A new algorithm for gravitational wave propagation

Casey Handmer and Bela Szilagyi

Casey Handmer (graduate student at Caltech) and Bela Szilagyi (senior research fellow at Caltech) discuss the finer points of null cone geometry.

Gravitational wave evolution – spectral style.

Colliding black holes create powerful ripples in spacetime. Of this we are certain. Directly detecting these ripples, or gravitational waves, is one of the hardest unsolved problems in physics. Inferring physical characteristics of black hole binaries and other gravitationally energetic events from their radiation requires accurate numerical simulation for matched filtering.

But gravitational wave simulations are typically plagued by a lack of gauge invariance. Waveform precision and validity is undermined by coordinate choice and movement. Simulations require an extraction methodology to obtain gauge invariant waveforms. These waveforms are used to build a template bank for detection with LIGO and other gravitational wave observatories.

Here we present a method for characteristic waveform evolution that uses spectral methods for greatly improved accuracy and efficiency. Building on the Spectral Einstein Code (SpEC), our algorithm exploits a number of well known analytic results in numerical form, including both Laurent and Magnus expansions. These expansions permit us to sneakily sidestep several singularities and infinities that would otherwise have to be dealt with in an inefficient and approximate fashion.

We baselined performance against a legacy finite difference code solving the same problem, managing to achieve comparable accuracy with an efficiency improvement of two orders of magnitude. In the future, our evolution algorithm will form the foundation upon which we will extract waveforms and other physically interesting information from the simulations.

Find out what all the fuss is about in the CQG paper

Read the full article in Classical and Quantum Gravity:
Spectral characteristic evolution: a new algorithm for gravitational wave propagation
Casey J Handmer and Béla Szilágyi
2015 Class. Quantum Grav. 32 025008

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