Showcase - Numerical Relativity Media

The Numerical Relativity snapshots

The numerical simulations of black holes, especially of binary black holes, has come of age during the last years. The orbital evolution of the singularities and the production of gravitational waves are routinely simulated for several interesting cases. From these simulations visual animations and pictures are produced.
The focus of the Jena Numerical Relativity Group are binary black hole evolutions with and without spin.


Binary black hole simulations (25 MB).
Click the picture to watch the animation.

Event Horizons Pic

Event horizons for the final inspiral, collision and merger of two black holes shown in x-y-t diagrams. The time-axis points upwards.
Click the picture to see the movie (6.6 MB) or
Click here to see more animations and pictures.
At each instant of time the intersection of the x-y-plane with a spherical black hole is a circle. Stacking these time slices gives the graphical representation of the event horizon as two tubes that merge as time progresses. For a head-on collision, the resulting picture is called the "pair of pants". For orbiting black holes it can be called the "twisted pants".

Binary black hole merger (variation of color)


Binary black hole merger (red on blue), diagonally upwards
Binary black hole merger (red on blue), diagonally downwards
Binary black hole merger, unequal mass, mass ratio 2:1

Simulation of 42 black holes starting from rest spelling E=mc2 (2007). Nowadays the numerical methods are stable and efficient so that it has become possible to evolve such systems all the way through the merger. Plotted is the conformal factor.Click the picture for an animation.
Click here to show a short description.

AEI Multiple Black Holes
First multiple black hole simulation The puncture method allows the numerical treatment of black holes on R3 1. This is a technical simplification compared to excision methods, which depending on their implementation require specific grids, coordinates, and discretizations of derivatives at the excision boundary for each black hole. Furthermore, methods that rely on comoving coordinates 2, 3, which are well adapted to quasi-circular inspirals of two black holes, do not immediately generalize to three or more black holes. After setting the puncture initial data, a puncture code in principle does not even need to know the location of the black holes, since the BSSN formulation with the appropriate treatment of the conformal factor allows us to evolve the gravitational fields on R3 without reference to the punctures. In practice, the puncture tracks are computed, for example, to add resolution near the punctures in a mesh refinement code. The first proof of principle simulation that puncture evolutions generalize to more than two black holes with minimal changes to a binary code was performed in 1997 4. Since this was an unpublished report, we summarize one of these simulations here. 30 black holes were arranged in a planar configuration using Brill-Lindquist data, see Fig. Evolutions were performed using the fixed puncture method with the ADM formulation, maximal slicing, and vanishing shift, using an early version of the BAM code 5, 6. Shown is the lapse at t = 0.5M, which was initialized to one and collapsed quickly towards zero near the punctures, thereby marking the location of the black holes. These simulations were not stable on orbital time scales, so neither the full merger nor waveforms were computed. The apparent horizon for a three black hole evolution and merger of this type was computed in 7. Despite the probably well-placed expectation that the recent moving puncture evolutions generalize in the same way since fields are evolved on R3 , we want to emphasize that it was important to actually prove that this is the case 8. For example, one could have worried that the gauge conditions behave in an unexpected manner. The bottom line is that the moving puncture method generalizes without significant changes from two to three black holes 8, 9.

1 S. Brandt and B. Brügmann, Phys. Rev. Lett. 78, 3606 (1997), gr-qc/9703066.
2 B. Brügmann, W. Tichy, and N. Jansen, Phys. Rev. Lett. 92, 211101 (2004), gr-qc/0312112
3 M. A. Scheel, H. P. Pfeiffer, L. Lindblom, L. E. Kidder, O. Rinne, and S. A. Teukolsky, Phys. Rev. D 74, 104006 (2006), gr-qc/0607056
4 B. Brügmann, Evolution of 30 black holes spelling AEI (1997), talk for site visit of the Fachbeirat, Albert Einstein Institute. Unpublished.
5 B. Brügmann, Phys. Rev. D 54, 7361 (1996), gr-qc/9608050.
6 B. Brügmann, Int. J. Mod. Phys. 8, 85 (1999), gr-qc/9708035
7 P. Diener, Class. Quantum Grav. 20, 4901 (2003), gr-qc/0305039.
8 M. Campanelli, C. O. Lousto, and Y. Zlochower, Phys. Rev. D77, 101501 (2008)
9 C. O. Lousto and Y. Zlochower, Phys. Rev. D77, 024034 (2008)


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