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

A source-free integration method for black hole perturbations and self-force computation: Radial fall

Perturbations of Schwarzschild-Droste black holes in the Regge-Wheeler gauge benefit from the availability of a wave equation and from the gauge invariance of the wave function, but lack smoothness. Nevertheless, the even perturbations belong to the C\textsuperscript{0} continuity class, if the wave function and its derivatives satisfy specific conditions on the discontinuities, known as jump conditions, at the particle position. These conditions suggest a new way for dealing with finite element integration in time domain. The forward time value in the upper node of the $(t, r^*$) grid cell is obtained by the linear combination of the three preceding node values and of analytic expressions based on the jump conditions. The numerical integration does not deal directly with the source term, the associated singularities and the potential. This amounts to an indirect integration of the wave equation. The known wave forms at infinity are recovered and the wave function at the particle position is shown. In this series of papers, the radial trajectory is dealt with first, being this method of integration applicable to generic orbits of EMRI (Extreme Mass Ratio Inspiral).Comment: This arXiv version differs from the one to be published by Phys. Rev. D for the use of British English and other minor editorial difference

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

Postseismic deformation and body forces shaping the Apennines and adjacent sedimentary basins in Umbria-Marche

The geodynamic complexity of the Apennines and adjacent sedimentary basins in Umbria-Marche (North-Central Italy) makes the dynamics of the present day deformation and its relationships with the seismicity less well understood. In this paper, we argue that, further to buoyancy forces, postseismic deformation of earthquakes taking place on the Apennines contributes to the regional deformation. We investigate the interaction between the normal faulting system responsible of the 1997 Umbria-Marche earthquake sequence (Colfiorito fault) and the low angle normal faulting system bordering the sedimentary basins, namely the Altotiberina fault. We set-up a 2D finite element model of the lithosphere-asthenosphere accounting for lateral heterogeneities and investigate how this heterogeneous structure is capable of localizing strain under the Umbria-Marche sedimentary basins, providing a way for the Colfiorito fault to influence the evolution of the Altotiberina fault. We show how the two different length and time scale processes, namely postseismic deformation and buoyancy, are complementary in shaping the Apennines and adjacent sedimentary basins. The high resolution deformation patterns modeled in this study can hardly be reproduced by a model accounting only for external forces such as a rotating or subducting or retreating Adria

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