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Register a new userADM canonical formalism for gravitating spinning objects
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In general relativity, systems of spinning classical particles are implemented into the canonical formalism of Arnowitt, Deser, and Misner [1]. The implementation is made with the aid of a symmetric stress-energy tensor and not a 4-dimensional covariant action functional. The formalism is valid to terms linear in the single spin variables and up to and including the next-to-leading order approximation in the gravitational spin-interaction part. The field-source terms for the spinning particles occurring in the Hamiltonian are obtained from their expressions in Minkowski space with canonical variables through 3-dimensional covariant generalizations as well as from a suitable shift of projections of the curved spacetime stress-energy tensor originally given within covariant spin supplementary conditions. The applied coordinate conditions are the generalized isotropic ones introduced by Arnowitt, Deser, and Misner. As applications, the Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling, recently obtained by Damour, Jaranowski, and Schaefer [2], is rederived and the derivation of the next-to-leading order gravitational spin(1)-spin(2) Hamiltonian, shown for the first time in [3], is presented.
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We consider the lagrangian of a self-interacting complex scalar field admitting generically Q-balls solutions. This model is extended by minimal coupling to electromagnetism and to gravity. A stationnary, axially-symmetric ansatz for the different fields is used in order to reduce the classical equations. The system of non-linear partial differential equations obtained becomes a boundary value problem by supplementing a suitable set of boundary conditions. We obtain numerical evidences that the angular excitations of uncharged Q-balls, which exist in flat space-time, get continuously deformed by the Maxwell and the Einstein terms. The electromagnetic and gravitating properties of several solutions, including the spinning Q-balls, are emphasized.
Following the method of Buchbinder and Lyahovich, we carry out a canonical formalism for a higher-curvature gravity in which the Lagrangian density ${cal L}$ is given in terms of a function of the salar curvature $R$ as ${cal L}=sqrt{-det g_{mu u}}f(R)$. The local Hamiltonian is obtained by a canonical transformation which interchanges a pair of the generalized coordinate and its canonical momentum coming from the higher derivative of the metric.
We systematically derive an action for a nonrelativistic spinning partile in flat background and discuss its canonical formulation in both Lagrangian and Hamiltonian approaches. This action is taken as the starting point for deriving the corresponding action in a curved background. It is achieved by following our recently developed technique of localising the flat space galilean symmetry cite{BMM1, BMM3, BMM2}. The coupling of the spinning particle to a Newton-Cartan background is obtained naturally. The equation of motion is found to differ from the geodesic equation, in agreement with earlier findings. Results for both the flat space limit and the spinless theory (in curved background) are reproduced. Specifically, the geodesic equation is also obtained in the latter case.
We prove under certain assumptions no-hair theorems for non-canonical self-gravitating static multiple scalar fields in spherically symmetric spacetimes. It is shown that the only static, spherically symmetric and asymptotically flat black hole solutions consist of the Schwarzschild metric and a constant multi-scalar map. We also prove that there are no static, horizonless, asymptotically flat, spherically symmetric solutions with static scalar fields and a regular center. The last theorem shows that the static, asymptotically flat, spherically symmetric reflecting compact objects with Neumann boundary conditions can not support a non-trivial self-gravitating non-canonical (and canonical) multi-scalar map in their exterior spacetime regions. In order to prove the no-hair theorems we derive a new divergence identity.
Teukolsky equations for $|s|=2$ provide efficient ways to solve for curvature perturbations around Kerr black holes. Imposing regularity conditions on these perturbations on the future (past) horizon corresponds to imposing an in-going (out-going) wave boundary condition. For exotic compact objects (ECOs) with external Kerr spacetime, however, it is not yet clear how to physically impose boundary conditions for curvature perturbations on their boundaries. We address this problem using the Membrane Paradigm, by considering a family of fiducial observers (FIDOs) that float right above the horizon of a linearly perturbed Kerr black hole. From the reference frame of these observers, the ECO will experience tidal perturbations due to in-going gravitational waves, respond to these waves, and generate out-going waves. As it also turns out, if both in-going and out-going waves exist near the horizon, the Newman Penrose (NP) quantity $psi_0$ will be numerically dominated by the in-going wave, while the NP quantity $psi_4$ will be dominated by the out-going wave. In this way, we obtain the ECO boundary condition in the form of a relation between $psi_0$ and the complex conjugate of $psi_4$, in a way that is determined by the ECOs tidal response in the FIDO frame. We explore several ways to modify gravitational-wave dispersion in the FIDO frame, and deduce the corresponding ECO boundary condition for Teukolsky functions. We subsequently obtain the boundary condition for $psi_4$ alone, as well as for the Sasaki-Nakamura and Detweilers functions. As it also turns out, reflection of spinning ECOs will generically mix between different $ell$ components of the perturbations fields, and be different for perturbations with different parities. We also apply our boundary condition to computing gravitational-wave echoes from spinning ECOs, and solve for the spinning ECOs quasi-normal modes.
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