Principal Investigators: Marcus Ansorg, Reinhard Meinel

*
The project B1 is concerned with two major problems:
The investigation of axisymmetric and stationary configurations and
the calculation of physically relevant initial data of binary systems.
The first issue deals with self-gravitating equilibrium configurations
that are composed of black holes and/or perfect fluid bodies.
In the past years, the second one has led to advancements in the multi-domain
pseudo-spectral methods used to solve the constraint equations
for binary systems. In the future, a further
development and an appropriate adaptation of the numerical methods
to the specific problem being considered is necessary for both subjects.
*

- The investigation of axisymmetric and stationary configurations.
In this context, we consider self-gravitating equilibrium configurations, which are composed of black holes and/or perfect fluid bodies. The corresponding Einstein field equations yield a free elliptic boundary value problem in which the unknown surface shapes of the fluid bodies form a part of the solution. For the numerical solution procedure we utilize multi-domain pseudo-spectral methods, which are capable of achieving exponential convergence of the numerical approximations. In particular, we introduce appropriate coordinate mappings in order to ensure a rapid fall-off of the spectral coefficients in each domain as the resolution is increased. In the past five years, we have used these methods to carry out a detailed investigation of equilibrium configurations of both spheroidal and toroidal shape for a variety of equations of state including homogeneous and polytropic ones. A specific result is the generic parametric transition of sufficiently thin fluid rings to extreme Kerr black holes. Moreover, we started the highly accurate computation and investigation of equilibrium configurations of self-gravitating tori orbiting around black holes. One interesting result is that the individual Komar mass of the black hole can become negative although the spacetime is physically acceptable.

- The calculation of physically relevant initial data of binary systems.
The highly accurate calculation of physically relevant initial data corresponding to a binary system composed of black holes and/or neutron stars is an essential contribution to the projects B5, B6 and B7 in which the orbital motion of binaries is to be computed. In the `3+1'-splitting of space and time, the Einstein equations are solved as a Cauchy-problem in which initial data have to be prescribed on a space-like hypersurface. These initial data are not completely free but need to satisfy the so-called constraint equations. However, these equations do not determine the data uniquely. As a consequence, a given initial data set obeying the constraints may possess unphysical properties such as some undesired gravitational radiation. It is therefore essential to consider additional requirements such as a specific quasi-stationary framework or the so-called waveless formulation in which the physical attributes on the initial time-slice are approximated in an appropriate manner. In the past three years we have advanced the multi-domain pseudo-spectral methods described above to the solution of the constraint equations for binary systems. In particular, we have explored the so-called puncture and excision techniques to compute binary black hole initial data.

Former Associates | |||

Marcus Ansorg | Professor, PI 2007-2009 | ||

Joerg Hennig | Postdoc, 2007-2010 | ||

Stefan Horatschek | Ph.D. Student, 2004-2010 | ||

Andreas Kleinwächter | Staff, 2003-2010 | ||

Hendrick Labranche | Ph.D. Student, 2004-2010 | ||

Reinhard Meinel | Professor, PI 2003-2010 | ||

Gernot Neugebauer | Advisor, PI 2003-2006 | ||

David Petroff | Postdoc, 2003-2010 |

[1]
*The Axisymmetric Case for the Post-Newtonian Dedekind Ellipsoids*

N. Gürlebeck and D. Petroff,
Astrophys.J. 722, 1207 (2010)

[2]
*Universal properties of distorted Kerr-Newman black holes*

M. Ansorg, J. Hennig and C. Cederbaum,
(2010)

[3]
*Uniformly Rotating Homogeneous Rings in post-Newtonian Gravity*

S. Horatschek and D. Petroff,
Mon. Not. R. Astron. Soc., vol. 408, p. 1749 (2010)

[4]
*Non-axisymmetric configurations in the post-Newtonian Approximation to General Relativity*

N. Gürlebeck and D. Petroff,
submitted to Proceedings of the 12th Marcel Grossmann Meeting (Paris, July 12-18, 2009)

[5]
*Regularity of Cauchy horizons in S2xS1 Gowdy spacetimes*

J. Hennig and M. Ansorg,
Class. Quantum Grav., vol. 27, 065010 (2010)

[6]
*A universal inequality for axisymmetric and stationary black holes with surrounding matter in the Einstein-Maxwell theory*

J. Hennig, C. Cederbaum and M. Ansorg,
Commun. Math. Phys., vol. 293, p. 449 (2010)

[7]
*Non-existence of stationary two-black-hole configurations*

J. Hennig and G. Neugebauer,
submitted to Proceedings of the 12th Marcel Grossmann Meeting (Paris, July 12-18, 2009)

[8]
*Relativistic figures of equilibrium: from Maclaurin spheroids to Kerr black holes*

R. Meinel,
submitted to Proceedings of the 12th Marcel Grossmann Meeting (Paris, July 12-18, 2009)

[9]
*On the solution space of differentially rotating neutron stars in general relativity*

M. Ansorg, D. Gondek-Rosińska and L. Villain,
Mon. Not. R. Astron. Soc., vol. 396, p. 2359 (2009)

[10]
*Non-existence of stationary two-black-hole configurations*

G. Neugebauer and J. Hennig,
Gen. Relativ. Grav. 41, 2113 (2009)

[11]
*The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory: study in terms of soliton methods*

J. Hennig and M. Ansorg,
Ann. Henri Poincaré 10, 1075 (2009)

[12]
*Inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory*

M. Ansorg and J. Hennig,
Phys. Rev. Lett. 102, 221102 (2009)

[13]
*A fully pseudospectral scheme for solving singular hyperbolic equations on conformally compactified space-times*

J. Hennig and M. Ansorg,
Journal of Hyperbolic Differential Equations 6 No. 1, 161 (2009)

[14]
*On the Multipole Moments of a Rigidly Rotating Fluid Body*

R. Filter and A. Kleinwächter,
Ann. Phys. (Berlin) 18, 102 (2009)

[15]
*A Roche Model for Uniformly Rotating Rings*

S. Horatschek and D. Petroff,
Mon. Not. R. Astron. Soc., vol. 392, p. 1211 (2009)

[16]
*The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter*

M. Ansorg and J. Hennig,
Class. Quantum Grav. 25, 222001 (2008)

[17]
*Uniformly Rotating Homogeneous and Polytropic Rings in Newtonian Gravity*

D. Petroff and S. Horatschek,
Mon. Not. R. Astron. Soc., vol. 389, p. 156 (2008)

[18]
*A universal inequality between angular momentum and horizon area for axisymmetric and stationary black holes with surrounding matter*

J. Hennig, M. Ansorg and C. Cederbaum,
Class. Quantum Grav. 25, 162002 (2008)

[19]
*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)

[20]
*A universal constraint between charge and rotation rate for degenerate black holes surrounded by matter*

M. Ansorg, H. Pfister,
Class. Quantum Grav. 25, 035009 (2008)

[21]
*Thermodynamic Description of Inelastic Collisions in General Relativity*

G. Neugebauer and J. Hennig,
Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity, edited by H. Kleinert, R.T. Jantzen and R. Ruffini, World Scientific, Singapore, 2008, p. 2228

[22]
*Quasi-Stationary Routes to the Kerr Black Hole*

R. Meinel,
Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity, edited by H. Kleinert, R.T. Jantzen and R. Ruffini, World Scientific, Singapore, 2008, p. 2234

[23]
*Quasi-Stationary Routes to the Kerr Black Hole*

R. Meinel,
Proceedings of the 11th Marcel Grossmann Meeting on General Relativity, World Scienti?c, 2234, (2008)

[24]
*Recoil velocities from equal-mass binary black-hole mergers: a systematic investigation of spin-orbit aligned configurations*

D. Pollney, C. Reisswig, L. Rezzolla, B. Szilagyi, M. Ansorg, B. Deris, P. Diener, E. N. Dorband, M. Koppitz, A. Nagar, E. Schnetter,
Phys. Rev. D 76, 124002 (2007)

[25]
*Thermodynamic Description of Inelastic Collisions in General Relativity*

J. Hennig, G. Neugebauer and M. Ansorg,
ApJ 663, 450 (2007)

[26]
*Gravitational Waves from Extreme Mass Ratio Inspirals in Nonpure Kerr Spacetimes*

E. Barausse, L. Rezzolla, D. Petroff and M. Ansorg,
Phys. Rev. D 75, 064026 (2007)

[27]
*The Parametric Transition of Strange Matter Rings to a Black Hole*

H. Labranche, D. Petroff and M. Ansorg,
Gen. Rel. Grav. 39, 129 (2007)

[28]
*Slowly Rotating Homogeneous Stars and the Heun Equation*

D. Petroff,
Class. Quantum Grav. 24, 1055 (2007)

[29]
*Collisions of rigidly rotating disks of dust in general relativity*

J. Hennig and G. Neugebauer,
Phys. Rev. D 74, 064025 (2006)

[30]
*Numerical evolutions of a black hole-neutron star system in full General Relativity*

F. Löffler, L. Rezzolla, M. Ansorg,
Phys. Rev. D 74, 104018 (2006)

[31]
*Negative Komar Mass of Single Objects in Regular, Asymptotically Flat Spacetimes*

M. Ansorg and D. Petroff,
Class. Quantum Grav. 23, L81 (2006)

[32]
*The Ernst equation and ergosurfaces*

P. T. Chrusciel, G.-M. Greuel, R. Meinel and S. J. Szybka,
Class. Quantum Grav. 23, 4399 (2006)

[33]
*On the black hole limit of rotating fluid bodies in equilibrium*

R. Meinel,
Class. Quantum Grav. 23, 1359 (2006)

[34]
*The extreme distortion of black holes due to matter*

D. Petroff and M. Ansorg,
gr-qc/0511102

[35]
*Uniformly rotating rings in general relativity*

T. Fischer, S. Horatschek and M. Ansorg,
Mon. Not. Roy. Astron. Soc. 364, 943 (2005)

[36]
*Black holes surrounded by uniformly rotating rings*

M. Ansorg and D. Petroff,
Phys. Rev. D 72, 024019 (2005)

[37]
*Equilibrium configurations of homogeneous fluids in general relativity*

M. Ansorg, T. Fischer, A. Kleinwächter, R. Meinel, D. Petroff and K. Schöbel,
Mon. Not. Roy. Astron. Soc. 355, 682 (2004)

[38]
*Maximal mass of uniformly rotating homogeneous stars in Einsteinian gravity*

K. Schöbel and M. Ansorg,
Astron. Astrophys. 405, 405 (2003)

[39]
*Progress in relativistic gravitational theory using the inverse scattering method*

G. Neugebauer and R. Meinel,
J. Math. Phys. 44, 3407 (2003)

[40]
*Relativistic Figures of Equilibrium*

R. Meinel, M. Ansorg, A. Kleinwächter, G. Neugebauer and D. Petroff,
Book: Cambridge University Press, Cambridge UK (2008)

[41]
*Parametric Transitions of Stationary and Axisymmetric Bodies to Black Holes*

H. Labranche,
Ph.D. thesis, University of Jena

[42]
*Rotierende Flüssigkeitsringe in Newtonscher und Einsteinscher Gravitationstheorie*

S. Horatschek,
Ph.D. thesis, University of Jena

[43]
*Untersuchung rotierender relativistischer Sterne*

R. Mohazzab,
Diploma thesis, University of Jena

[44]
*Analytical and Numerical Studies of Self-Gravitating Figures of Equilibrium*

D. Petroff,
Habilitation thesis, University of Jena

[45]
*Symmetrien relativistischer Gleichgewichtsfiguren*

M. Fröb,
Diploma thesis, University of Jena

[46]
*Charakterisierung der horizontnahen Raumzeit extremer schwarzer Löcher*

J. Zschoche,
Diploma thesis, University of Jena

[47]
*Lösungen der Ernst-Gleichungen mit rationalen Achsenpotentialen*

F. Maucher,
Diploma thesis, University of Jena

[48]
*Multipolmomente axialsymmetrisch stationärer Raumzeiten und die Quadrupol-Vermutung*

R. Filter,
Diploma thesis, University of Jena

[49]
*Untersuchungen zum Black-Hole-Grenzfall einer rotierenden Scheibenlösung*

W. Schumacher,
Diploma thesis, University of Jena

[50]
*Untersuchungen zur extremen Kerr-Metrik in Horizontnähe*

S. Rosemann,
Diploma thesis, University of Jena

[51]
*Rotierende Quarksterne*

C. Teichmüller,
Diploma thesis, University of Jena

[52]
*Constructive uniqueness proofs of stationary vacuum Black Hole spacetimes including the case of degenerate horizons*

S. Pauliuk,
Diploma thesis, University of Jena

[53]
*Untersuchungen des Mass-Shedding-Limits rotierender Flüssigkeiten in Newtonscher und Einsteinscher Gravitationstheorie*

T. Pähtz,
Diploma thesis, University of Jena

[54]
*Staubkonfigurationen in der Einsteinschen Gravitationstheorie*

N. Gürlebeck,
Diploma thesis, University of Jena

[55]
*Untersuchungen zu Randwertproblemen der Einsteinschen Feldgleichungen*

T. Bocklitz,
Diploma thesis, University of Jena

[56]
*Post-Newtonsche Entwicklung des Gravitationsfeldes einer rotierenden Staubscheibe*

T. Kiefer,
Diploma thesis, University of Jena

[57]
*Relativistische Gleichgewichtskonfigurationen für ideale Flüssigkeiten mit einer polytropen Zustandsgleichung*

P. Tölle,
Diploma thesis, University of Jena

[58]
*Stabilitätsuntersuchung von relativistischen, kugelsymmetrischen Quarksternen*

G. Busch,
Diploma thesis, University of Jena

[59]
*Rotierende Ringe mit zentralem Schwarzen Loch, beschrieben durch die Chandrasekhar-Zustandsgleichung*

R. Nolte,
Diploma thesis, University of Jena

[60]
*Spinteilchen in der Einsteinschen Gravitationstheorie*

M. Queck,
Diploma thesis, University of Jena

[61]
*Untersuchungen zu rotierenden Ringen in der allgemeinen Relativitätstheorie*

S. Horatschek,
Diploma thesis, University of Jena

[62]
*Untersuchung quasistationärer Übergänge zu Schwarzen Löchern*

T. Fischer,
Diploma thesis, University of Jena

[63]
*Die Grenzmasse homogener relativistischer Sternmodelle*

K. Schöbel,
Diploma thesis, University of Jena