General Relativity and Cosmology
?We have a wide variety of research interests including
 Gravitational waves
 Theoretical cosmology
 Computational astrophysics
 Mathematical and computational gravity
See below for a brief description of each of these areas and available postgraduate projects.
Staff
Students
 Dumsani Ndzinisa (PhD)
 Jonathan Hakata (MSc)
Research associates
 Dr P. J. van der Walt
Postdoctoral researchers
Former members
 Prof. Julien Larena
 Dr Apratim Ganguly
 Dr Aurelien Hees
 Dr Bishop Mongwane
 Landman Bester (PhD)
 Neo Mohapi (PhD)
 Vuyile Sixaba (MSc)
 Michelle Kogel (MSc)
 Thembinkosi Dyeyi (MSc)
 Amy Bray (MSc)
 LR Venter (PhD)
 JP Adamiak (PhD)
Publications
A full list of publications of members of the group can be found here.
Available Postgraduate Projects
Honours projects
 Numerical simulation of colliding gravitational plane waves (Dr. Chris Stevens)
 Numerical simulation of binary black hole mergers (Dr. Chris Stevens)
 Numerical methods for partial differential equations (Dr. Chris Stevens)
 Derivation and solution of the Black Scholes option pricing model (Dr. Chris Stevens)
Masters projects
 Smoothness of null infinity in General Relativity (Dr. Chris Stevens)
 Dark energy generation from colliding gravitational plane waves (Dr. Chris Stevens)
 Bondi mass loss formula without gauge simplifications (Dr. Chris Stevens)
PhD projects
 The generalised conformal field equations with matter  Applications (Dr. Chris Stevens)
Research Projects
Gravitational Waves
Gravitational waves are dynamical distortions of spacetime, predicted by Einstein's theory of general relativity. Though they have never been directly observed (they are very weak), they are created whenever massive bodies accelerate. Numerous new experiments hope to use these signals to observe exotic processes in the universe, such as black hole mergers, and test theories of gravity.
We are involved in numerical modelling of strong sources of gravitational waves, most notably black hole and neutron star binaries. This work involves casting the Einstein equations in the form of an evolution system, which we implement in a computer code. From our models we are able to determine the dynamics of the spacetime, such as the evolution of black hole event horizons, and the emitted gravitational waves. We are using these results to develop new predictions about black hole astrophysics, comparing with analytical results, and building gravitational wave templates to aid detecting them by experiment.
Selected publications:
 "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: 10.1088/20418205/732/1/L13.
 "Inspiralmergerringdown waveforms for blackhole binaries with nonprecessing 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.
Related courses at Rhodes:

Partial Differential Equations (3rd year)
 General Relativity (honours)
More information about GWs:
 A Gravitational Wave Tutorial
 Chris Engelbrecht Summer School on Gravitational Waves 2013
 Experiments: LIGO  Virgo  NGO
 Demos and games:
 Einstein @ Home
Theoretical Cosmology
Cosmology is the study of the large scale structures of spacetime and the origin and evolution of our Universe. The standard model of cosmology is now well established, but the natures of Dark Matter and Dark Energy remain unknown and are among the most important theoretical issues of modern physics. At Rhodes University, we are mostly involved in testing the Cosmological principle, either by studying the Copernican principle, or the averaging/backreaction issue. We also study modification of gravity in order to probe the validity of the equivalence principle on astrophysical and cosmological scales. Our work concentrates on theoretical modelisations and predictions. These studies are an important step in understanding the geometry of the Universe on the large scales in greater details, in order to prepare the way for future observations such as those of EUCLID or the SKA.
Selected publications:
 Observables in a lattice Universe, JeanPhilippe Bruneton and Julien Larena, Class. Quantum Grav. 30 (2013) 025002.
 Does the growth of structure affect our dynamical models of the universe? The averaging, backreaction and fitting problems in cosmology, Chris Clarkson, George Ellis, Julien Larena and Obinna Umeh, Rept. Prog. Phys. 74 (2011) 112901.
 Observational cosmology using characteristic numerical relativity: Characteristic formalism on null geodesics, and (Rhodes U.), Phys.Rev. D85 (2012) 044016.
 Observational cosmology using characteristic numerical relativity, and , Phys.Rev. D82 (2010) 084001.
 The Hubble rate in averaged cosmology, Obinna Umeh, Julien Larena and Chris Clarkson. JCAP 1103 (2011) 029.
 Rendering Dark Energy Void, Sean February, Julien Larena, Mathew Smith and Chris Clarkson, Mon. Not. Roy. Astron. Soc. 405:2231,2010.
Computational Astrophysics
The equations governing black holes, neutron stars and cosmological scenerios like the big bang, can not be solved analytically on paper and pencil. Instead, we study these system using largescale computer models which incorporate as much of the physical scenerios as possible: general relativity, maxwell equations, fluid dynamics, etc.
Our group is a leading collaborator in developing one of the primary computing codes used to model relativistic astrophysics for a diverse set of projects ranging from binary black hole evolutions, to supernova core collapse. The Llama evolution code incorporates an implementation of the Einstein evolution equations and is coupled to a matter model. The code is parallelized to run efficiently on highperformance computing architectures and large cluster computers. Research in this area ranges over a wide range of disciplines, including developing new numerical schemes, improved reformulations of the evolution equations and gauges, and new analysis tools to help understand and visualize the results of models. A particularly active project at Rhodes involves developing new schemes for modelling gravitational waves through a characteristic formulation of the Einstein equations.?
Selected publications:
 "ThreeDimensional GeneralRelativistic Hydrodynamic Simulations of Binary Neutron Star Coalescence and Stellar Collapse with Multipatch Grids"
C. Reisswig, R. Haas, C.D. Ott, E. Abdikamalov, P. Moesta, D. Pollney, E. Schnetter. (2013) ePrint: arXiv:1212.1191.  "General relativistic nullcone evolutions with a highorder scheme" Christian Reisswig, Nigel T. Bishop, Denis Pollney (2013) ePrint: arXiv:1208.3891.
 "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.
Related courses at Rhodes:
 Partial Differential Equations (3rd year)
 Numerical Analysis (3rd year)
 General Relativity (honours)
 Cosmology (honours)
 Numerical Modelling (honours)
More information about our astro codes:
Mathematical and computational gravity
Mathematical general relativity ties fundamental problems of gravitational physics with beautiful questions in mathematics. The object is the study of manifolds equipped with a Lorentzian metric satisfying the Einstein field equations. Due to the broad scope of questions one can ask about the physics, many different areas of mathematics are employed such as group theory, topology, differential geometry and partial differential equations.
Our groups main focus is on
 Initial boundary value problems for the Einstein equations (and their numerical implementation)
 The conformal field equations (and their numerical implementation) and global structure of spacetimes
Selected publications:
 Beyer, Florian, Frauendiener, Jörg, Chris Stevens, and Ben Whale. “The numerical initial boundary value problem for the generalized conformal field equations.” Physical Review D 96 (2017): 084020.
 Frauendiener, Jörg, Chris Stevens, and Ben Whale. “Numerical evolution of plane gravitational waves in the FriedrichNagy gauge.” Physical Review D 89.10 (2014): 104026.
Related courses at Rhodes:
 Partial Differential Equations (3rd year)
 Numerical Analysis (3rd year)
 General Relativity (honours)
 Numerical Modelling (honours)
 Analytical Mechanics (honours)
Last Modified: Wed, 06 Feb 2019 09:48:55 SAST