Skip to main content
School of Physical and Chemical Sciences

Numerical and Mathematical Relativity

Studying the equations of General Relativity and beyond, both analytically and with state-of-the-art simulations. 

Novel numerical and mathematical approaches can shed light on the structure and stability of spacetimes in general relativity and gravitational theories beyond it. This understanding can help us to answer questions about why the Universe has the features it does, and how generic these are in similar types of gravitational theories, spacetimes with different asymptotic behaviours or higher dimensional spacetimes.

For instance, mathematical studies of the well posedness of gravitational theories and associated numerical techniques have recently been applied in testing fundamental physics using gravitational waveforms from binary black holes. Researchers from the GWI have contributed significantly to these advances, building on their role as key developers of the numerical relativity code GRChombo.

 

Key questions

Rigidity of black holes

  • Is the Kerr family the only asymptotically flat, stationary, vacuum black hole spacetimes?
  • Similarly, is the Kerr-AdS family the only asymptotically Anti de Sitter, stationary, vacuum black hole spacetimes?
  • Highlighted publication: Unique continuation from infinity for linear waves

Asymptotics of the gravitational field:
  • How is the asymptotic behaviour of the gravitational field encoded in the initial data?
  • How generic are the standard assumptions used in the analysis of Bondi-Metzner-Sachs (BMS) charges and gravitational memory effects?
  • Highlighted publication: Polyhomogeneous expansions from time symmetric initial data

Beyond GR theories:

Gravitational waves in a modified gravity theory

Black hole environments:

  • What are the structures that form around black holes when they are immersed in dark matter or other matter beyond the Standard Model particles
  • How do such structures impact on gravitational waveforms, and can this be distinguished from other effects like modified gravity?
  • Highlighted publication: The effect of wave dark matter on equal mass black hole mergers

A black hole moving through matter creates an overdense tail that gives a drag force

Higher dimensional spacetimes:

A higher dimensional black hole with a disc like instability

Spinorial methods:
Numerical methods:

Cosmological spacetimes:

A numerical relativity simulation of a cosmological spacetime in the early universe.

Asymptotically Anti de Sitter (AdS) spacetimes:

 

Relevant Members

Members of the GWI with interests in mathematical and numerical relativity include:

  • Llibert Aresté Saló 
  • David Berman
  • Sam Brady 
  • Katy Clough
  • Pau Figueras 
  • Lidia Joana Gomes Da Silva
  • Tong Tong Hu
  • Aron Kovacs
  • Jordan Marajh
  • Charalampos Markakis  
  • Lorenzo Rossi
  • Robert Sansom
  • Arick Shao 
  • Juan Valiente Kroon 
  • Areef Waeming
  • Shunhui Yao

(See Our Members for contact links)

 

Events and Outreach

 

Highlighted Publications

  • The effect of wave dark matter on equal mass black hole mergers,
    J. C. Aurrekoetxea, K. Clough, J. Bamber and P. G. Ferreira [arxiv:2311.18156]

  • Conformal Methods in General Relativity,
    Juan A. Valiente Kroon, available at this link
Back to top