Prof. Harald PfeifferGroup Leader
Numerical Relativity and Gravitational Wave Astrophysics
Einstein’s theory of gravity (called General Relativity) makes many fascinating predictions: (1) space and time are intertwined into a warped ‘space-time’ where the rate of flow of time is variable and where the usual Euclidean geometry does not work (2) the existence of objects – named ‘black holes’ – which are so compact that nothing can escape their gravitational pull. (3) the existence of perturbations of space-time itself traveling at the speed of light, called ‘gravitational waves’.
My research focuses on a deeper understanding of the bizarre objects in our Universe that are governed by extreme gravity and on gravity itself. I am trying to answer questions like
- How does space and time behave when black holes collide?
- What are the properties of coalescing black holes and neutron stars in our universe?
- How does one program current and future super-computers to study gravity?
I am pursuing these questions with a variety of interrelated approaches:
Einstein’s equations are very, very complicated. In many interesting cases, they must be solved by super-computers. I am developing the computational tools that make such solutions possible. I am also applying the resulting computer programs to study some of the most exciting events in the universe: The inspiral and the merger of pairs of black holes or neutron stars. Such simulations provide crucial information for the gravitational wave analyses of current and future gravitational wave detectors like LIGO and Virgo. Future detectors like the space-mission ‘LISA’ will observe different types of systems (most notably, binaries where one partner is much less massive than the other one) which requires the development of new computational techniques. The higher sensitivity of future detectors also requires more accurate simulations to extract all science possible.
LIGO and Virgo have already observed some stunning gravitational wave events, and with increased sensitivity, the number of observations and the variety of sources will increase. These instruments rely on knowledge of the gravitational waveforms of events, to increase the search sensitivity, to characterize the systems detected, and to confront Einstein’s General Relativity with the experimental measurements. The construction of waveform models for coalescing black holes and neutron stars requires a combination of numerical simulations with analytical approximate solutions of Einstein’s equations, which I pursue in collaboration with colleagues at the Albert-Einstein-Institute.
Analysis of LIGO & Virgo data
Gravitational waves measured by the LIGO and Virgo detectors are interpreted using the results of numerical and analytical waveform modelling. I am participating in these analyses, with two main questions in mind:
- What can GW observations tell us about the spins of the colliding objects, and how can we extract this information?
- Are current and future GW observations subject to systematic errors due to incomplete knowledge of the expected waveforms?
Properties of Einstein’s equations
A more theoretical focus of my research is a deeper understanding of the properties of Einstein’s equations. A better understanding of the ‘internal workings’ of gravity is interesting in its own right, and will yield better approaches to the more observationally oriented research foci mentioned above. For instance, recent work about the gravitational redshift of a black hole in numerical relativity promises new connection to perturbative self-force calculations of a small body orbiting a large black hole.
 Redshift factor and the first law of binary black hole mechanics in numerical simulations.
Aaron Zimmerman, Adam G. M. Lewis, Harald P. Pfeiffer.
Phys.Rev.Lett. 117 (2016) no.19, 191101
 Observation of Gravitational Waves from a Binary Black Hole Merger.
LIGO Scientific and Virgo Collaborations (B.P. Abbott (Caltech) et al.).
Phys.Rev.Lett. 116 (2016) no.6, 061102. LIGO-P150914
 Comparing Post-Newtonian and Numerical-Relativity Precession Dynamics
Serguei Ossokine, Michael Boyle, Lawrence E. Kidder, Harald P. Pfeiffer, Mark A. Scheel, Béla Szilágyi.
Phys.Rev. D92 (2015) no.10, 104028. DOI: 10.1103/PhysRevD.92.104028
 Effective-one-body model for black-hole binaries with generic mass ratios and spins.
Andrea Taracchini et al.
Phys.Rev. D89 (2014) no.6, 061502. DOI: 10.1103/PhysRevD.89.061502
 Catalog of 174 Binary Black Hole Simulations for Gravitational Wave Astronomy.
Abdul H. Mroue et al.
Phys.Rev.Lett. 111 (2013) no.24, 241104. DOI: 10.1103/PhysRevLett.111.241104
 High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions.
Michael Boyle, Duncan A. Brown, Lawrence E. Kidder, Abdul H. Mroue, Harald P. Pfeiffer, Mark A. Scheel, Gregory B. Cook, Saul A. Teukolsky
Phys.Rev. D76 (2007) 124038. DOI: 10.1103/PhysRevD.76.124038
 Excision boundary conditions for black hole initial data.
Gregory B. Cook, Harald P. Pfeiffer
Phys.Rev. D70 (2004) 104016. DOI: 10.1103/PhysRevD.70.104016
 A Multidomain spectral method for solving elliptic equations.
Harald P. Pfeiffer, Lawrence E. Kidder, Mark A. Scheel, Saul A. Teukolsky
Comput.Phys.Commun. 152 (2003) 253-273. DOI: 10.1016/S0010-4655(02)00847-0
2014-2017 Associate Professor, Canadian Institute for Theoretical Astrophysics, University of Toronto
2009-2014 Assistant Professor, Canadian Institute for Theoretical Astrophysics, University of Toronto
2006-2009 Senior Postdoctoral Scholar in Physics, California Institute of Technology
2003-2006 Sherman Fairchild Postdoctoral Scholar in Physics, California Institute of Technology
1998-2003 PhD in Physics, Cornell University
1997-1998 Part III of the Mathematical Tripos, Cambridge University
1994-1997 Study in Physics, Universität Bayreuth