Geometric dynamics of calcium oscillations ODEs systems.
Geometrical and topological structure of magnetic fields generated by rectilinear wires.
Geometrical interpretation of solutions of certain PDEs.
Geometrical modeling of material aging.
Geometrodynamics of wormholes
Gli universi ipersferici, il gruppo conforme ed il campo gravitazionale di Newton.
Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case
Global Waves with Non-Positive Energy in General Relativity
2000 Mathematics Subject Classification: 35Lxx, 35Pxx, 81Uxx, 83Cxx.The theory of the waves equations has a long history since M. Riesz and J. Hadamard. It is impossible to cite all the important results in the area, but we mention the authors related with our work: J. Leray [34] and Y. Choquet-Bruhat [9] (Cauchy problem), P. Lax and R. Phillips [33] (scattering theory for a compactly supported perturbation), L. H¨ ormander [27] and J-M. Bony [7] (microlocal analysis). In all these domains, V. Petkov has...
Gravitational ionization : periodic orbits of binary systems perturbed by gravitational radiation
Gravitational lensing from a spacetime perspective.
Gravitational radiation from accreting neutron stars
Neutron stars may emit steady gravitational wave signals that will be among the first kinds of gravitational wave signals that the new generation of interferometric detectors will search for. I consider here the possibility that accreting neutron stars may be driven into the steady emission of gravitational waves. I estimate the amplitudes that the waves may have if the accretion takes place at the Eddington limit, such as may happen when a neutron star spirals inside a giant star in the endphase...
Gravitational scattering of electromagnetic field by Schwarzschild black-hole
Gravitational waveforms from spinning objects
According to general relativity, a binary consisting of spinning bodies will precess due to spin-orbit and spin-spin coupling. The corresponding modulation of its gravitational waves might be a serious problem for detecting such waves with simple post-Newtonian templates. A new family of templates that takes into account the complications arising from the orbital precession is proposed and its application and performance are discussed.
Gravitational waves from coalescing binaries: a hierarchical signal detection strategy
The detection of gravitational waves from coalescing compact binaries would be a computationally intensive process if a single bank of template waveforms (i.e., a one step search) is used. We present, in this paper, an alternative method which is a hierarchical search strategy involving two template banks. We show that the computational power required by such a two step search, for an on-line detection of the one parameter family of Newtonian signals, is 1/8 of that required when an on-line one...
Gravitational-wave data analysis. Formalism and sample applications: the Gaussian Case.
Gravity, strings, modular and quasimodular forms
Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in the description of non-perturbative effects, in higher-order corrections of scalar-field spaces, ...The latter often appear as gravitational instantons i.e. as special solutions of Einstein’s equations. In the present lecture notes we present a class of such solutions in four dimensions, obtained by...
Groupes conformes en relativité générale
Hidden symmetries of the gravitational contact structure of the classical phase space of general relativistic test particle
The phase space of general relativistic test particle is defined as the 1-jet space of motions. A Lorentzian metric defines the canonical contact structure on the odd-dimensional phase space. In the paper we study infinitesimal symmetries of the gravitational contact phase structure which are not generated by spacetime infinitesimal symmetries, i.e. they are hidden symmetries. We prove that Killing multivector fields admit hidden symmetries of the gravitational contact phase structure and we give...
Homogeneous systems of higher-order ordinary differential equations
The concept of homogeneity, which picks out sprays from the general run of systems of second-order ordinary differential equations in the geometrical theory of such equations, is generalized so as to apply to equations of higher order. Certain properties of the geometric concomitants of a spray are shown to continue to hold for higher-order systems. Third-order equations play a special role, because a strong form of homogeneity may apply to them. The key example of a single third-order equation...
Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times