82 research outputs found
An introduction to relativistic hydrodynamics
This lecture provides some introduction to perfect fluid dynamics within the
framework of general relativity. The presentation is based on the
Carter-Lichnerowicz approach. It has the advantage over the more traditional
approach of leading very straightforwardly to important conservation laws, such
as the relativistic generalizations of Bernoulli's theorem or Kelvin's
circulation theorem. It also permits to get easily first integrals of motion
which are particularly useful for computing equilibrium configurations of
relativistic stars in rotation or in binary systems. The presentation is
relatively self-contained and does not require any a priori knowledge of
general relativity. In particular, the three types of derivatives involved in
relativistic hydrodynamics are introduced in detail: this concerns the Lie,
exterior and covariant derivatives.Comment: 37 pages, 5 figures, lecture given at the School "Astrophysical Fluid
Dynamics" (Cargese, France, 9-13 May 2005) organized by B. Dubrulle & M.
Rieutord (EDP Sciences, in press
Models of rotating boson stars and geodesics around them: new type of orbits
We have developed a highly accurate numerical code capable of solving the
coupled Einstein-Klein-Gordon system, in order to construct rotating boson
stars in general relativity. Free fields and self-interacting fields, with
quartic and sextic potentials, are considered. In particular, we present the
first numerical solutions of rotating boson stars with rotational quantum
number and , as well as the first determination of the maximum mass
of free-field boson stars with . We have also investigated timelike
geodesics in the spacetime generated by a rotating boson star for ,
and . A numerical integration of the geodesic equation has enabled us to
identify a peculiar type of orbits: the zero-angular-momentum ones. These
orbits pass very close to the center and are qualitatively different from
orbits around a Kerr black hole. Should such orbits be observed, they would put
stringent constraints on astrophysical compact objects like the Galactic
center
Thermodynamics of magnetized binary compact objects
Binary systems of compact objects with electromagnetic field are modeled by
helically symmetric Einstein-Maxwell spacetimes with charged and magnetized
perfect fluids. Previously derived thermodynamic laws for helically-symmetric
perfect-fluid spacetimes are extended to include the electromagnetic fields,
and electric currents and charges; the first law is written as a relation
between the change in the asymptotic Noether charge \dl Q and the changes in
the area and electric charge of black holes, and in the vorticity, baryon rest
mass, entropy, charge and magnetic flux of the magnetized fluid. Using the
conservation laws of the circulation of magnetized flow found by Bekenstein and
Oron for the ideal magnetohydrodynamic (MHD) fluid, and also for the flow with
zero conducting current, we show that, for nearby equilibria that conserve the
quantities mentioned above, the relation \dl Q=0 is satisfied. We also
discuss a formulation for computing numerical solutions of magnetized binary
compact objects in equilibrium with emphasis on a first integral of the ideal
MHD-Euler equation.Comment: 21 pages, to appear in PR
Last orbits of binary black holes
Binary black hole systems in the pre-coalescence stage are numerically
constructed by demanding that the associated spacetime admits a helical Killing
vector. Comparison with third order post-Newtonian calculations indicates a
rather good agreement until the innermost stable circular orbit.Comment: 4 pages, 2 figures, invited talk at Journees Relativistes 2001, to
appear in International Journal of Modern Physics
Analytic black branes in Lifshitz-like backgrounds and thermalization
Using black brane solutions in 5d Lifshitz-like backgrounds with arbitrary
dynamical exponent , we construct the Vaidya geometry, asymptoting to the
Lifshitz-like spacetime, which represents a thin shell infalling at the speed
of light. We apply the new Lifshitz-Vaidya background to study the
thermalization process of the quark-gluon plasma via the thin shell approach
previously successfully used in several backgrounds. We find that the
thermalization depends on the chosen direction because of the spatial
anisotropy. The plasma thermalizes thus faster in the transversal direction
than in the longitudinal one. To probe the system described by the
Lifshitz-like backgrounds, we also calculate the holographic entanglement
entropy for the subsystems delineated along both transversal and longitudinal
directions. We show that the entropy has some universality in the behavior for
both subsystems. At the same time, we find that certain characteristics
strongly depend on the critical exponent .Comment: 39 pages, 23 figures; v3: typos corrected, references and
clarifications added, version published in JHE
Thermalization of holographic Wilson loops in spacetimes with spatial anisotropy
In this paper, we study behaviour of Wilson loops in the boost-invariant
nonequilibrium anisotropic quark-gluon plasma produced in heavy-ion collisions
within the holographic approach. We describe the thermalization studying the
evolution of the Vaidya metric in the boost-invariant and spatially anisotropic
background. To probe the system during this process we calculate rectangular
Wilson loops oriented in different spatial directions. We find that anisotropic
effects are more visible for the Wilson loops lying in the transversal plane
unlike the Wilson loops with partially longitudinal orientation. In particular,
we observe that the Wilson loops can thermalizes first unlike to the order of
the isotropic model. We see that Wilson loops on transversal contours have the
shortest thermalization time. We also calculate the string tension and the
pseudopotential at different temperatures for the static quark-gluon plasma. We
show that the pseudopotential related to the configuration on the transversal
plane has the screened Cornell form. We also show that the jet-quenching
parameter related with the average of the light-like Wilson loop exhibits the
dependence on orientations.Comment: 39 pages, 12 figures; v3: typos corrected, to appear in Nucl. Phys.
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