69 research outputs found
Does Pressure Increase or Decrease Active Gravitational Mass Density?
It is known that, for a static fluid sphere, the GeneralRelativistic (GR)
Effective Mass Energy Density (EMD) appears to be (rho + 3 p), where rho is the
bare mass density, p is the isotropic pressure, from a purely localized view
point. But since there is no truly local definition of ``gravitational field'',
such a notion could actually be misleading. On the other hand, by using the
Tolman mass formula, we point out that, from a global perspective, the Active
Gravitational Mass Energy Density (AGMD) is sqrt{g_{00}} (rho + 3 p) and which
is obviously smaller than (rho + 3p) because g_{00} < 1. Then we show that the
AGMD eventually is (rho - 3p), i.e., exactly opposite to what is generally
believed. We further identify the AGMD to be proportional to the Ricci Scalar.
By using this fundamental and intersting property, we obtain the GR virial
theorem in terms of appropriate ``proper energies''.Comment: The originally accepted journal version, subsequent modifications
remove
General Relativistic Stars : Polytropic Equations of State
In this paper, the gravitational field equations for static spherically
symmetric perfect fluid models with a polytropic equation of state,
, are recast into two complementary 3-dimensional {\it
regular} systems of ordinary differential equations on compact state spaces.
The systems are analyzed numerically and qualitatively, using the theory of
dynamical systems. Certain key solutions are shown to form building blocks
which, to a large extent, determine the remaining solution structure. In one
formulation, there exists a monotone function that forces the general
relativistic solutions towards a part of the boundary of the state space that
corresponds to the low pressure limit. The solutions on this boundary describe
Newtonian models and thus the relationship to the Newtonian solution space is
clearly displayed. It is numerically demonstrated that general relativistic
models have finite radii when the polytropic index satisfies and infinite radii when . When ,
there exists a 1-parameter set of models with finite radii and a finite number,
depending on , with infinite radii.Comment: 31 pages, 10 figure
The Stability of an Isentropic Model for a Gaseous Relativistic Star
We show that the isentropic subclass of Buchdahl's exact solution for a
gaseous relativistic star is stable and gravitationally bound for all values of
the compactness ratio , where is the total mass and is
the radius of the configuration in geometrized units] in the range, , corresponding to the {\em regular} behaviour of the solution. This
result is in agreement with the expectation and opposite to the earlier claim
found in the literature.Comment: 9 pages (including 1 table); accepted for publication in GR
Approximate analytic expressions for circular orbits around rapidly rotating compact stars
We calculate stationary configurations of rapidly rotating compact stars in
general relativity, to study the properties of circular orbits of test
particles in the equatorial plane. We search for simple, but precise,
analytical formulae for the orbital frequency, specific angular momentum and
binding energy of a test particle, valid for any equation of state and for any
rotation frequency of the rigidly rotating compact star, up to the
mass-shedding limit. Numerical calculations are performed using precise 2-D
codes based on multi-domain spectral methods. Models of rigidly rotating
neutron stars and the space-time outside them are calculated for several
equations of state of dense matter. Calculations are also performed for quark
stars consisting of self-bound quark matter. At the mass-shedding limit, the
rotational frequency converges to a Schwarzschildian orbital frequency at the
equator. We show that orbital frequency for any orbit outside equator is also
approximated by a Schwarzschildian formula. Using a simple approximation for
the frame-dragging term, we obtain approximate expressions for the specific
angular momentum and specific energy on the corotating circular orbits in the
equatorial plane of neutron star, which are valid down to the stellar equator.
The formulae recover reference numerical values with typically 1% of accuracy
for neutron stars with M > 0.5 M_sun. They are less precise for quark stars
consisting of self-bound quark matter.Comment: 6 pages, 6 figures, A&A in pres
Gaussian integration with rescaling of abscissas and weights
An algorithm for integration of polynomial functions with variable weight is
considered. It provides extension of the Gaussian integration, with appropriate
scaling of the abscissas and weights. Method is a good alternative to usually
adopted interval splitting.Comment: 14 pages, 5 figure
Generalized Fermi-Dirac Functions and Derivatives: Properties and Evaluation
The generalized Fermi-Dirac functions and their derivatives are important in
evaluating the thermodynamic quantities of partially degenerate electrons in
hot dense stellar plasmas. New recursion relations of the generalized
Fermi-Dirac functions have been found. An effective numerical method to
evaluate the derivatives of the generalized Fermi-Dirac functions up to third
order with respect to both degeneracy and temperature is then proposed,
following Aparicio. A Fortran program based on this method, together with a
sample test case, is provided. Accuracy and domain of reliability of some
other, popularly used analytic approximations of the generalized Fermi-Dirac
functions for extreme conditions are investigated and compared with our
results.Comment: accepted for publication in Comp. Phys. Com
Gravitational instability of finite isothermal spheres in general relativity. Analogy with neutron stars
We investigate the effects of relativity on the gravitational instability of
finite isothermal gaseous spheres. In the first part of the paper, we treat the
gravitational field within the framework of Newtonian mechanics but we use a
relativistic equation of state in the condition of hydrostatic equilibrium. In
the second part of the paper, we study the full general relativistic problem
for a gas described by an equation of state such that the
pressure is proportional to the energy density (``isothermal'' distribution).
For , this equation of state describes the core of neutron stars. The
mass-density diagram displays some damped oscillations and there exists a
critical value of mass-energy above which no equilibrium state is possible. We
show analytically that the mass peaks are associated with new modes of
instability. These results are strikingly similar to those obtained by Antonov
[Vest. Leningr. Gos. Univ. 7, 135 (1962)] and Lynden-Bell & Wood (1968) for a
classical isothermal gas. Our study completes the analogy between isothermal
spheres and neutron stars investigated by Yabushita [MNRAS 167, 95 (1974)].Comment: Submitted to Astron. Astrophy
Excitation of the odd-parity quasi-normal modes of compact objects
The gravitational radiation generated by a particle in a close unbounded
orbit around a neutron star is computed as a means to study the importance of
the modes of the neutron star. For simplicity, attention is restricted to
odd parity (``axial'') modes which do not couple to the neutron star's fluid
modes. We find that for realistic neutron star models, particles in unbounded
orbits only weakly excite the modes; we conjecture that this is also the
case for astrophysically interesting sources of neutron star perturbations. We
also find that for cases in which there is significant excitation of quadrupole
modes, there is comparable excitation of higher multipole modes.Comment: 18 pages, 21 figures, submitted to Phys. Rev.
Truncated post-Newtonian neutron star model
As a preliminary step towards simulating binary neutron star coalescing
problem, we test a post-Newtonian approach by constructing a single neutron
star model. We expand the Tolman-Oppenheimer-Volkov equation of hydrostatic
equilibrium by the power of , where is the speed of light, and
truncate at the various order. We solve the system using the polytropic
equation of state with index and 3, and show how this
approximation converges together with mass-radius relations. Next, we solve the
Hamiltonian constraint equation with these density profiles as trial functions,
and examine the differences in the final metric. We conclude the second
`post-Newtonian' approximation is close enough to describe general relativistic
single star. The result of this report will be useful for further binary
studies.
(Note to readers) This paper was accepted for publication in Physical Review
D. [access code dsj637]. However, since I was strongly suggested that the
contents of this paper should be included as a section in our group's future
paper, I gave up the publication.Comment: 5 pages, RevTeX, 3 eps figs, epsf.sty, accepted for publication in
PRD (Brief Report), but will not appea
Phase transitions in rotating neutron stars cores: back bending, stability, corequakes and pulsar timing
The back-bending phenomenon for compact stars is studied by means of
analytical equations of state, for both constant-pressure phase transitions and
the transitions through the mixed-phase region. We restrict ourselves to the
case of normal rotating configurations, with baryon mass below the maximum
allowable baryon mass for non-rotating stars. We use high-precision 2-D
multi-domain spectral code LORENE to search the parameter space for possible
instability regions, and possible changes in the stability character of
rotating stars with phase transitions in their cores. Conditions on the density
jump in constant-pressure phase transitions, leading to the existence of the
unstable segments in the evolutionary sequences of spinning down isolated
normal neutron stars, are derived. Conjectures concerning the existence of two
disjoint families of non-rotating and rotating stationary configurations of
neutron stars are formulated. Particular case of EOSs leading to marginal
instability of static and rotating configurations is also studied: marginal
instability point in non-rotating configurations continues to exist in all
evolutionary spin-down tracks. The fate of rotating stars entering the region
of instability is discussed. The change in radius, energy release, and spin-up
associated with the corequake in rotating neutron star, triggered by the
instability, are calculated. The energy release is found to be very weakly
dependent on the angular momentum of collapsing star.Comment: 13 pages, 15 figures, accepted by A&
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