Ian Hinder's Home Page

Research interests

Eccentric binary black hole orbits

Recently, I have been studying inspiraling binary black hole systems which are on eccentric (non-circular) orbits in numerical relativity. It has been known for a long time that eccentric orbits at large distances will circularize due to the emission of gravitational radiation, but it is not clear whether this happens with systems that have significant eccentricity in the last few orbits before merger. We have found, for the systems we studied, that for eccentricities below about 0.4, such orbits circularize due to the emission of gravitational radiation. This is determined by measuring the spin of the final black hole, which is found to be the same as that obtained for a circular orbit. See the paper Circularization and Final Spin in Eccentric Binary Black Hole Inspirals (preprint)

Numerical relativity and post-Newtonian approximations

I have compared binary black hole orbits simulated at Penn State with post-Newtonian predictions. There was good agreement up to the last few cycles before merger, consistent with results published in the literature.

Stability of second order in space finite difference schemes

I have studied the stability properties of finite difference discretizations of time evolution PDEs which are first order in time but second order in space. Whilst for general first order symmetrizable hyperbolic systems, a straightforward discretization can be proved to be conditionally stable, second order in space systems must be analysed on a case by case basis. See the paper Numerical stability for finite difference approximations of Einstein's equations (preprint, J. Comput. Phys. 218, 607-634, 2006)

Kranc, and automated code generation

I work with Sascha Husa and Christiane Lechner on the Kranc Mathematica package. This package was written by us, and allows you to automatically generate computer code for solving time evolution partial differential equations numerically using the Cactus infrastructure, in a fraction of the time it would take to write such a system by hand. The first version has been released, and is available under the GPL licence for anyone to use. See the paper Kranc: a Mathematica application to generate numerical codes for tensorial evolution equations (preprint, Comp. Phys. Comm. 174, 983-104, 2006).

Well-posedness and formulations of the Einstein equations

There are many ways that the Einstein equations for gravity can be written as an initial value problem. Not all of these formulations are well-posed in the PDE sense. I have studied this issue, specifically for second order in space systems.

Apples with Apples numerical relativity code comparison project

There is an effort underway to compare the different codes used by groups around the world for solving the Einstein equations. The Apples with Apples project invites contributions from any group with a numerical relativity code, and proposes standardized testbeds for the purpose of comparison.

I have contributed tests of the NOR system, generated using the Kranc package mentioned above. See the paper Implementation of standard testbeds for numerical relativity (preprint)

Papers

Page last modified on 15-May-2008.