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Numerical Relativity

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Gravity is one of the four fundamental interactions in physics. Einstein's General Theory of Relativity contains Newton's theory of gravity as a classical boundary case and describes gravity as the curvature of space-time. Experiments have confirmed the General Theory of Relativity with high accuracy, e.g. for the deflection of light rays and time measurements in GPS. It describes black holes, the Big Bang and gravitational waves.

Einsteinsche Feldgleichung Einsteinsche Feldgleichung

In numerical relativity, Einstein's field equations are solved on the computer.

Numerical solving these 10 coupled, highly nonlinear partial differential equations allows the investigation of

  • physical properties of astrophysical systems such as the fusion of black holes or neutron stars
  • mathematical properties of spacetimes such as geometry or horizons.

Numerical relativity complements analytical methods and perturbation theory, and allows the calculation of phenomena that cannot be investigated by other methods.

Of particular interest is the calculation of gravitational waves. While the methods of perturbation theory provide the waveforms in the phase of the spiralling in of binary black holes, it is possible in numerical relativity theory to determine waveforms of the fusion phase. These simulated gravitational wave signals are helpful in the detection of gravitational waves.

Solving Einstein's field equations on the computer is a big challenge. It is necessary to cover many different topics.

  • Physics is the goal, but also essential to understand and interpret the results of numerical simulations.
  • Simulations are performed on high-performance computers so that they can be completed within a reasonable time.
  • Mathematics is needed to rewrite Einstein's field equations into a well-founded initial value problem.
  • Numerics provides methods of high accuracy to discretize the Einstein equations and calculate solutions.


Prof. Dr. Bernd Brügmann Show content
Prof. B. Brügmann Image: B. Brügmann

Short CV

  • 1987. M.S. in Mathematik, Syracuse University, USA
  • 1993. Ph.D. in Physik, Syracuse University, USA
  • 1993 - 1995. MPI for Physik, München
  • 1995 - 2002. MPI for Gravitational physics, Potsdam
  • 2002 - 2004. Associate Professor, Penn State University, USA
  • Since 2004 Professor, professorchip for Gravitational theory, FSU Jena
Prof. Dr. Sebastiano Bernuzzi Show content
S. Bernuzzi Image: S. Bernuzzi

Short CV

  • 2009 PhD in Theoretischer Physik, Universität Parma, Italy
  • 2009-2014 Postdoc at the TPI
  • 2014-2015 Senior Postdoc at TAPIR/Caltech
  • 2014-2017: Rita Levi Montalcini fellow, Universität Parma, Italy
  • 2017: Habilitation
  • 2017-2018 Associate Professor, Universität Parma, Italy
  • 2017-2022 ERC-StG fellow
  • Since 2018 Professor at the TPI
Maximilian Kölsch Show content
Maximilian Kölsch Image: M. Kölsch

Short CV

  • 2011-2017: 1. Staatsexamen Mathematik and Physik
  • 2015-2017: Erweiterungsprüfung Astronomie
  • Since 2017: Scientific staff member  at the TPI
Francesco Fabbri Show content

Short CV

  • 2014-2017: M.Sc. Astrophysik und Kosmologie at the Università degli Studi di Trieste (University of Trieste), Thema: General Relativistic Simulations of Binary Neutron Stars Mergers: An Engine for Short Gamma Ray Bursts (at University of Trento)
  • Since 2017: Scientific staff member at the TPI
Sarah Renkhoff Show content

Short CV

  • 2016 - 2018: M.Sc. Physics at the TPI Jena, Masterarbeit: "Apparent Horizons in Numerical Spacetimes: A New Apparent Horizon Finder for bamps"
  • Since 2018: Scientific staff member at the TPI
Ondrej Zelenka Show content

Short CV

  • 2017-2019: Mgr. Theoretical Physics, Charles University in Prague, thesis: Dynamics of spinning test particles in curved spacetimes
  • Since 2019: Scientific staff member at the TPI
Daniela Cors Show content

Short CV

  • 2017-2018: MSc in Physics at University College London, UK. Research project: "Derivation of the Lorentz force law from the Einstein-Maxwell field equations".
  • Since 2019: Scientific member of the TPI
Florian Atteneder Show content

Short CV

  • 2017-2019: M.Sc. Physik an der Karl-Franzens-Universität Graz (Österreich). Masterarbeit: „The rotating mass shell in the general theory of relativity“
  • Since 2020: Scientific member of the TPI

Former members

Dr. Niclas Moldenhauer Show content
Dr. Tim Dittrich Show content
Dr. Marcus Bugner Show content
Dr. Hannes Rütter Show content
  • Until 2018: Scientific staff member at the TPI, Dissertation
  • Afterwards: Postdoc at the Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute, Potsdam)
Reetika Dudi Show content
  • Until 2019: Scientific staff member at the TPI
  • Afterwards: Postdoc at the Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute, Potsdam)
Vivek Chaurasia Show content
  • Until 2020: Scientific staff member at the TPI
  • Afterwards: Postdoc at Stockholm University
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