Project B7;     (2005 - 2014)

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Orbiting Black Holes

    Principal Investigators: Bernd Brügmann

Project B7 is aimed at the computation of the orbital motion of two black holes shortly before their collision and merger. One major goal is to model the gravitational waves that are generated in the process. This requires the numerical solution of the Einstein equations of general relativity in the regime of highly dynamic and highly non-linear gravitational fields.


Computer simulation of a black hole collision. When two black holes merge into one, enormous amounts of energy are released in the form of gravitational waves. (Click for full size.)

The time evolution of two orbiting black holes can be divided into three phases. At sufficiently large separations of the black holes their motion follows approximately the Kepler laws and can be described by post-Newtonian expansions. Over the course of millions of years the orbits become slowly tighter and tighter due to the emission of energy and angular momentum in the form of gravitational waves, i.e. the black holes perform a gradual inspiral leading finally to the collision and merger of the two black holes. The final orbit is reached when the radial infall motion overtakes the orbital motion. The collision and merger phase of the black holes is also known as the plunge from the last stable orbit. Once the black holes have merged, the resulting single distorted black hole enters the ring-down phase during which the black hole settles down to a stationary, axisymmetric black hole.

The two-body problem of general relativity in the strong field regime is still not satisfactorily solved, although there has been significant progress in the last few years. The numerical solution of the full Einstein equations (in their standard form ten non-linear, coupled partial differential equations) is a very complex problem, and for two black holes there is the additional challenge to deal with the spacetime singularities that are encountered in the interior of black holes. Given initial data for configurations of two black holes, the time evolution of the system is computed. Currently, typical runs are limited by the achievable evolution time before the simulations become too inaccurate, or before the computer code becomes unstable and crashes at numerical infinities. State of the art are simulations that cover about four full orbits of two black holes shortly before their merger.

Astrophysical considerations make it likely that the last few orbits of two black holes and the ensuing collision are the source of particularly strong gravitational waves. The final phase of a binary system of two black holes with a total mass of about 30 solar masses constitutes one of the most likely sources for the gravitational wave detectors GEO, LIGO, and VIRGO based on the frequency dependent sensitivity of these interferometric detectors. The planned space based detector LISA will detect gravitational waves from the mergers of supermassive black holes at the center of galaxies, to which the simulations in Project B7 apply equally well.

Main focus of this project are the last 1 to 10 orbits of two black holes during which the spiral becomes significantly steeper. In addition, the merger phase will be computed, so that gravitational wave forms are available for the entire strongly relativistic regime of the motion of two black holes. This area of numerical relativity requires the development of new analytical and numerical methods, as well as their implementation on supercomputers.


  Bernd Brügmann   Professor, PI 2005
  Sebastiano Bernuzzi   Postdoc, 2010
  Marcus Bugner   PhD Student, 2013-2014
  Tim Dietrich   PhD Student, 2012-2014
  Enno Harms   PhD Student, 2012-2014
  David Hilditch   Postdoc, 2008-2014
  Charalampos Markakis   Postdoc, 2013-2014
  Niclas Moldenhauer   PhD Student, 2012-2014
  Andreas Weyhausen   PhD Student, 2014

Former Associates
  Jason Grigsby   Postdoc, 2009-2011
  Roman Gold   PhD Student, 2008-2011
  Jose Gonzalez   Postdoc, 2005-2007
  Mark Hannam   Postdoc, 2005
  Sascha Husa   Postdoc,
  Andreas Kleinwächter   Staff, 2010
  Doreen Mueller   PhD Student, 2007-2010
  Frank Ohme   Student, 2007-2008
  Milton Ruiz   Postdoc, 2009-2010
  Lucia Santamaria   PhD Student, 2006-2007
  Ulrich Sperhake   Postdoc, 2005-2008
  Marcus Thierfelder   Postdoc, 2007-2012
  Helvi Witek   Student, 2007-2008


[1] Quasi-universal properties of neutron star mergers
S. Bernuzzi, A. Nagar, S. Balmelli, T. Dietrich, M. Ujevic, preprint

[2] Maximum elastic deformations of relativistic stars
N. Johnson-McDaniel, B. Owen, Phys. Rev. D88, 044004

[3] Gravitational wave constraints on the shape of neutron stars
N. Johnson-McDaniel, Phys. Rev. D88, 044016

[4] Compact binary evolutions with the Z4c formulation
D. Hilditch, S. Bernuzzi, M. Thierfelder, Z. Cao, W. Tichy, B. Brügmann, Phys. Rev. D88, 084057

[5] Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion
T. Damour, A. Nagar, S. Bernuzzi, Phys. Rev. D87, 084035

[6] Numerical solution of the 2+1 Teukolsky equation on a hyperboloidal and horizon penetrating foliation of Kerr and application to late-time decays
E. Harms, S. Bernuzzi, B. Brügmann, Class.Quant.Grav. 30 115013

[7] The Transient Gravitational-Wave Sky
N. Anderson, et al., Class.Quant.Grav. 30 193002

[8] Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration
I. Hinder, et al., Class.Quant.Grav. 31 025012

[9] Mergers of binary neutron stars with realistic spin
S. Bernuzzi, T. Dietrich, W. Tichy, B. Brügmann, preprint

[10] Eccentric binary neutron star mergers
R. Gold, S. Bernuzzi, M. Thierfelder, B. Brügmann, F. Pretorius, Phys. Rev. D86, 121501

[11] Accuracy of numerical relativity waveforms from binary neutron star mergers and their comparison with post-Newtonian waveforms
S. Bernuzzi, M. Thierfelder, B. Brügmann, Phys. Rev. D85, 104030

[12] Tidal effects in binary neutron star coalescence
S. Bernuzzi, A. Nagar, M. Thierfelder, B. Brügmann, Phys. Rev. D86, 044030

[13] Horizon-absorption effects in coalescing black-hole binaries: An effective-one-body study of the non-spinning case
S. Bernuzzi, A. Nagar, A. Zenginoglu, Phys. Rev. D86, 104038

[14] Shear modulus of the hadron-quark mixed phase
N. McDaniel, B. Owen, Phys. Rev. D86, 063006

[15] Characterization of the gravitational wave emission of three black holes
P. Galaviz, B. Brügmann, Phys. Rev. D83, 084013 (2011)

[16] Stability and chaos of hierarchical three black hole configurations
Galaviz, Pablo, Phys. Rev. D84 104038

[17] Binary black hole coalescence in the extreme-mass-ratio limit: testing and improving the effective-one-body multipolar waveform
S. Bernuzzi, A. Nagar, A. Zenginoglu, Phys. Rev. D83, 064010

[18] Binary black hole coalescence in the large-mass-ratio limit: the hyperboloidal layer method and waveforms at null infinity
S. Bernuzzi, A. Nagar, A. Zenginoglu, Phys. Rev. D84, 084026

[19] The trumpet solution from spherical gravitational collapse with puncture gauges
M. Thierfelder, S. Bernuzzi, D. Hilditch, B. Brüegmann, L. Rezzolla, Phys.Rev. D84, 064022 (2011)

[20] Numerical relativity simulations of binary neutron stars
M. Thierfelder, S. Bernuzzi, B. Brügmann, Phys. Rev. D84, 044012

[21] Numerical evolution of multiple black holes with accurate initial data
P. Galaviz, B. Brügmann, Z. Cao, Phys. Rev. D82, 024005 (2010)

[22] Dynamical shift condition for unequal mass black hole binaries
D. Müller, J. Grigsby and B. Brügmann, Phys. Rev. D82 064044 (2010)

[23] Toward a dynamical shift condition for unequal mass black hole binary simulations
D. Müller, B. Brügmann, Class.Quant.Grav. 27 (2010) 114008

[24] Status of NINJA: The Numerical INJection Analysis project
B.Brügmann and others, Proceedings of Numerical Relativity and Data Analysis NRDA 2008 (Syracuse NY, August 2008), Class. Quant. Grav. 26 (2009), 114008

[25] Testing gravitational-wave searches with numerical relativity waveforms: Results from the first Numerical INJection Analysis (NINJA) project
B. Brügmann and others, Class. Quant. Grav. 26, 165008 (2009)

[26] "Complete" gravitational waveforms for black-hole binaries with non-precessing spins
P. Ajith, M. Hannam, S. Husa, Y. Chen, B. Brügmann, N. Dorband, D. M�üller, F. Ohme, D. Pollney, C. Reisswig, L. Santamaria, J. Seiler, Astro-ph, CO (2009) Report nr. LIGO-P0900085

[27] Gravitational-wave detectability of equal-mass black-hole binaries with aligned spins
Christian Reisswig and Sascha Husa and Luciano Rezzolla and Ernst Nils Dorband and Denis Pollney and Jennifer Seiler, Subj. to astro-ph,CO.,GA,HE

[28] Unambigous determination of gravitational waveforms from binary black hole mergers
C. Reisswig, N. Bishop, D. Pollney and B. Szilagyi,

[29] The Samurai Project: verifying the consistency of black- hole-binary waveforms for gravitational-wave detection
M. Hannam, S. Husa, J. G. Baker, M. Boyle, B. Brügmann, T. Chu, N. Dorband, F. Herrmann, I. Hinder, B. J. Kelly, L. E. Kidder, P. Laguna, K. D. Matthews, J. R. van Meter, H. P. Pfei?er, D. Pollney, C. Reisswig, M. A. Scheel, D. Shoemaker, Phys. Rev. D 79, 084025 (2009)

[30] Numerical black hole initial data with low eccentricity based on post-Newtonian orbital parameters
B. Walther, B. Brügmann, and D. Müller, Phys. Rev. D79, 124040 (2009)

[31] Radiation from low-momentum zoom-whirl orbits (2009)
R. Gold and B. Brügmann, Class.Quant.Grav.27:084035,2010

[32] Hyperboloidal foliations with scri-fixing in spherical symmetry
A. Zenginoglu, S. Husa, Class. Quantum Grav. 25, 19 (2008)

[33] A template bank for gravitational waveforms from coalescing binary black holes: I. non-spinning binaries
P. Ajith, S. Babak, Y. Chen, M. Hewitson, B. Krishnan, A. M. Sintes, J. T. Whelan, B. Brügmann, P. Diener, N. Dorband, J. Gonzalez, M. Hannam, S. Husa, D. Pollney, L. Rezzolla, L. Santamaria, U. Sperhake, J. Thornburg, Phys. Rev. D 77, 104017 (2008)

[34] Eccentric binary black-hole mergers: The transition from inspiral to plunge in general relativity
U. Sperhake, E. Berti, V. Cardoso, J. A. Gonzalez, B. Brügmann, M. Ansorg, Phys.Rev.D 78, 064069 (2008)

[35] Wormholes and trumpets: the Schwarzschild spacetime for the moving-puncture generation
Mark Hannam, Sascha Husa, Frank Ohme, Bernd Brügmann, Niall O'Murchadha, Phys. Rev. D 78, 064020 (2008)

[36] Accurate Effective-One-Body waveforms of inspiralling and coalescing black-hole binaries
T. Damour, A. Nagar, M. Hannam, S. Husa, B. Brügmann, Phys.Rev.D78 (2008), 044039

[37] The high-energy collision of two black holes
U. Sperhake, V. Cardoso, F. Pretorius, E. Berti, J. A. Gonzalez, Phys.Rev.Lett.101:161101,(2008)

[38] Transformation of the multipolar components of gravitational radiation under rotations and boosts
L. Gualtieri, E. Berti, V. Cardoso, U. Sperhake, Phys.Rev.D78:044024,(2008)

[39] Resolving Super Massive Black Holes with LISA
Stanislav Babak, Mark Hannam, Sascha Husa, Bernard F. Schutz, (2008)

[40] Black-hole binary simulations: the mass ratio 10:1
Gonzalez, Jose A. and Sperhake, Ulrich and Brügmann, Bernd, Phys.Rev.D79:124006,(2009)

[41] Mining information from binary black hole mergers: a comparison of estimation methods for complex exponentials in noise
E. Berti, V. Cardoso, J. A. Gonzalez, U. Sperhake, Phys.Rev.D75, 124017 (2007)

[42] Binary black holes on a budget: Simulations using workstations
P. Marronetti, W. Tichy, B. Brügmann, J. A. Gonzalez, M. Hannam, S. Husa, U. Sperhake, Class.Quant.Grav.24, S43-S58 (2007)

[43] Supermassive recoil velocities for binary black-hole mergers with antialigned spins.
J. A. Gonzalez, M. D. Hannam, U. Sperhake, B. Brügmann, S. Husa, Phys.Rev.Lett.98, 231101 (2007)

[44] Inspiral, merger and ringdown of unequal mass black hole binaries: a multipolar analysis
E. Berti, V. Cardoso, J. A. Gonzalez, U. Sperhake, M. Hannam, S. Husa, B. Brügmann, Phys.Rev.D76, 064034 (2007)

[45] Phenomenological template family for black-hole coalescence waveforms
P. Ajith, S. Babak, Y. Chen, M. Hewitson, B. Krishnan, J. T. Whelan, B. Brügmann, P. Diener, J. Gonzalez, M. Hannam, S. Husa, M. Koppitz, D. Pollney, L. Rezzolla, L. Santamaria, A. M. Sintes, U. Sperhake, J. Thornburg, Class.Quant.Grav.24, S689-S700 (2007)

[46] Head-On collisions of different initial data
U. Sperhake, B. Brügmann, J. Gonzalez, M. Hannam, S. Husa, Proceedings of 11th Marcel Grossmann Meeting on General Relativity, (World Scientific, Singapore 2007), p. 1612

[47] Reducing eccentricity in black-hole binary evolutions with initial parameters from post-Newtonian inspiral
Sascha Husa, Mark Hannam, Josa A. Gonzalez, Ulrich Sperhake, Bernd Brügmann, Phys.Rev.D77:044037 (2008)

[48] Where post-Newtonian and numerical-relativity waveforms meet
M. Hannam, S. Husa, U. Sperhake, B. Brügmann, J. A. Gonzalez, Phys.Rev.D77:044020 (2008)

[49] Exploring black hole superkicks
B. Brügmann, J. Gonzalez, M. Hannam, S. Husa, U. Sperhake, Phys.Rev.D77:124047 (2008)

[50] Data formats for numerical relativity waves
D. Brown, S. Fairhurst, B. Krishnan, R.A. Mercer, R.K. Kopparapu, L. Santamaria, J.T. Whelan, LIGO-T070072-00-Z (2007)

[51] High-spin binary black hole mergers
P. Marronetti, W. Tichy, B. Brügmann, J. Gonzalez, U. Sperhake, Phys. Rev. D 77 (2008) 064010

[52] Implementation of standard testbeds for numerical relativity
M. C. Babiuc, S. Husa, I. Hinder, C. Lechner, E. Schnetter, B. Szilagyi, Y. Zlochower, N. Dorband, D. Pollney, J. Winicour, Class.Quant.Grav.25:125012,(2008)

[53] Multipolar analysis of spinning binaries
E. Berti, V. Cardoso, J. A. Gonzalez, U. Sperhake, B. Brügmann, To appear in the proceedings of GR18: 18th International Conference on General Relativity and Gravitation 7th Edoardo Amaldi Conference on Gravitational Waves Amaldi7), Sydney, Australia, 8-13 Jul 2007. Class.Quant.Grav.25:114035,(2008)

[54] Comparison between numerical relativity and a new class of post-Newtonian gravitational-wave phase evolutions: the non-spinning equal-mass
A. Gopakumar, M. Hannam, S. Husa, B. Brügmann, Phys.Rev.D78:064026,(2008)

[55] Comparison between numerical-relativity and post-Newtonian waveforms from spinning binaries: the orbital hang-up case
M. Hannam, S. Husa, B. Brügmann, A. Gopakumar, Phys.Rev.D78:104007,(2008)

[56] Reducing phase error in long numerical binary black hole evolutions with sixth order finite differencing
S. Husa, J. A, Gonzalez, M. Hannam, B. Brügmann, U. Sperhake, Class.Quant.Grav.25:105006,(2008)

[57] Numerical modeling of black holes as sources of gravitational waves in a nutshell
S. Husa, Eur. Phys. J. Special Topics 152, 183-207 (2007)

[58] Marginally trapped tubes and dynamical horizons
I. Booth, L. Brits, J. A. Gonzalez and C. Van Den Broeck, Class. Quant. Grav. 23, 413 (2006)

[59] Metric of a tidally perturbed spinning black hole
N. Yunes and J. A. Gonzalez, Phys. Rev. D73, 024010 (2006)

[60] Relativistic three-body effects in black hole coalescence
M. Campanelli, M. Dettwyler, M. Hannam, and C. O. Lousto, Phys.Rev. D74, 087503 (2006)

[61] Geometry and Regularity of Moving Punctures
M. Hannam, S. Husa, D. Pollney, B. Brügmann, and N. 'O Murchadha, Phys.Rev.Lett.99, 241102 (2007)

[62] Hydro-without-Hydro Framework for Simulations of Black Hole-Neutron Star Binaries,
C. F. Sopuerta, U. Sperhake, P. Laguna, Class.Quant.Grav. 23, S579-S598 (2006)

[63] Binary black-hole evolutions of excision and puncture data,
U. Sperhake, Phys.Rev.D76, 104015 (2007)

[64] Binary black hole initial data from matched asymptotic expansions
N. Yunes, W. Tichy, B. J. Owen, and B. Brügmann, Phys.Rev. D74, 104011 (2006)

[65] Hyperboloidal data and evolution
S. Husa, C. Schneemann, and T. Vogel, To appear in Proceedings of the 2005 Spanish Relativity Meeting, AIP Conference Proceedings (2006), Report number AEI-20050183

[66] Total recoil: the maximum kick from nonspinning black-hole binary inspiral
J. A. Gonzalez, U. Sperhake, B. Brügmann, M. Hannam, S. Husa, Phys.Rev.Lett. 98 (2007) 091101

[67] Calibration of Moving Puncture Simulations
B. Brügmann, J. A. Gonzalez, M. Hannam, S. Husa, U. Sperhake, W. Tichy, Phys.Rev.D77:024027 (2008)

[68] Beyond the Bowen-York extrinsic curvature for spinning black holes
M. Hannam, S. Husa, B. Brügmann, J. A. Gonzalez, U. Sperhake, Class.Quant.Grav.24, S15-S24 (2007)

[69] Where do moving punctures go?
M. Hannam, S. Husa, N. O Murchadha, B. Brügmann, J. A. Gonzalez, U. Sperhake, J.Phys.Conf.Ser.66, 012047 (2007) Proceedings for 29th Spanish Relativity Meeting

[70] Dynamical evolution of quasi-circular binary black hole data
M. Alcubierre, B. Brügmann, P. Diener, F.S. Guzman, I. Hawke, S. Hawley, F. Herrmann, M. Koppitz, D. Pollney, E. Seidel and J. Thornburg, Phys. Rev. D 72, 044004 (2005)

[71] Generalized harmonic spatial coordinates and hyperbolic shift conditions
M. Alcubierre, A. Corichi, J. A. Gonzalez, D. Nunez, B. Reimann and M. Salgado, Phys. Rev. D72, 124018 (2005)


[72] Numerical Simulations of Black Hole Binaries with Unequal Masses
Doreen Müller, PhD Thesis, University of Jena

[73] Eccentric binaries of compact objects in strong-field gravity
Roman Gold, PhD Thesis, University of Jena

[74] Numerical simulations of three black holes
Pablo Galaviz, PhD Thesis, University of Jena

[75] Numerical Simulations of Astrophysical Black-Hole Binaries (2009)
U. Sperhake, Habilitation Thesis

[76] Event Horizon Finder for Black Holes
M. Thierfelder, Diploma Thesis

[77] Numerical Integration of Post Newtonian Dynamics and Determination of Non Eccentric Initial Data for Binary Systems of Compact Objects
B. Walther, Diploma Thesis

[78] Alternative Formulations of the Einstein Equations for Binary Black Hole Simulations
H. Witek, Diploma Thesis

[79] Slicing conditions in spherical symmetry
F. Ohme, Diploma Thesis