- Gravitation, gravitational waves, black holes
- Numerical methods for solving the Einstein equations

My research is focussed on the study of black holes in general relativity. Black holes, another prediction of general relativity, are the end-state of gravitational collapse for which the local spacetime has been distorted to such an extent that light can not escape the gravitational well.

Although they are one of the earliest predictions of Einstein's theory of relativity, gravitational waves have never been directly observed. If detectable, however, they promise to open a new spectrum for observing the universe. Large-scale interferometers currently under construction (LIGO, Virgo) expect to make first dectections within the next five years, opening up the new field of gravitational wave astronomy.I've been particularly involved in studying the two-body problem in general relativity -- the problem of how two black holes orbit each other, creating dynamical distortions in the local spacetime. These distortions have a number of physical consequences which may be observable. In particular, they carry gravitational energy away from the black holes, in the form of gravitational waves.

To study how gravitational waves are generated and their structure, my collaborators and I have built a simulation code which solves the Einstein equations as an evolution problem. This allows us to model astrophysical scenerios such as binary black hole and neutron star mergers, accurately reproducing the local spacetime distortions due to the dynamical gravitational fields.

The models which we are simulating are leading to a better understanding of a number of interesting mathematical and physical questions related to the relativistic two-body problem.

- Black hole interactions: spins, mass loss, recoils
- Gravitational wave templates for generic black hole mergers
- Nonlinear effects in the merger process
- Tests of general relativity and alternate theories

On a more technical level, I am working on methods to improve the accuracy of our model code:

- Asymptotic techniques for measuring gravitational waves
- Boundary conditions for nonlinear wave equations
- Time integration schemes
- Coordinate choices for improved accuracy
- High performance computing

(A full list of my publications can be found here.)

*"Energy versus Angular Momentum in Black Hole Binaries"*Thibault Damour, Alessandro Nagar, Denis Pollney, Christian Reisswig.**Phys.Rev.Lett. 108 (2012) 131101**DOI: 10.1103/PhysRevLett.108.131101.*"Gravitational memory in binary black hole mergers"*Denis Pollney, Christian Reisswig.**Astrophys.J. 732 (2011) L13**DOI: 10.1088/2041-8205/732/1/L13.*"Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity"*C. Reisswig, N.T. Bishop, D. Pollney, B. Szilagyi,**Class.Quant.Grav. 27 (2010) 075014,**DOI: 10.1088/0264-9381/27/7/075014.*"High accuracy binary black hole simulations with an extended wave zone"*

Denis Pollney, Christian Reisswig, Erik Schnetter, Nils Dorband, Peter Diener.**Phys.Rev. D83 (2011) 044045**DOI: 10.1103/PhysRevD.83.044045.*"Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins"*

P. Ajith, M. Hannam, S. Husa, Y. Chen, B. Bruegmann, N. Dorband, D. Muller, F. Ohme, D. Pollney, C. Reisswig et al..**Phys.Rev.Lett. 106 (2011) 241101**DOI: 10.1103/PhysRevLett.106.241101.*"Gravitational-wave detectability of equal-mass black-hole binaries with aligned spins"*

Christian Reisswig, Sascha Husa, Luciano Rezzolla, Ernst Nils Dorband, Denis Pollney, Jennifer Seiler.**Phys.Rev. D80 (2009) 124026**DOI: 10.1103/PhysRevD.80.124026.

**Calculus of Variations**(2nd year, 15 lectures): A new course for 2013, we will introduce Lagrangian action principles to solve optimization problems and develop some key results in classical mechanics.**Partial Differential Equations**(3rd year, 39 lectures): We introduce the method of characteristics as a basis for understanding the structure of differential equations, classifying equations as hyperbolic, parabolic or elliptic and studying their classical solutions. We introduce Fourier series and the Fourier transform as solution methods.**Numerical modelling**(honours, 26 lectures): We use numerical techniques to study some simple models of fluid flow, introduce the Navier-Stokes equations, finite-volume methods and the development of shocks in numerical solutions. Follows the text "*Numerical Methods for Conservation Laws*," by Randall J. LeVeque.

If you are interested in doing an honours project related to either relativity and/or computational modelling, please come see me to work out a project that fits your interests. I'm currently offering the following projects:

**Title:** *Geometry of the Kerr spacetime***Prior knowledge:** General Relativity, Matlab**Description:** The Kerr metric describes the unique solution for a stationary rotating black hole in general relativity. We will explore the properties of this spacetime, possibly including the horizon structure, geodesics and the ergosphere, embedding diagrams, and how to extract energy from rotating black holes.

**Title:** *Simulating the motion of N interacting particles in three dimensions***Prior Knowledge:** Numerical Analysis, Matlab**Description:** The N-body problem involves predicting the motion of N particles due to gravitational interaction. We will solve the problem using a Matlab code (or computer language of choice) and finite difference approximations. With sufficient progress, we will parallelize the code using MPI (Message Passing Interface) to be run on a supercomputer.

**Title:** *Post-Newtonian simulation of black hole spacetimes***Prior Knowledge:** Numerical Analysis, General Relativity**Description:** The post-Newtonian (PN) equations are ODEs which approximate

the motion of bodies in general relativity in the limit of low velocities.

We will use low-order PN approximation to examine the problem of two

orbiting black holes, and examine properties of the system, such as energy

conservation and the evolution of eccentricity.

**Title:** *Shallow water wave equation***Prior Knowledge:** Numerical Analysis, Matlab**Description:** We will develop a computational model for a classic nonlinear PDE describing the motion of a water wave, and examine its properties, including bore formation and the appearance of solitons.

Initially we will construct models in one dimension, and with sufficient progress we'll move on to a two dimensional solution.

Last Modified**: Tue, 05 Feb 2013 16:03:09 SAST**