Self-force and motion of stars around black holes

Through detection by low gravitational wave space interferometers, the capture of stars by supermassive black holes will constitute a giant step forward in the understanding of gravitation in strong field. The impact of the perturbations on the motion of the star is computed via the tail, the back-scattered part of the perturbations, or via a radiative Green function. In the former approach, the self-force acts upon the background geodesic, while in the latter, the geodesic is conceived in the total (background plus perturbations) field. Regularisations (mode-sum and Riemann-Hurwitz $\zeta$ function) intervene to cancel divergencies coming from the infinitesimal size of the particle. The non-adiabatic trajectories require the most sophisticated techniques for studying the evolution of the motion, like the self-consistent approach.Comment: To be published on 21 Rencontres de Blois: Windows on the Universe, http://confs.obspm.fr/Blois2009/, 4 pages 1 figur

Indirect (source-free) integration method. II. Self-force consistent radial fall

We apply our method of indirect integration, described in Part I, at fourth order, to the radial fall affected by the self-force. The Mode-Sum regularisation is performed in the Regge-Wheeler gauge using the equivalence with the harmonic gauge for this orbit. We consider also the motion subjected to a self-consistent and iterative correction determined by the self-force through osculating stretches of geodesics. The convergence of the results confirms the validity of the integration method. This work complements and justifies the analysis and the results appeared in Int. J. Geom. Meth. Mod. Phys., 11, 1450090 (2014).Comment: To appear in Int. J. Geom. Meth. Mod. Phy

Modeling of Kashmir Aftershock Decay Based on Static Coulomb Stress Changes and Laboratory-Derived Rate-and-State Dependent Friction Law

We model the spatial and temporal evolution of October 8, 2005 Kashmir earthquake\u2019s aftershock activity using the rate-and-state dependent friction model incorporating uncertainties in computed coseismic stress perturbations. We estimated the best possible value for frictional resistance \u2018\u2018Arn\u2019\u2019, background seismicity rate \u2018\u2018r\u2019\u2019 and coef\ufb01cient of stress variation \u2018\u2018CV\u2019\u2019 using maximum log-likelihood method. For the whole Kashmir earthquake sequence, we measure a frictional resistance Arn * 0.0185 MPa, r * 20 M3.7? events/year and CV = 0.94 \ub1 0.01. The spatial and temporal forecasted seismicity rate of modeled aftershocks \ufb01ts well with the spatial and temporal distribution of observed aftershocks that occurred in the regions with positive static stress changes as well as in the apparent stress shadow region. To quantify the effect of secondary aftershock triggering, we have re-run the estimations for 100 stochastically declustered catalogs showing that the effect of aftershock-induced secondary stress changes is obviously minor compared to the overall uncertainties, and that the stress variability related to uncertain slip model inversions and receiver mechanisms remains the major factor to provide a reasonable data \ufb01t

Author Correction: 3D shear wave velocity model of the crust and uppermost mantle beneath the Tyrrhenian basin and margins

An amendment to this paper has been published and can be accessed via a link at the top of the pape

Spinal epidural angiolipoma causing spinal cord compression. A case report

adipose tissue and proliferating abnormal blood vessels, which result in spinal cord compression requiring an urgent surgical removal. We report a case of woman with spinal angiolipoma.Case presentation. The patient is a 26 years old woman with past medical history of a low grade urothelial bladder carcinoma removed 4 months before she consults at our department, 2 months later the patient presented a lower limbs weakness. The clinical exam at the admission found a patient with paraparesis, hypoesthesia at the level of Th4 and urinary urgency. The spinal MRI objectified a spinal cord compression by a lesion located at the epidural space from Th2 to Th4. The patient was operated and a fatty well vascularized tumour distinct from the epidural fat was removed through a Th2 to Th4 laminectomy. The pathology study was in favour of an angiolipoma. Days after the operation the patient recovered totally, the weakness and the urinary urgency disappeared. The patient is flowed since 24 months she got pregnant.Conclusion. Spinal angiolipoma is a rare tumour with a clinic of spinal cord compression, MRI is the gold standard in diagnosis it shows a fatty lesion with a large enhancement, surgery is the perfect treatment with good outcome and exceptional recurrence.adipose tissue and proliferating abnormal blood vessels, which result in spinal cord compression requiring an urgent surgical removal. We report a case of woman with spinal angiolipoma.Case presentation. The patient is a 26 years old woman with past medical history of a low grade urothelial bladder carcinoma removed 4 months before she consults at our department, 2 months later the patient presented a lower limbs weakness. The clinical exam at the admission found a patient with paraparesis, hypoesthesia at the level of Th4 and urinary urgency. The spinal MRI objectified a spinal cord compression by a lesion located at the epidural space from Th2 to Th4. The patient was operated and a fatty well vascularized tumour distinct from the epidural fat was removed through a Th2 to Th4 laminectomy. The pathology study was in favour of an angiolipoma. Days after the operation the patient recovered totally, the weakness and the urinary urgency disappeared. The patient is flowed since 24 months she got pregnant.Conclusion. Spinal angiolipoma is a rare tumour with a clinic of spinal cord compression, MRI is the gold standard in diagnosis it shows a fatty lesion with a large enhancement, surgery is the perfect treatment with good outcome and exceptional recurrence.INTRODUCTIO

Fourth order indirect integration method for black hole perturbations: even modes

On the basis of a recently proposed strategy of finite element integration in time domain for partial differential equations with a singular source term, we present a fourth order algorithm for non-rotating black hole perturbations in the Regge-Wheeler gauge. Herein, we address even perturbations induced by a particle plunging in. The forward time value at the upper node of the $(r^*,t)$ grid cell is obtained by an algebraic sum of i) the preceding node values of the same cell, ii) analytic expressions, related to the jump conditions on the wave function and its derivatives, iii) the values of the wave function at adjacent cells. In this approach, the numerical integration does not deal with the source and potential terms directly, for cells crossed by the particle world line. This scheme has also been applied to circular and eccentric orbits and it will be object of a forthcoming publication.Comment: This series of papers deals with EMRI for LISA. With the respect to the v1 version, the algorithm has been improved; convergence tests and references have been added; v2 is composed by 23 pages, and 6 figures. Paper accepted by Class. Quantum Gravity for the special issue on Theory Meets Data Analysis at Comparable and Extreme Mass Ratios (Capra and NRDA) at Perimeier Institute in June 201

Avoiding selection bias in gravitational wave astronomy

When searching for gravitational waves in the data from ground-based gravitational wave detectors it is common to use a detection threshold to reduce the number of background events which are unlikely to be the signals of interest. However, imposing such a threshold will also discard some real signals with low amplitude, which can potentially bias any inferences drawn from the population of detected signals. We show how this selection bias is naturally avoided by using the full information from the search, considering both the selected data and our ignorance of the data that are thrown away, and considering all relevant signal and noise models. This approach produces unbiased estimates of parameters even in the presence of false alarms and incomplete data. This can be seen as an extension of previous methods into the high false rate regime where we are able to show that the quality of parameter inference can be optimised by lowering thresholds and increasing the false alarm rate.Comment: 13 pages, 2 figure