Search results for "General relativity"
showing 10 items of 1057 documents
A relativistic approach to gravitational instability in the expanding Universe: second-order Lagrangian solutions
1994
A Lagrangian relativistic approach to the non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is considered. Solutions are given at second order in perturbation theory for the relevant fluid and geometric quantities and compared with the corresponding ones in the Newtonian approximation. Specifically, we compute the density, the volume expansion scalar, the shear, the ``electric" part, or tide, and the ``magnetic" part of the Weyl tensor. The evolution of the shear and the tide beyond the linear regime strongly depends on the ratio of the characteristic size of the perturbation to the cosmological horizon distance. For perturbations on sub--horizon scal…
On the algebraic types of the Bel–Robinson tensor
2008
The Bel-Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov-Bel classification of the Weyl tensor. The new classes correspond to degenerate type I space-times which have already been introduced in literature from another point of view. The Petrov-Bel types and the additional ones are intrinsically characterized in terms of the sole Bel-Robinson tensor, and an algorithm is proposed that enables the different classes to be distinguished. Results are presented that solve the problem of obtaining the Weyl tensor from the Bel-Robinson tensor in regular cases.
Two-Perfect Fluid Interpretation of an Energy Tensor
1990
The paper contains the necessary and sufficient conditions for a given energy tensor to be interpreted as a sum of two perfect fluids. Given a tensor of this class, the decomposition in two perfect fluids (which is determined up to a couple of real functions) is obtained.
The Athena X-ray Integral Field Unit: a consolidated design for the system requirement review of the preliminary definition phase
2023
The Athena X-ray Integral Unit (X-IFU) is the high resolution X-ray spectrometer, studied since 2015 for flying in the mid-30s on the Athena space X-ray Observatory, a versatile observatory designed to address the Hot and Energetic Universe science theme, selected in November 2013 by the Survey Science Committee. Based on a large format array of Transition Edge Sensors (TES), it aims to provide spatially resolved X-ray spectroscopy, with a spectral resolution of 2.5 eV (up to 7 keV) over an hexagonal field of view of 5 arc minutes (equivalent diameter). The X-IFU entered its System Requirement Review (SRR) in June 2022, at about the same time when ESA called for an overall X-IFU redesign (i…
GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
2017
On August 14, 2017 at 10 30:43 UTC, the Advanced Virgo detector and the two Advanced LIGO detectors coherently observed a transient gravitational-wave signal produced by the coalescence of two stellar mass black holes, with a false-alarm rate of 1 in 27 000 years. The signal was observed with a three-detector network matched-filter signal-to-noise ratio of 18. The inferred masses of the initial black holes are 30.5-3.0+5.7M and 25.3-4.2+2.8M (at the 90% credible level). The luminosity distance of the source is 540-210+130 Mpc, corresponding to a redshift of z=0.11-0.04+0.03. A network of three detectors improves the sky localization of the source, reducing the area of the 90% credible regio…
The overtone level spacing of a black hole quasinormal frequencies: a fingerprint of a local $SL(2,\mathbb{R})$ symmetry
2023
The imaginary part of the quasinormal frequencies spectrum for a static and spherically symmetric black hole is analytically known to be equally spaced, both for the highly damped and the weakly damped families of quasinormal modes. Some interesting attempts have been made in the last twenty years to understand in simple ways this level spacing for the only case of highly damped quasinormal frequencies. Here, we show that the overtone level spacing, for both the highly damped and weakly damped families of quasinormal modes, can simply be understood as a fingerprint of a hidden local $SL(2,\mathbb{R})$ symmetry, near different regions of the black hole spacetime, i.e. the near-horizon and th…
Painlevé-II approach to binary black hole merger dynamics: universality from integrability
2022
The binary black hole merger waveform is both simple and universal. Adopting an effective asymptotic description of the dynamics, we aim at accounting for such universality in terms of underlying (effective) integrable structures. More specifically, under a ``wave-mean flow'' perspective, we propose that fast degrees of freedom corresponding to the observed waveform would be subject to effective linear dynamics, propagating on a slowly evolving background subject to (effective) non-linear integrable dynamics. The Painlevé property of the latter would be implemented in terms of the so-called Painlevé-II transcendent, providing a structural link between i) orbital (in particular, EMRI) dynami…
Horizons in a binary black hole merger I: Geometry and area increase
2020
Recent advances in numerical relativity have revealed how marginally trapped surfaces behave when black holes merge. It is now known that interesting topological features emerge during the merger, and marginally trapped surfaces can have self-intersections. This paper presents the most detailed study yet of the physical and geometric aspects of this scenario. For the case of a head-on collision of non-spinning black holes, we study in detail the world tube formed by the evolution of marginally trapped surfaces. In the first of this two-part study, we focus on geometrical properties of the dynamical horizons, i.e. the world tube traced out by the time evolution of marginally outer trapped su…
On Einstein bilinear form
2012
From physical motivations and from geometrical interpretations of the Einstein equations, we give a justi cation of the non-triviality and non-degeneracy of Einstein bilinear form introduced in [1].
On the analytical expression of the multicompacton and some exact compact solutions of a nonlinear diffusive Burgers’type equation
2018
International audience; We consider the nonlinear diffusive Burgers' equation as a model equation for signals propagation on the nonlinear electrical transmission line with intersite nonlinearities. By applying the extend sine-cosine method and using an appropriate modification of the Double-Exp function method, we successfully derived on one hand the exact analytical solutions of two types of solitary waves with strictly finite extension or compact support: kinks and pulses, and on the other hand the exact solution for two interacting pulse solitary waves with compact support. These analytical results indicate that the speed of the pulse compactons doesn't depends explicitly on the pulse a…