Bernd Bruegmann - Numerical relativity: the two body problem

- The "pure" two body problem in GR: cannot do point particles, but vacuum (black holes)
- Progress in the inspiral/plunge/merger/ringdown problem:

	7M		30M		100M	200M	>600M
	1997	1999	2001	2004	2006
	
- 3+1, evolution + constraints Einstein equations
	- 5000 flop's per point
	- even infinite-power supercomputer would not have helped

- history:
	1995: 3D Schwarzschild (NCSA)
	1999: grazing collisions (AEI,Texas/PSU)
	2001: plunge from ISCO (AEI)
	2004: one orbit (PSU)
	2005: orbit, merger, waves (AEI/PSU/Pretorius)
	2006: several orbits before merger (Pretorius/others)

- recent breakthroughs:
	2005: constraint damping for harmonic code (Pretorius)
	2006: moving punctures (LSU/Goddard)
	
- last orbit = 100M; last ten orbits = 2000M; 10 orbits allow contact with PN

- Jena: very nice visualization of event horizons merging for equal and equal masses

- ongoing work:
	- numerical and analytical validation
	- mathematical, numerical analysis
		- Hannam et al. 2007, Brown 2007, geometry and regularity of moving punctures (they work because/despite underresolution; puncture wormholes become throats)
	- numerical efficiency
	
	- gold rush in parameter space
		- equal mass, no spin, no eccentricity
			- 9 orbits, phase error 4M after 1800M, amplitude error 2%; matches PN nicely with last 5 orbits
		- unequal mass, no spin, no eccentricity
			- 1:4 (1:10 in progress), recoil computed
		- spin, mostly equal mass
			- precession and flip effects
		- eccentric
			- in progress
	- limitations:
		- parameter space mapping, larger mass ratios problematic
		- runtimes: two weeks for 10 orbits
		- accuracy: seems fine, but l>2?

	- gravitational-wave templates including fully relativistic merger
		- compare with PN waveforms
		- design analytic templates
		- study parameter-space metric
		- set up analysis pipeline
		
- kicks
	- no spin, 175 km/s max at mass ratio 1:2.8; nontrivial with PN methods
	- spin kicks
		- surprisingly large recoil velocities even for equal masses; linear scaling with spin (for a/M < 0.8)
		- aligned/antialigned to axis: 390 km/s
		- Kidder 1995: leading PN spin-orbit contributions to radiated linear momentum
		- largest results (1300 km/s for extremal) for spins in orbital plane

		- kicks of 0.01c are large compared to galactic velocities, but not with the final velocities of inspiral (0.5c!)
		
	- astrophysics:
		- galaxies without central black holes?
		- extreme kicks suppressed? evolved away?
		- alignment of spins before coalescence (Bogdanovic et al 2007)

- conclusions: long-standing goal reached