Session Y11: Computational Physics and the Cosmos

Visualizing the Curvature of Spacetime: Vortex and Tendex Lines of Head-On Merging Binary Black Holes

Merging black holes and the gravitational waves they emit are important sources for gravitational-wave detectors like Advanced LIGO. When black holes merge, the spacetime around them becomes curved in a dynamic, turbulent way, like a storm in spacetime. In this project, we use analogs of electric and magnetic field lines to visualize the curved spacetime of merging black holes. A non-spinning black hole will produce tendicity; along tendex lines (analogs of electric field lines), objects are stretched and squeezed. A spinning black hole will produce tendicity but will also twist the spacetime around it like a tornado, producing vorticity; along vortex lines (analogs of magnetic field lines), objects are twisted. In this talk, I will present the first movies of vortex and tended lines from simulations of colliding black holes. Such movies will help build intuition of the dynamics of spacetime around binary black holes.   

A new tool to check the accuracy of Analytic Spacetimes for binary black holes

~Analytical spacetimes are an important and useful tool to study dynamics of binary compact objects and many astrophysically important phenomenon associated with them.~~Here we describe a new tool to measure the accuracy of these spacetimes by directly comparing the geodesic structure of~ a family of analytical spacetime with counterparts constructed using full numerical relativity simulations Our idea is to construct coordinate independent scalars by contracting the components of Riemann tensor with the combination of a set of four orthonormal vectors associated with geodesics. By comparing the coordinate independent scalars during evolution we measure how much the analytical spacetimes are similar to more accurate known solution that is the numerical one. I will present some preliminary tests using these techniques.We hope this tool is useful to find limitations of analytical spacetimes.   

Generation of Vector Potentials for General Relativity Simulations

In studies of highly relativistic magnetized accretion flows around compact objects, many different numerical codes can be employed. Based on the formalism each uses, some codes evolve the magnetic field $B$, while others evolve the magnetic vector potential $A$, defined such that these two fields are related via the curl: $B=\nabla\times A$. Here, we discuss how to generate vector potentials corresponding to specified magnetic fields on staggered grids, a surprisingly difficult task on finite cubic domains. The codes we have developed solve this problem in multiple ways: one of them via a cell-by-cell method, whose scaling is nearly linear in the number of grid cells, and the other by directly solving the overall linear algebra problem. Here we discuss the successes these algorithm have in generating smooth vector potential configurations to be used for numerical simulations.   

Probing The Non-Linearity in Galaxy Clusters Through The Analysis of Fractal Dimension

The study of large scale structure (LSS) of the universe using both all-sky surveys and numerical simulations has become an increasingly important tool to calculate different cosmological parameters. We developed a new computational technique to analyze the fractal properties of the galaxies under the study. This thesis uses both real and simulated data combined with a unique approach to characterizing LSS. The main tools of the research are the wavelet transform methods as applied to fractal based-point processes statistics. Specifically, this thesis calculates the fractal dimension as a function of the cosmological redshift using the Baryon Oscillation Spectroscopic Survey (BOSS). We compare these results to mock data sets produced by the Sloan Digital Sky Survey (SDSS). Taking advantage of the self-similarity and localization properties of the wavelets, allows us to compute the fractal dimension of galaxies in narrow redshift bins. The narrow bins assure that dynamical evolution has not occurred. Because fractal behavior provides us with an indication about linear and non-linear regimes, we believe that we can use this measure to demarcate the point at which dark energy becomes the dominant component governing the evolution of the universe.