66 research outputs found
Innermost stable circular orbits around magnetized rotating massive stars
In 1998, Shibata and Sasaki [Phys. Rev. D 58, 104011 (1998)] presented an
approximate analytical formula for the radius of the innermost stable circular
orbit (ISCO) of a neutral test particle around a massive, rotating and deformed
source. In the present paper, we generalize their expression by including the
magnetic dipole moment. We show that our approximate analytical formulas are
accurate enough by comparing them with the six-parametric exact solution
calculated by Pach\'on et. al. [Phys. Rev. D 73, 104038 (2006)] along with the
numerical data presented by Berti and Stergioulas [MNRAS 350, 1416 (2004)] for
realistic neutron stars. As a main result, we find that in general, the radius
at ISCO exhibits a decreasing behavior with increasing magnetic field. However,
for magnetic fields below 100GT the variation of the radius at ISCO is
negligible and hence the non-magnetized approximate expression can be used. In
addition, we derive approximate analytical formulas for angular velocity,
energy and angular momentum of the test particle at ISCO.Comment: 8 pages, 3 figure
Approaches to the Monopole-Dynamic Dipole Vacuum Solution Concerning the Structure of its Ernst's Potential on the Symmetry Axis
The FHP algorithm allows to obtain the relativistic multipole moments of a
vacuum stationary axisymmetric solution in terms of coefficients which appear
in the expansion of its Ernst's potential on the symmetry axis. First of all,
we will use this result in order to determine, at a certain approximation
degree, the Ernst's potential on the symmetry axis of the metric whose only
multipole moments are mass and angular momentum.
By using Sibgatullin's method we analyse a series of exacts solutions with
the afore mentioned multipole characteristic. Besides, we present an
approximate solution whose Ernst's potential is introduced as a power series of
a dimensionless parameter. The calculation of its multipole moments allows us
to understand the existing differences between both approximations to the
proposed pure multipole solution.Comment: 24 pages, plain TeX. To be published in General Relativity and
Gravitatio
From geodesics of the multipole solutions to the perturbed Kepler problem
A static and axisymmetric solution of the Einstein vacuum equations with a
finite number of Relativistic Multipole Moments (RMM) is written in MSA
coordinates up to certain order of approximation, and the structure of its
metric components is explicitly shown. From the equation of equatorial
geodesics we obtain the Binet equation for the orbits and it allows us to
determine the gravitational potential that leads to the equivalent classical
orbital equations of the perturbed Kepler problem. The relativistic corrections
to Keplerian motion are provided by the different contributions of the RMM of
the source starting from the Monopole (Schwarzschild correction). In
particular, the perihelion precession of the orbit is calculated in terms of
the quadrupole and 2-pole moments. Since the MSA coordinates generalize the
Schwarzschild coordinates, the result obtained allows measurement of the
relevance of the quadrupole moment in the first order correction to the
perihelion frequency-shift
The Dynamical Behaviour of Test Particles in a Quasi-Spherical Spacetime and the Physical Meaning of Superenergy
We calculate the instantaneous proper radial acceleration of test particles
(as measured by a locally defined Lorentzian observer) in a Weyl spacetime,
close to the horizon. As expected from the Israel theorem, there appear some
bifurcations with respect to the spherically symmetric case (Schwarzschild),
which are explained in terms of the behaviour of the superenergy, bringing out
the physical relevance of this quantity in the study of general relativistic
systems.Comment: 14 pages, Latex. 4 figures. New references added. Typos corrected. To
appear in Int. J. Theor. Phy
Thermal Conduction in Systems out of Hydrostatic Equilibrium
We analyse the effects of thermal conduction in a relativistic fluid, just
after its departure from hydrostatic equilibrium, on a time scale of the order
of thermal relaxation time. It is obtained that the resulting evolution will
critically depend on a parameter defined in terms of thermodynamic variables,
which is constrained by causality requirements.Comment: 16 pages, emTex (LaTex 2.09). To appear in Classical and Quantum
Gravit
How can exact and approximate solutions of Einstein's field equations be compared?
The problem of comparison of the stationary axisymmetric vacuum solutions
obtained within the framework of exact and approximate approaches for the
description of the same general relativistic systems is considered. We suggest
two ways of carrying out such comparison: (i) through the calculation of the
Ernst complex potential associated with the approximate solution whose form on
the symmetry axis is subsequently used for the identification of the exact
solution possessing the same multipole structure, and (ii) the generation of
approximate solutions from exact ones by expanding the latter in series of
powers of a small parameter. The central result of our paper is the derivation
of the correct approximate analogues of the double-Kerr solution possessing the
physically meaningful equilibrium configurations. We also show that the
interpretation of an approximate solution originally attributed to it on the
basis of some general physical suppositions may not coincide with its true
nature established with the aid of a more accurate technique.Comment: 32 pages, 5 figure
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