Complete list of talks

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.