Regularization of the second-order gravitational perturbations produced by a compact object

The equations for the second-order gravitational perturbations produced by a compact-object have highly singular source terms at the point particle limit. At this limit the standard retarded solutions to these equations are ill-defined. Here we construct well-defined and physically meaningful solutions to these equations. These solutions are important for practical calculations: the planned gravitational-wave detector LISA requires preparation of waveform templates for the potential gravitational-waves. Construction of templates with desired accuracy for extreme mass ratio binaries, in which a compact-object inspirals towards a supermassive black-hole, requires calculation of the second-order gravitational perturbations produced by the compact-object.Comment: 12 pages, discussion expanded, to be published in Phys. Rev. D Rapid Communicatio

Construction of the second-order gravitational perturbations produced by a compact object

Accurate calculation of the gradual inspiral motion in an extreme mass-ratio binary system, in which a compact-object inspirals towards a supermassive black-hole requires calculation of the interaction between the compact-object and the gravitational perturbations that it induces. These metric perturbations satisfy linear partial differential equations on a curved background spacetime induced by the supermassive black-hole. At the point particle limit the second-order perturbations equations have source terms that diverge as $r^{-4}$, where $r$ is the distance from the particle. This singular behavior renders the standard retarded solutions of these equations ill-defined. Here we resolve this problem and construct well-defined and physically meaningful solutions to these equations. We recently presented an outline of this resolution [E. Rosenthal, Phys. Rev. D 72, 121503 (2005)]. Here we provide the full details of this analysis. These second-order solutions are important for practical calculations: the planned gravitational-wave detector LISA requires preparation of waveform templates for the expected gravitational-waves. Construction of templates with desired accuracy for extreme mass-ratio binaries requires accurate calculation of the inspiral motion including the interaction with the second-order gravitational perturbations.Comment: 30 page

Regularization of second-order scalar perturbation produced by a point-particle with a nonlinear coupling

Accurate calculation of the motion of a compact object in a background spacetime induced by a supermassive black hole is required for the future detection of such binary systems by the gravitational-wave detector LISA. Reaching the desired accuracy requires calculation of the second-order gravitational perturbations produced by the compact object. At the point particle limit the second-order gravitational perturbation equations turn out to have highly singular source terms, for which the standard retarded solutions diverge. Here we study a simplified scalar toy-model in which a point particle induces a nonlinear scalar field in a given curved spacetime. The corresponding second-order scalar perturbation equation in this model is found to have a similar singular source term, and therefore its standard retarded solutions diverge. We develop a regularization method for constructing well-defined causal solutions for this equation. Notably these solutions differ from the standard retarded solutions, which are ill-defined in this case.Comment: 14 page

The Thorium Molten Salt Reactor : Moving on from the MSBR

A re-evaluation of the Molten Salt Breeder Reactor concept has revealed problems related to its safety and to the complexity of the reprocessing considered. A reflection is carried out anew in view of finding innovative solutions leading to the Thorium Molten Salt Reactor concept. Several main constraints are established and serve as guides to parametric evaluations. These then give an understanding of the influence of important core parameters on the reactor's operation. The aim of this paper is to discuss this vast research domain and to single out the Molten Salt Reactor configurations that deserve further evaluation.Comment: 11 pages, 8 figures, 6 table

Orbital evolution of a test particle around a black hole: Indirect determination of the self force in the post Newtonian approximation

Comparing the corrections to Kepler's law with orbital evolution under a self force, we extract the finite, already regularized part of the latter in a specific gauge. We apply this method to a quasi-circular orbit around a Schwarzschild black hole of an extreme mass ratio binary, and determine the first- and second-order conservative gravitational self force in a post Newtonian expansion. We use these results in the construction of the gravitational waveform, and revisit the question of the relative contribution of the self force and spin-orbit coupling.Comment: 5 pages, 2 figure

FUNCTIONAL HETEROGENEITY OF MURINE LYMPHOID CELLS : V. LYMPHOCYTES LACKING DETECTABLE SURFACE ϑ OR IMMUNOGLOBULIN DETERMINANTS

An appreciable percent (3–14%) of the lymphocyte-like cells of the mouse spleen lack both the θ-isoantigen and sufficient surface immunoglobulin to be detected by conventional immunofluorescence or autoradiographic procedures. These θ-,Ig- cells are increased in frequency after treatment of mice with antithymocyte serum or in mice that have been thymectomized, irradiated (850 R), and reconstituted with bone marrow cells. Moreover, in chimeric C57BL/6 mice in which the T cells are derived from (BALB/c x C57BL/6)F1 donors, θ-,Ig- cells also lack BALB/c histocompatibility antigens. These experiments indicate that θ-,Ig- cells are not θ- T lymphocytes. Removal of complement receptor lymphocytes from spleen cell populations increases the frequency of θ-,Ig- cells, indicating that such cells lack the complement receptor. Partially purified populations of θ-,Ig- cells have been obtained by cytolysis by anti-θ- and anti-κ-antibody and complement and by density gradient ultracentrifugation. These cells closely resemble lymphocytes in morphology. The only exceptional feature is the existence of prominent nucleoli. The θ-,Ig- cells lack hemoglobin and endogenous peroxidases, are not actively phagocytic, and do not adhere to glass. This suggests they are not of the erythroid, myeloid, or monocytoid lines. [3H]Thymidine labeling studies indicate that θ-,Ig- cells are members of a relatively slowly dividing cell pool. Whether θ-,Ig- cells are members of the "classical" B lymphocyte line or belong to another, as yet undescribed, lineage is not yet certain

Second-order gravitational self-force

We derive an expression for the second-order gravitational self-force that acts on a self-gravitating compact-object moving in a curved background spacetime. First we develop a new method of derivation and apply it to the derivation of the first-order gravitational self-force. Here we find that our result conforms with the previously derived expression. Next we generalize our method and derive a new expression for the second-order gravitational self-force. This study also has a practical motivation: The data analysis for the planned gravitational wave detector LISA requires construction of waveforms templates for the expected gravitational waves. Calculation of the two leading orders of the gravitational self-force will enable one to construct highly accurate waveform templates, which are needed for the data analysis of gravitational-waves that are emitted from extreme mass-ratio binaries.Comment: 35 page