List of talks

Abstract: We discuss how a point-particle effective action can be constructed based on irreducible representations of the Poincare group, analogous to elementary particle fields. The action leads to equations of motion which can be of the form of the Matthisson-Papapetrou-Dixon equations, but they can also take on a different structure. We discuss subtleties coming from different supplementary conditions on the spin that can be imposed, on the canonical structure of the variables, and applications to binaries of extreme mass-ratio.

Abstract: The gravitational interaction of a binary system is dominated by the mass-monopoles of the bodies. However, the structure of the bodies leads to spin and tidal effects, which leave an imprint in the dynamics and gravitational radiation of a binary at subleading orders. We discuss how these effects can be incorporated in the post-Newtonian approximation. We furthermore discuss how a modification of gravity away from general relativity could influence the internal structure of the bodies and associated post-Newtonian effects. We comment on post-Newtonian formalisms with an emphasis on Hamiltonian methods.

Abstract: The recent observation of gravitational waves from binary black holes and neutron stars by LIGO and Virgo marks the beginning of a new era for astronomy and astrophysics. Potential future discoveries might range from a better understanding of our universe to hints on the quantum nature of gravity. In order to make full use of gravitational wave observations, one needs very accurate predictions for the gravitational interaction of binary systems and the emitted gravitational waves. Hence it is interesting to study connections to methods used for the calculation of gravitational scattering of particles. These methods, one of them being the so called double copy, have enabled high-order calculations with little effort compared to the traditional Feynman-rule approach. The present talk discusses recent literature in this area and ongoing work.

Abstract: Gravitational waves can be used to test general relativity (GR) in the highly dynamical strong-field regime. Scalar-tensor theories of gravity are natural alternatives to GR that can manifest nonperturbative phenomena in neutron stars (NSs). One such phenomenon, known as dynamical scalarization, occurs in coalescing binary NS systems. Ground-based gravitational-wave detectors may be sensitive to this effect, and thus could potentially further constrain scalar-tensor theories. This type of analysis requires waveform models of dynamically scalarizing systems; in this work we devise an analytic model of dynamical scalarization using an effective action approach. For the first time, we compute the Newtonian-order Hamiltonian describing the dynamics of a dynamically scalarizing binary in a self-consistent manner. Despite only working to leading order, the model accurately predicts the frequency at which dynamical scalarization occurs. In conjunction with Landau theory, our model allows one to definitively establish dynamical scalarization as a second-order phase transition. We also connect dynamical scalarization to the related phenomena of spontaneous scalarization and induced scalarization; these phenomena are naturally encompassed into our effective action approach.

Abstract: Um Gravitationswellen zu verstehen, werden Einsteins Gleichungen auf Großrechnern gelöst. Gezeigt werden numerische Simulationen der größten Crashs im Universum: kollidierende Schwarze Löcher erzeugen Gravitationswellen, die dann auf der Erde gemessen werden. Raumzeitwellen von Neutronensternen konnte man bislang noch nicht direkt messen. Allerdings gab es für den indirekten Nachweis bereits 1990 den Nobelpreis für Physik.

Abstract: Black holes binaries are the most prominent source for current gravitational wave observatories. Spin effect are expected to be important in particular for long waveforms, as demonstrated by the event GW151226. This talk discusses recent analytic results for spin effects of black hole binaries. The leading order spin effects in the post-Newtonian approximation can be summed to all orders in spin, leading to a connection between spin effects in comparable mass binaries and test body motion in Kerr spacetime. Furthermore, spin effects were computed to fourth order in the post-Newtonian approximation. We give an outlook how these recent results can improve models for spin effects in the strong-field regime. For these investigations it turns out to be useful to understand the choice of a center of the black holes as a gauge symmetry in a point-particle action.

Abstract: Gravitational waves were predicted by Einstein 100 years ago. Einstein believed that their effect in realistic situations is too small to ever be measured. In later years he even doubted they exist at all. However, observations of the orbital decay of binary pulsars showed that they do exist. About one year ago, the Laser Interferometer Gravitational-Wave Observatory (LIGO) measured a coincident interaction of a gravitational wave, emitted from a binary black hole merger, with its two interferometers. We discuss the prospects of these observatories for astrophysics and fundamental physics. Of particular interest are tidal deformations of neutron stars and gravito-magnetic effects which twist the spacetime.

Abstract: The recent detection of a gravitational wave from a binary black hole merger by the aLIGO detectors herald the age of gravitational wave astronomy. Compact binaries are indeed the most promising source for the network of advanced gravitational wave detectors. The influence of finite-size effects (e.g., spin or tidal deformation) on the binary evolution can be large. This talk gives an overview of recent progress in the analytic description of finite-size effects through an action principle for spinning point-particles. These spinning point-particles serve as an analytic model for extended bodies. The internal structure can be modelled by augmenting the point-particle with higher-order multipole moments. We discuss in detail dynamical tidal effects of neutron stars due to resonances of oscillation modes of the object with the orbital motion, its Effective One Body implementation, and a comparison of the emitted gravitational waves with full numerical simulations.

Abstract: Compact binaries are the most promising source for the network of advanced gravitational wave detectors, which demonstrated its abilities with the recent observation of a gravitational wave from a binary black hole merger. If the binary contains a neutron star, then the influence of tidal effects on the binary evolution can be large. The tidal bulge of the neutron star is usually assumed to follow the external tidal force almost instantly. However, this assumption breaks down if the varying tidal force is in resonance with an oscillation mode of the neutron star: the tides become dynamical. We discuss how in this case the neutron star can be modelled by an effective point particle with dynamical quadrupole degrees of freedom. The equations of motion take on the form of the Mathisson-Papapetrou-Dixon equations, completed by a dynamical equation for the quadrupole. The Hamiltonian in the extreme mass ratio case is derived. It is briefly discussed how this Hamiltonian and a post-Newtonian description of dynamical tides can be combined in the effective one body Hamiltonian, without giving rise to a pole at the light ring in the potentials.

Abstract: The recent detection of a gravitational wave from a binary black hole merger by the aLIGO detectors heralds the age of gravitational wave astronomy. Compact binaries composed of black holes and/ or neutron stars are the most promising source for the network of advanced gravitational wave detectors. The influence of finite-size effects (e.g., spin or tidal deformation) on the binary evolution can be large. This talk gives an overview of recent progress in the analytic description of finite-size effects by the use of effective field theory methods. The effective action of the compact objects takes the form of a point-particle action augmented by dynamical degrees of freedom related to its multipole moments. This enabled the computation of spin effects to a very high order using methods from quantum field theory, i.e., Feynman integral calculus. While spin effects are very important for the dynamics of black holes, tidal deformation effects are crucial for neutron stars and can provide hints on the nuclear equation of state. We model tidal effects in terms of an effective harmonic oscillator action for a dynamical quadrupole. This model can describe resonances of oscillation modes of the neutron star with the orbital motion.

Abstract: The recent detection of a gravitational wave from a binary black hole merger by the aLIGO detectors herald the age of gravitational wave astronomy. Compact binaries are indeed the most promising source for the network of advanced gravitational wave detectors. The influence of finite-size effects (e.g., spin or tidal deformation) on the binary evolution can be large. This talk gives an overview of recent progress in the analytic description of finite-size effects through an action principle for spinning point-particles. These spinning point-particles serve as an analytic model for extended bodies. The internal structure can be modelled by augmenting the point-particle with higher-order multipole moments. We discuss in detail dynamical tidal effects of neutron stars due to resonances of oscillation modes of the object with the orbital motion, its Effective One Body implementation, and a comparison of the emitted gravitational waves with full numerical simulations.

Abstract: Compact binaries are the most promising source for the advanced gravitational wave detectors, which will start operating this year. The influence of spin on the binary evolution is an important consequence of general relativity and can be large. It is argued that the spin supplementary condition, which is related to the observer dependence of the center, can by understood as a gauge symmetry in the action principle of spinning point-particles. These spinning point-particles serve as an analytic model for extended bodies. The internal structure can be modelled by augmenting the point-particle with higher-order multipole moments. Consequences of the recently discovered universal (equation of state independent) relations between the multipole moments of neutron stars are discussed.

Abstract: Compact binaries are the most promising source for the advanced gravitational wave detectors, which will start operating this year. The influence of finite-size effects (e.g., spin or tidal deformation) on the binary evolution is can be large. This talk gives an overview of the analytic description of finte-size effects through an action principle for spinning point-particles. These spinning point-particles serve as an analytic model for extended bodies. The internal structure can be modelled by augmenting the point-particle with higher-order multipole moments. The multipole moments are in general composed of further dynamical degrees of freedom related to oscillation modes of the bodies, which can be excited through tidal interaction. Consequences of the recently discovered universal (equation of state independent) relations between the multipole moments of neutron stars are discussed.

Abstract: The large-scale gravitational interaction of spinning compact objects, like neutron stars and black holes, can be described using a point-particle effective action. This action can be used as a starting point for calculation of the dynamics and gravitational waves for binary systems in the post-Newtonian approximation. The effective action contains several parameters describing spin-induced and tidal-induced deformations, and the moment of inertia. It was found recently that these quantities are related by approximately equation-of-state-independent (universal) relations in the case of neutron stars. Possible implications for binary systems and their gravitational waves are discussed.

Abstract: The large-scale gravitational interaction of spinning compact objects, like neutron stars and black holes, can be described using a point-particle effective action. This action can be used as a starting point for calculation of the dynamics and gravitational waves for binary systems in the post-Newtonian approximation. The effective action contains several parameters describing spin-induced and tidal-induced deformations, and the moment of inertia. It was found recently that these quantities are related by approximately equation-of-state-independent (universal) relations in the case of neutron stars. Possible implications for binary systems and their gravitational waves are discussed.

Abstract: Compact binaries are the most promising source for the advanced gravitational wave detectors, which will start operating this year. The influence of spin on the binary evolution is an important consequence of general relativity and can be large. This talk gives an overview of the analytic description of spin in special and general relativity. The center of the object turns out to be observer dependent and leads to the so called spin supplementary condition. The latter can be understood as a gauge for the spin and can be incorporated in an action principle for spinning point-particles. These spinning point-particles serve as an analytic model for extended bodies. The internal structure can be modelled by augmenting the point-particle with higher-order multipole moments. Consequences of the recently discovered universal (equation of state independent) relations between the multipole moments of neutron stars are discussed.

Abstract: The multipoles of the spacetime of black holes and neutron stars are important for accretion models. In this talk, I will review an effective point-particle theory as a model for the multipoles structure of these compact objects. This model is ideal for applications in the post-Newtonian approximation for binary systems and can therefore be tested though pulsar timing and gravitational waves in the future. The spin or dipole moment can lead to precession of the orbital plane, which leads, e.g., to a modulated gravitational wave signal. Starting from the quadrupole moment, the internal structure of the objects is imprinted in their gravitational fields. For compact objects, the internal structure in turn is governed by strong gravitational fields. In principle, the multipolar structure can be used for fundamental physics (strong-field tests of gravity) or astrophysics (measurement of spins, structure of neutron stars, ...), where the recently discovered universal properties of neutron stars play an important role. Interesting prospects also arise from the possibility that tidal forces can excite oscillation modes of the objects.

Abstract: In this talk, I will review analytic approximations for compact binaries, with a focus on the post-Newtonian approximation and gravitational waves. Special attention is payed on the influence of the multipoles of the single objects. The spin or dipole moment can lead to precession of the orbital plane, which leads to a modulated gravitational wave signal. Starting with the quadrupole moment, the internal structure of the objects is imprinted in their gravitational fields. For compact objects, like black holes or neutron stars, the internal structure in turn is governed by strong gravitational fields. In principle, multipole effects in the motion and gravitational waves of binaries can be used for fundamental physics (strong-field tests of gravity) or astrophysics (measurement of spins, structure of neutron stars, ...). Interesting prospects also arise from the possibility that tidal forces can excite oscillation modes of the objects. The relevant properties of single neutron stars (multipoles, oscillation modes) can be obtained using numerical methods, which is briefly reviewed here.

Abstract: Eddington inspired Born Infeld gravity theory has been revived two years ago and has the interesting feature (among others) to avoid some sort of curvature singularities. Further, the model is viable since it is completely equivalent to GR in vacuum and thus passes all experimental tests of GR. After reviewing the Eddington inspired Born Infeld modification to General Relativity, we explicitly show the degeneracy between the modification and the equation of state of the sourcing matter. We further reveal the mechanism behind the singularity avoidance process in this model. However, problems can arise in this theory by means of curvature singularities at the surface of stars. But it seems to be be possible to cure this problem by an extension of the theory. We argue that Eddington inspired Born Infeld gravity and its extensions are very useful to study modifications of the coupling between matter and gravity.

Abstract: In this talk we focus on the influence of the internal structure of compact objects on the dynamics of binary systems. We explain how an effective point-particle action for a compact object can be constructed that accounts for its internal structure. (This philosophy is borrowed from effective field theories in quantum theory, but here only the classical limit is relevant.) We argue that, if this action is used within weak-field approximations for binaries, then internal strong gravity effects of the individual objects are still represented correctly. As an important example, we discuss a resonant excitation of the objects' oscillation modes through tidal forces. In an adiabatic (vanishing frequency) approximation tidal interactions are encoded in the Love constants, which depend on the internal structure of the star. For neutron stars a general relativistic definition of the Love numbers is necessary and was only found in recent years. In the present talk an extension to nonvanishing frequencies is discussed. The frequency-dependent Love number is in fact a propagator for an effective field theory description of a compact object. The poles of this propagator give rise to resonances of tidal forces and oscillation modes of the star.

Abstract: Observations of compact objects can reveal invaluable information about the strong gravity regime. A breakdown of general relativity in this regime can not lead to different properties of black holes, but can also drastically influence the internal structure of neutron stars.

In this talk we focus on the influence of the internal structure of compact objects on the dynamics of binary systems. We explain how an effective point-particle action for a compact object can be constructed that accounts for its internal structure. (This philosophy is borrowed from effective field theories in quantum theory, but here only the classical limit is relevant.) We argue that, if this action is used within weak-field approximations for binaries, then internal strong gravity effects of the individual objects are still represented correctly. As an important example, we discuss a resonant excitation of the objects' oscillation modes through tidal forces. We discuss possible implications for strong-field effects of scalar-tensor theories.

Abstract: Tidal interaction plays an important role in the inspiral of compact binaries involving neutron stars. In an adiabatic (vanishing frequency) approximation these are encode in the Love constants, which depend on the internal structure of the star. For neutron stars a general relativistic definition of the Love numbers is necessary and was only found in recent years by Hinderer, Damour&Nagar, and Poisson. In the present talk an extension to nonvanishing frequencies is discussed. The frequency-dependent Love number is in fact a propagator for an effective field theory description of a compact object. The poles of this propagator give rise to resonances of tidal forces and oscillation modes of the star.

Abstract: This lecture discusses oscillation modes of stars in Newtonian gravity. These modes are important astrophysical observables. As a particular mechanism to excite the modes, we consider tidal forces raised by a companion star. Such systems can exhibit resonances of oscillations modes and orbital motion. This lecture is based on the first sections of arXiv:1306.5820 and an outlook to the relativistic case in arXiv:1304.2228 is given.

Abstract: Tidal interactions are of great importance for the inspiral and merger of binaries involving neutron stars. Effective point-particle actions for the binary's constituents allow a treatment of these interactions within approximations schemes, such as the post-Newtonian approximation. Analytic effective one-body models implementing tidal interactions can provide accurate gravitational wave forms for binary neutron stars.

In the present talk we discuss how resonances of the neutron star's oscillation modes with the tidal field/orbital motion can be incorporated in this framework. These resonances were treated in great detail in the Newtonian limit. There tidal interactions can be described using an amplitude formulation for perturbations of the star and overlap integrals giving the external force. We reformulate this Newtonian framework in a novel way using an effective action. We argue that this reformulation can be generalized to the general relativistic case. We outline our plan to achieve this generalization. However, we also discuss several subtle problem that must be addressed.

Abstract: We discuss action principles for extended objects in gravitational and electromagnetic fields. Based on a generic worldline Lagrangian, equations of motion can be derived which agree with the ones obtained by Dixon. While in Dixon's approach the conservation of energy-momentum plays the central role, in the action approach the condition on covariance of the generic Lagrangian is crucial. The equations of motion are discussed for the gravitational case, including contributions from the quadrupole. The quadrupole encodes information about the internal structure of the extended object. In particular, we investigate quadrupole deformation due to spin and tidal interactions. The latter is analogous to polarization in electromagnetism. The relevance of these corrections is studied by deriving a solution for the equations of motion for a simplified configuration in a Kerr background geometry. Further, an inclusion of oscillation modes of the object via the quadrupole is considered. This provides a formalism to analytically describe resonances of orbital motion and oscillation modes in general relativity.

Abstract: Eddington inspired Born Infeld gravity theory has been revived two years ago and has the interesting feature (among others) to avoid some sort of curvature singularities. Further, the model is viable since it is completely equivalent to GR in vacuum and thus passes all experimental tests of GR. After reviewing the Eddington inspired Born Infeld modification to General Relativity, we explicitly show the degeneracy between the modification and the equation of state of the sourcing matter. We further reveal the mechanism behind the singularity avoidance process in this model. However, problems can arise in this theory by means of curvature singularities at the surface of stars. But it seems to be be possible to cure this problem by an extension of the theory. We argue that Eddington inspired Born Infeld gravity and its extensions are very useful to study modifications of the coupling between matter and gravity.

Abstract: Compact objects in general relativity approximately move along geodesics of spacetime. Corrections due to spin (dipole), quadrupole, and higher multipoles were derived, e.g., by Mathisson, Papapetrou, and Dixon long ago. We discuss how Dixon’s quadrupole can be related to astrophysical objects like neutron stars or black holes. In particular, we investigate quadrupole deformation due to spin and tidal interactions. Further, an inclusion of oscillation modes of the ob- ject via the quadrupole is considered. For this purpose the Newtonian case is reviewed and formulated in a novel manner. Problems for an extension to the general relativistic case and a tentative solution are discussed.

Abstract: Compact objects in general relativity approximately move along geodesics of spacetime. Corrections to their equations of motion due to spin (dipole), quadrupole, and higher multipoles were derived, e.g., by Mathisson, Papapetrou, and Dixon. These corrections can be modeled by an extension of the point mass action. We couple such actions to the gravitational field within the canonical formalism of Arnowitt, Deser, and Misner. Based on these developments, approximate post-Newtonian Hamiltonians describing the motion of self-gravitating compact astrophysical binaries can be calculated.

We discuss how Dixon's quadrupole can be related to astrophysical objects like neutron stars or black holes. This is not only important for the post-Newtonian approximation, but also in small mass ratio situations. Quadrupole effects can encode information about the internal structure of the compact objects, e.g., they allow a distinction between black holes and neutron stars, and also different equations of state. Furthermore, an inclusion of oscillation modes of the object via the quadrupole is considered. For this purpose the Newtonian case is reviewed and formulated in a novel manner. Problems for an extension to the general relativistic case and a tentative solution are discussed.

Abstract: The inspiral of compact objects like black holes or neutron stars can be approximated using point masses very well. However, very interesting astronomical information is contained in effects to gravitational waves arising from the object's higher multipoles (or their finite size). Some of these effects can be modeled by an extension of the point mass action. Based on such an action, contributions of dipole (i.e., spin) and quadrupole to the post-Newtonian (PN) approximation can be obtained. The quadrupole effects are the first which encode information of the internal structure of the compact objects, e.g., they allow an distinction between black holes and neutron stars and also different equations of state. Furthermore, based on the extension of the point-mass action, the influence of internal structure on the motion of test bodies in extreme mass ratio situations is investigated.

Abstract: We present a recent investigation (arXiv:1205.3926) on the motion of test bodies with internal structure in General Relativity. We utilize a multipolar approximation scheme along the lines of Mathisson-Papapetrou-Dixon including the quadrupolar order. For the quadrupole an explicit model is required, which crucially depends on the internal structure. We adopt a quadrupole model inspired by effective actions recently proposed in the context of the post-Newtonian approximation (including spin-squared and tidal contributions). The motion of these test bodies is studied in the equatorial plane of the Kerr geometry, where it can be characterized by an effective potential or the binding energy. We compare our findings to recent results for the conservative part of the self-force in astrophysically realistic situations.

Abstract: Diese Doktorarbeit behandelt die kanonische Formulierung des Eigendrehimpulses, oder Spins, in der Allgemeinen Relativitätstheorie. Der (eichfixierte) kanonische Formalismus der Allgemeinen Relativitätstheorie wurde vor gut einem halben Jahrhundert durch Arnowitt, Deser, und Misner (ADM) entdeckt. Innerhalb kürzester Zeit gelang die Ankopplung an Punktmassen, Skalarfelder, Spin-1/2 (Dirac) Felder und Spin-1 (Maxwell) Felder. Klassische Spinteilchen jedoch fehlten in dieser Sammlung auf Grund mehrerer konzeptueller Probleme. Innerhalb dieser Doktorarbeit gelang es, diese Probleme zu lösen und klassische Spinteilchen in den ADM Formalismus zu implementieren. Eine wichtige Anwendung ist die post-Newtonsche Näherung der konservativen Dynamik rotierender Schwarzer Löcher und/oder Neutronensterne, für die kanonische Methoden ideal geeignet sind. Sämtliche spinabhängigen konservativen Hamiltonfunktionen wurden bis einschließlich der dritten post-Newtonschen Ordnung berechnet (dies schließt auch spininduzierte Quadrupolbeiträge mit ein). Dies ist ein wichtiger Beitrag zum Verständnis gravitativ wechselwirkender Binärsysteme als Quellen von Gravitationswellen.

Abstract: The inspiral of compact objects like black holes or neutron stars can be approximated using point masses very well. However, very interesting astronomical information is contained in effects to gravitational waves arising from the object's higher multipoles (or their finite size). Some of these effects can be modeled by an extension of the point mass action. Based on such an action, contributions of dipole (i.e., spin) and quadrupole to the post-Newtonian (PN) approximation can be obtained. The quadrupole effects are the first which encode information of the internal structure of the compact objects, e.g., they allow an distinction between black holes and neutron stars and also different equations of state.

Abstract: Compact objects like black holes or neutron stars can approximately be described by point masses very well. However, very interesting astronomical information might be contained in effects to gravitational waves arising from the object's higher multipoles (or their finite size). Some of these effects can be modeled by an extension of the point mass action. Based on such an action, contributions of dipole (i.e., spin) and quadrupole to the post-Newtonian (PN) approximation can be obtained. The potential relevance of recent results (such as arXiv:1104.3079 and arXiv:1002.2093) for gravitational wave astronomy is briefly discussed.

Abstract: The extension of the canonical formalism of Arnowitt, Deser and Misner from point-masses to spinning objects is a long standing problem in general relativity. Two independent approaches to a solution of this problem are given in this talk. The first approach is based on an action functional and is similar to the original derivation of Arnowitt, Deser and Misner for non-spinning objects. This action approach currently covers the pole-dipole approximation of self-gravitating extended bodies to linear order in spin. Similarities to the canonical formulation of (classical) Dirac fields coupled to gravity are pointed out. The second approach is based on an explicit order-by-order construction of the canonical formalism within the post-Newtonian approximation scheme. Here the generators of global rotations and translations play a crucial role. As an application, spin contributions to next-to-leading order in the post-Newtonian approximation scheme are presented. The canonical formulation at higher orders in spin, which includes quadrupole deformation effects, is discussed.

Abstract: An extension of the canonical formalism of Arnowitt, Deser, and Misner from point-masses to spinning objects is presented. The derivation of this extension is based on an action functional and is similar to the original derivation of Arnowitt, Deser, and Misner for non-spinning objects. This action approach currently covers the pole-dipole approximation of self-gravitating extended bodies to linear order in spin. As an application, spin contributions to the conservative next-to-leading order in the post-Newtonian approximation scheme are presented. Also higher orders and radiation reaction effects in the Hamiltonian due to spin are discussed.

Abstract: The extension of the canonical formalism of Arnowitt, Deser and Misner from point-masses to spinning objects is a long standing problem in General Relativity. Two independent approaches to a solution of this problem are given in this talk. The first is based on an explicit order-by-order construction of the canonical formalism within the post-Newtonian approximation scheme. Here the global Poincare algebra is the important consistency condition. The second approach is based on an action functional and is similar to the original derivation of Arnowitt, Deser and Misner for non-spinning objects. A comparison to the canonical formulation of the Dirac field coupled to gravity is made. As an application, spin and quadrupole contributions to next-to-leading order in the post-Newtonian approximation scheme are presented.

Abstract: The extension of the canonical formalism of Arnowitt, Deser and Misner from point-masses to spinning objects is a long standing problem in General Relativity. Two independent approaches to a solution of this problem are given in this talk. The first is based on an explicit order-by-order construction of the canonical formalism within the post-Newtonian approximation scheme. Here the global Poincare algebra is the important consistency condition. The second approach is based on an action functional and is similar to the original derivation of Arnowitt, Deser and Misner for non-spinning objects. A comparison to the canonical formulation of the Dirac field coupled to gravity is made. As an application, spin and quadrupole contributions to next-to-leading order in the post-Newtonian approximation scheme are presented.

Abstract: Extended test bodies in general relativity can be approximated using multipolar methods. Here we discuss the application of the multipole approximation to self-gravitating compact objects. Special emphasis is put to canonical methods. These allow for an efficient computation of the conservative dynamics in certain approximation schemes. In particular, spin and quadrupole contributions to the post-Newtonian approximation are given.

Abstract: Recently, different methods succeeded in calculating the spin dynamics at higher orders in the post-Newtonian (PN) approximation. This is an essential step toward the determination of more accurate templates for gravitational waves, to be used in future gravitational wave astronomy. In this talk we focus on the extension of the ADM canonical formalism to compact spinning objects. Using the global Poincare invariance of asymptotically flat spacetimes as the most important guiding consistency condition, this extension can be constructed order by order in the PN approximation. We succeeded in deriving all Hamiltonians for binary systems at the formal 2PN order, i.e., counting spin of the same order as linear momentum. This includes all next-to-leading order spin effects, sufficient for maximally rotating objects up to and including 3PN. The extension of our formalism to the formal 3PN and 3.5PN order will be discussed.

Abstract: We show how Hamiltonians for spinning black holes can be derived from the stress-energy tensor. The Hamiltonians fits into the canonical formalism of Arnowitt, Deser, and Misner and are given in their transverse-traceless gauge. All post-Newtonian next-to-leading order spin effects up to quadratic order in spin for binary black holes are presented in Hamiltonian form.