David Garfinkle

Ph.D., University of Chicago
Professor

Editor, Matters of Gravity
Associate, CIAR Cosmology and Gravity program
Einstein Online

186J Mathematics and Science Center
(248) 370-3411
[email protected]

Research Interests

Professor Garfinkle's research is in numerical relativity: the use of computer simulations to study the properties of strong gravitational fields. Much of his recent research has been on (i) properties of singularities (ii)  critical gravitational collapse and (iii) cosmic censorship.

Singularities occur in the centers of black holes and at the big bang at the beginning of the universe. These singularities are described by the Einstein field equations. While these equations are quite complicated, it has long been conjectured that some terms in the equations become dominant near a singularity and that as a consequence the approach to the singularity becomes simple. To test this conjecture, Garfinkle has performed computer simulations of the approach to the singularity.  At first these simulations (done in collaboration with Professor Beverly Berger) were of spacetimes with symmetry.  However, recently Garfinkle has simulated the general situation of spacetimes with no symmetry (Phys. Rev. Lett. 93, 161101 (2004)). The results support the so called BKL conjecture that the approach to the singularity is locally homogeneous and oscillatory.

Critical gravitational collapse refers to the scaling properties of gravitational collapse at and near the threshold of black hole formation. These properties are analogous to those of phase transitions in condensed matter physics and include (i) a power law relation between the mass of the black hole formed and the nearness to the black hole formation threshold and (ii) a self similarity of the 'critical solution' that is exactly at the threshold of black hole formation. These phenomena were found by Choptuik in numerical simulations of the collapse of a self-gravitating scalar field.   Garfinkle has investigated many aspects of these phenomena.  These include: (i) Scaling of tidal force for systems that just barely fail to form a black hole.  (ii) critical gravitational collapse in spacetime dimensions other than four. (iii) closed form solutions describing critical gravitational collapse.  (iv) critical gravitational collapse of a massive vector field. (v) an analog of critical gravitational collapse in Ricci flow.

Cosmic censorship is the question of whether the singularities that form in gravitational collapse are hidden inside black holes. There are exceptional cases where singularities are naked (i.e. not hidden inside black holes).  These include the critical solution of critical gravitational collapse.  However, it is thought (but not yet proved or disproved) that generic singularities are hidden inside black holes. Recently Garfinkle performed numerical simulations of the gravitational collapse of a scalar field with negative potential energy.  This system had been proposed as a counterexample to cosmic censorship. However, the result of Garfinkle's simulations is that the singularity is hidden inside a black hole.