Numerical simulations have contributed enormously to our understanding of gravitational physics and astrophysics. Numerical models of black-hole accretion disks, both fully relativistic and approximations can be directly compared to observation. With the help of gravitational wave detectors like advanced LIGO, we will soon compare first-principles numericalsimulations of black-hole binary mergers, neutron stars, and more to Nature's own simulation. Although other methods are used as well, Monte Carlo simulations are routinely used to extract information about the universe from the cosmic microwave background.
Numerical simulations have also become an essential tool in the pursuit of quantum gravity. Loop quantum gravity simulations probe the quantum corrections to classical singularities, possibly indicating that the universe began not with a Big Bang, but with a Big Bounce. Numerical simulations allow for the study of the radically different and combinatorial complex causal set model of spacetime.
My research follows two paths, each of which involves numerical simulations and gravitational physics. The path on which I spend most of my time is first-principles, fully relativistic simulations of astrophysical bodies. The other path is Causal Dynamical Triangulations (CDT), a purely numerical approach to quantum gravity that has made great strides in the short time since its inception.