a long term program to develop combined Cauchy and characteristic codes as investigative tools in numerical relativity. In the third stage attention is devoted to axisymmetric systems possessing two spatial degrees of freedom. In the second of two preliminary theoretical papers, the vacuum field equations for the characteristic region are obtained and the compactified equations are regularized.<br/
Combining cauchy and characteristic codes. V. cauchy-characteristic matching for a spherical spacetime containing a perfect fluid
This paper is part of a long term program to develop CCM (combined Cauchy and characteristic) codes as investigative tools in numerical relativity. The approach has two distinct features: (i) it dispenses with an outer boundary condition and replaces this with matching conditions at an interface between the Cauchy and characteristic regions, and (ii) by employing a compactified coordinate, it proves possible to generate global solutions. In this paper it is shown that CCM can be used effectively to model a spherically symmetric perfect fluid. A particular advantage of CCM in avoiding arbitrary mass inflow-outflow boundary conditions is pointed out. Results are presented which include fluid distributions which form black holes and those which give rise to mass outflow.<br/