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Welcome to my webpage!
My research is focused on developing numerical methods to attack the binary inspiral problem in general relativity. The main techniques I am exploring with my advisor Dr. Evans are the usage of co-rotating reference frames, the Hydro-without-Hydro approximation, and the Weak Radiation Reaction approximation (valid in quasi-circular orbits). We are currently testing these methods in a simplified scalar gravity theory - in particular we are using Nordström's second theory, which has several nice properties. In addition to building our 3+1 code, we have also performed semi-analytic calculations to determine how binary orbits evolve in Nordström's theory (we find similar results for the rates of energy and angular momentum loss as found by Peters and Mathews for GR). This testing phase is almost complete: our multi-processor code stably evolves quasi-circular binaries for hundreds of orbits, and the rate at which the orbit decays agrees with the prediction from the analytic calculations to within several percent. We are currently testing the code on binaries that have some eccentricity to see if they precess and circularize at the correct rates. Drafts of the papers describing the numerical and analytic calculations have been written, and the latest versions are available below (we intend to publish them in the near future).
Paper 2: Analytic Calculations
Below is a surface plot of the scalar field strength on an equitorial slice (click to enlarge), and a quicktime movie of an inspiral as observed in the co-rotating reference frame. Note that the binary has been given an artificially high orbital velocity so that the waves are easily visible (usually the deep potential wells centered on the stars dominate the color scale). Alternatively one can divide the scalar field by a superposition of the isolated star field solutions, which makes the wave component of the field clear. This was done in the movie - click to play.
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email: tmgarret@physics.unc.edu