Rhodes>Mathematics>Research>General Relativity and Cosmology

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.



  • Dumsani Ndzinisa (PhD)
  • Jonathan Hakata (MSc)

 Research associates 

  • Dr P. J. van der Walt

 Post-doctoral 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)
  • LR Venter (PhD)
  • JP Adamiak (PhD)


A full list of publications of members of the group can be found here.

Available Postgraduate Projects

Honours projects

Masters projects

PhD projects

  • The generalised conformal field equations with matter - Applications (Dr. Chris Stevens)
  • Non reflecting boundary conditions for Anti de-Sitter space-time (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: 10.1088/2041-8205/732/1/L13.
  • "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

Related courses at Rhodes:

  • Partial Differential Equations (3rd year)

  • General Relativity (honours)

More information about GWs:


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, Jean-Philippe 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, P.J. van der Walt and N.T. Bishop (Rhodes U.), Phys.Rev. D85 (2012) 044016.
  • Observational cosmology using characteristic numerical relativity, P.J. van der Walt and N.T. Bishop, 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 large-scale computer models which incorporate as much of the physical scenerios as possible: general relativity, maxwell equations, fluid dynamics, etc.Binary black holes [AEI/Benger].

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 high-performance 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:

  • "Three-Dimensional General-Relativistic 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) e-Print: arXiv:1212.1191.
  • "General relativistic null-cone evolutions with a high-order scheme" Christian Reisswig, Nigel T. Bishop, Denis Pollney (2013) e-Print: 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 space-times

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 Friedrich-Nagy 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: Sun, 16 Feb 2020 15:56:25 SAST