Principal Investigators: Gerhard Schäfer

*
Project A4 aims at developing schemes and constructing approximate analytical
solutions of the equations of motion resulting from the higher order
post-Newtonian (PN) Hamiltonians of spinning binary systems derived in recent
years. Another aim is the construction of approximate analytical or
semi-analytical solutions of damped inspiraling orbits.
*

Current Numerical Relativity is fast progressing in the determination of the orbital motions and spin precessions of spinning compact binaries. Compared with those results much analytical work has still to be done to analytically balance, complement, and support Numerical Relativity. A well-known analytical scheme is the Effective One Body (EOB) method. Although the PI of Project A4 has done some work within that scheme, the aim of A4 is different from EOB which, in higher order approximations, needs much input from Numerical Relativity. In some sense, the advanced EOB approach can be regarded as efficient analytical representation of Numerical Relativity results obtained through matching. Project A4, however, seeks solutions of the equations of motion resulting from the higher PN spinning binary Hamiltonians derived in the PI's research group including quadrupole terms from rotational deformation (spin-squared terms). Approximate analytical solutions are known in special cases only, like near-equal masses on circular orbits, equal masses or special values and orientations of the spins on general orbits, all in leading order PN approximations in the spin interactions. Only quite recently, in the PI's research group, an analytical solution of the eccentric motion of compact binaries with aligned spins and orbital angular momentum was obtained under the next-to-leading order spin-orbit coupling, see Project B4.

The motion of spinless binaries was solved analytically up to the highest known conservative level reading 3PN, the first time by the PI and his collaborators. Many forms of motions resulting from explicitly given binary Hamiltonians with spin are not known analytically but need urgent construction. Though previous those calculations have been performed within former Project B4, the proposed aim is much more involved, including developments of analytical approximation tools, so the topic seems to better fit into Project A4 than B4.

Treating spinning binaries as spin-extended ordinary binary systems, it is proposed to construct a more complete set of approximate analytical solutions of the orbital and spin motions of spinning binaries developing on most recent results in the theory of orbits in celestial mechanics and satellite geodesy as reported in, e.g., [M. Schneider and C. Cui, Deutsche Geodätische Komission, Reihe A 121 (2005); E. Mai, M. Schneider, and C. Cui, Deutsche Geodätische Komission, Reihe A 122 (2008)], where the power of Lie-series methods in solving N-body equations of motion with quadratically convergent series is clearly shown. Although these references are not concerned with spin, in a most recent paper in B4, [M. Tessmer, Phys. Rev. D 80:124034, (2009)], for a much simplified system, a first successful attempt has been made in applying Lie-series methods for solving equations of motion of spinning binaries.

It is evident that explicit solutions of the conservative equations of motion are very convenient starting points for the analytical treatment of dissipative effects from gravitational radiation emission as well as for the construction of related gravitational wave forms. The construction of damped solutions will be the subject of Project A4 too.

Thibault Damour | Advisor, 2003 | ||

Steven Hergt | Postdoc, 2011 | ||

Piotr Jaranowski | Advisor, 2003 | ||

Gerhard Schaefer | Professor, PI 2003 | ||

Jan Sperrhake | Student, 2010 | ||

Jan Steinhoff | Postdoc, 2010 | ||

Manuel Tessmer | PhD Student, 2011 | ||

Norbert Wex | Advisor, 2011 | ||

Former Associates | |||

Yvonne Blum | Student, 2004-2005 | ||

David Brizuela | Postdoc, 2009-2010 | ||

Michael Brügmann | PhD Student, 2004-2004 | ||

Guillaume Faye | Advisor, 2006-2010 | ||

Frank Herrmann | PhD Student, 2004-2004 | ||

Raoul-Martin Memmesheimer | Student, 2003-2004 | ||

Tilman Rothe | Student, 2008-2009 | ||

Jan Steinhoff | PhD Student, 2009-2010 | ||

Christian Thierfelder | Student, 2004-2005 | ||

Han Wang | Postdoc, 2007-2009 |

[1]
*Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems*

Thibault Damour, Piotr Jaranowski, Gerhard Schäfer,
Phys. Rev. D 89:064058 (2014)

[2]
*Aligned spins: Orbital elements, decaying orbits, and last stable circular orbit to high post-Newtonian orders*

Manuel Tessmer, Johannes Hartung, Gerhard Schäfer,
Class. Quantum Grav. 30, 015007 (2013)

[3]
*Canonical angles in a compact binary star system with spinning components: Approximative solution through next-to-leading-order spin-orbit interaction for circular orbits*

Manuel Tessmer, Jan Steinhoï¬€, Gerhard Schäfer,
Phys. Rev. D87:064035 (2013)

[4]
*Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians*

Johannes Hartung, Jan Steinhoï¬€, Gerhard Schäfer,
Ann. Phys. (Berlin) 525:359 (2013)

[5]
*Dimensional regularization of local singularities in the fourth post-Newtonian two-point-mass Hamiltonian*

Piotr Jaranowski, Gerhard Schäfer,
Phys. Rev. D87:081503(R) (2013)

[6]
*Observables of a test-mass along an inclined orbit in a post-Newtonian approximated Kerr spacetime to leading-order-quadratic-in-spin*

Steven Hergt, Abhay Shah, Gerhard Schäfer,
Phys. Rev. Lett. 111:021101 (2013)

[7]
*Towards the fourth post-Newtonian Hamiltonian for two-point-mass systems*

Piotr Jaranowski, Gerhard Schäfer,
Phys. Rev. D 86:061503(R) (2012)

[8]
*Influence of internal structure on the motion of test bodies in extreme mass ratio situations*

Jan Steinhoff, Dirk Puetzfeld,
Phys. Rev. D 86:044033 (2012)

[9]
*Elimination of the spin supplementary condition in the effective field theory approach to the post-Newtonian approximation*

Steven Hergt, Jan Steinhoff, Gerhard Schäfer,
Ann. Phys (N.Y.) 327:1494 (2012)

[10]
*Gravitational wave phasing for spinning compact binaries in inspiraling eccentric orbits*

Achamveedu Gopakumar, Gerhard Schäfer,
Phys. Rev. D 84:124007 (2011)

[11]
*Leading-order spin-orbit and spin(1)-spin(2) radiation-reaction Hamiltonians*

Han Wang, Jan Steinhoff, Jing Zeng, Gerhard Schäfer,
Phys. Rev. D 84:124005 (2011)

[12]
*Next-to-next-to-leading order post-Newtonian spin(1)-spin(2) Hamiltonian for self-gravitating binaries*

Johannes Hartung, Jan Steinhoff,
Ann. Phys. (Berlin) 523:919 (2011)

[13]
*Next-to-next-to-leading order post-Newtonian spin-orbit Hamiltonian for self-gravitating binaries*

Johannes Hartung, Jan Steinhoff,
Ann. Phys. (Berlin) 523:783 (2011)

[14]
*Canonical formulation of spin in general relativity*

Jan Steinhoff,
Ann. Phys. (Berlin) 523:296 (2011) [Dissertation]

[15]
*Next-to-leading order spin-orbit and spin(a)-spin(b) Hamiltonians for n gravitating spinning compact objects*

Johannes Hartung, Jan Steinhoff,
Phys. Rev. D 83:044008 (2011)

[16]
*Post-Minkowskian Hamiltonian for Gravitating N-Body Systems*

Tomas Ledvinka, Gerhard Schäfer, Jiri Bicak,
to be published in Proceedings of the 12th Marcel Grossmann Meeting on General Relativity

[17]
*Binary spinning black hole Hamiltonian in canonical center-of-mass and rest-frame coordinates through higher post-Newtonian order*

Tilman J. Rothe, Gerhard Schäfer,
J. Math. Phys. 51:082501 (2010)

[18]
*High-order perturbations of a spherical collapsing star*

David Brizuela, José M. Martín-García, Ulrich Sperhake, Kostas D. Kokkotas,
Phys. Rev. D 82:104039 (2010)

[19]
*Mode coupling of Schwarzschild perturbations: Ringdown frequencies*

Enrique Pazos, David Brizuela, José M. Martín-García, Manuel Tiglio,
Phys. Rev. D 82:104028 (2010)

[20]
*Interacting holographic tachyon model of dark energy*

Alberto Rozas-Fernández, David Brizuela, Norman Cruz,
Int. J. Mod. Phys. D 19:573 (2010)

[21]
*Fourth-post-Newtonian exact approximation to general relativity*

David Brizuela, Gerhard Schäfer,
Phys. Rev. D 81:084014 (2010)

[22]
*ADM canonical formulation with spin and application to post-Newtonian approximations*

Jan Steinhoff, Steven Hergt, Gerhard Schäfer,
to be published in Proceedings of the 12th Marcel Grossmann Meeting on General Relativity, edited by T. Damour, R.T. Jantzen and R. Ruffini, World Scientific, Singapore, 2010

[23]
*Canonical formulation of gravitating spinning objects at 3.5 post-Newtonian order*

Jan Steinhoff, Han Wang,
Phys. Rev. D 81:024022 (2010)

[24]
*Comment on two recent papers regarding next-to-leading order spin-spin effects in gravitational interaction*

Jan Steinhoff, Gerhard Schäfer,
Phys. Rev. D 80:088501 (2009)

[25]
*Canonical formulation of self-gravitating spinning-object systems*

Jan Steinhoff, Gerhard Schäfer,
EPL 87:50004 (2009)

[26]
*Spin-squared Hamiltonian of next-to-leading order gravitational interaction*

Jan Steinhoff, Steven Hergt, Gerhard Schäfer,
Phys. Rev. D 78:101503 (2008)

[27]
*ADM canonical formalism for gravitating spinning objects*

Jan Steinhoff, Gerhard Schäfer, Steven Hergt,
Phys. Rev. D 77:104018 (2008)

[28]
*Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincaré invariance*

Steven Hergt, Gerhard Schäfer,
Phys. Rev. D 78:124004 (2008)

[29]
*Relativistic closed-form Hamiltonian for many-body gravitating systems*

Tomas Ledvinka, Gerhard Schäfer, Jiri Bicak,
Phys. Rev. Lett. 100:251101 (2008)

[30]
*The next-to-leading order gravitational spin(1)-spin(2) dynamics in Hamiltonian form*

Jan Steinhoff, Steven Hergt, Gerhard Schäfer,
Phys. Rev. D 77:081501 (2008)

[31]
*Higher-order-in-spin interaction Hamiltonians for binary black holes from source terms of Kerr geomtery in approximate ADM coordinates*

Steven Hergt, Gerhard Schäfer,
Phys. Rev. D 77:104001 (2008)

[32]
*Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling*

Thibault Damour, Piotr Jaranowski, Gerhard Schäfer,
Phys. Rev. D 77:064032 (2008)

[33]
*Binary black hole coalescence in semi-analytic puncture evolution*

Achamveedu Gopakumar, Gerhard Schäfer,
Phys. Rev. D 77:104023 (2008)

[34]
*Gravitational recoil during binary black-hole coalescence using the effective one-body approach*

T. Damour and A. Gopakumar,
Phys. Rev. D 73:125006 (2006)

[35]
*Third post-Newtonian constrained canonical dynamics for binary point masses in harmonic coordinates*

R.-M. Memmesheimer and G. Schäfer,
Phys. Rev. D 71:044021 (2005)

[36]
*CFC+: Improved dynamics and gravitational waveforms from relativistic core collapse simulations*

P. Cerda-Duran, G. Faye, H. Dimmelmeier, J. A. Font, J.-M. Ibanez, E. Müller and G. Schäfer,
Astronomy & Astrophysics 439, 1033 (2005)

[37]
*Light deflection in the post-linear gravitational field of bounded pointlike masses*

M. H. Brügmann,
Phys. Rev. D 72:024012 (2005)

[38]
*A minimal no-radiation approximation to Einstein's field equations*

G. Schäfer, A. Gopakumar,
Phys. Rev. D 69:021501(R) (2004)

[39]
*A skeleton approximate solution of the Einstein field equations for multiple black-hole systems*

G. Faye, P. Jaranowski, and G. Schäfer,
Phys. Rev. D 69:124029 (2004)

[40]
*Motion and gravitational wave emission of spinning compact binaries*

Manuel Tessmer,
PhD thesis (2011)

[41]
*Hamiltonische Formulierung und Behandlung nichtlinearer Eigendrehimpulsbeiträge in Binärsystemen der Allgemeinen Relativitätstheorie*

Steven Hergt,
PhD thesis (2011)

[42]
*Canonical Formulation of Spin in General Relativity*

Jan Steinhoff,
PhD thesis (2010)

[43]
*Grenzfälle des post-Newtonschen Dreikörperproblems*

Tilman J. Rothe,
Diploma thesis (2009)

[44]
*Zur ADM-Eichung der Kerr-Metrik*

Steven Hergt,
Diploma thesis (2007)

[45]
*Dynamik geladener Teilchen mit Spin in post-Coulombscher Näherung höherer Ordnung*

Y. Blum,
Diploma thesis (2005)

[46]
*Kanonische Formulierung der post-Newtonschen / post-Coulombschen Punktteilchen-Dynamik höherer Ordnung in harmonischer / Lorentz-Eichung*

R.-M. Memmesheimer,
Diploma thesis (2004)

[47]
*Untersuchungen zur Skeleton-Näherungslösung der Einsteinschen Feldgleichungen für Binärsysteme*

Christian Thierfelder,
Diploma thesis (2004)

[48]
*Light deflection in the post-linear gravitational field of bounded point-like masses*

Michael H. Brügmann,
PhD thesis (2006)