2,328 research outputs found
Necessary and sufficient condition for hydrostatic equilibrium in general relativity
We present explicit examples to show that the `compatibility criterion' is
capable of providing a {\em necessary} and {\em sufficient} condition for any
regular configuration to be compatible with the state of hydrostatic
equilibrium. This conclusion is drawn on the basis of the finding that the
relation gives the necessary and sufficient condition for dynamical
stability of equilibrium configurations only when the compatibility criterion
for these configurations is appropriately satisfied. In this regard, we
construct an appropriate sequence composed of core-envelope models on the basis
of compatibility criterion, such that each member of this sequence satisfies
the extreme case of causality condition at the centre. The maximum
stable value of (which occurs for the model corresponding to
the maximum value of mass in the mass-radius relation) and the corresponding
central value of the local adiabatic index, , of
this model are found fully consistent with those of the corresponding {\em
absolute} values, , and ,
which impose strong constraints on these parameters of such models. In addition
to this example, we also study dynamical stability of pure adiabatic polytropic
configurations on the basis of variational method for the choice of the `trial
function', , as well as the mass-central density relation,
since the compatibility criterion is appropriately satisfied for these models.
The results of this example provide additional proof in favour of the statement
regarding compatibility criterion mentioned above.Comment: 31 pages (double-spaced) revtex style, 1 figure in `ps' forma
Dynamical stability of strange quark stars
We show that the mass-radius
relation corresponding to the MIT bag models of strange quark matter
(SQM) and the models obtained by Day et al (1998) do not provide the necessary
and sufficient condition for dynamical stability for the equilibrium
configurations, since such configurations can not even fulfill the necessary
condition of hydrostatic equilibrium provided by the exterior Schwarzschild
solution. These findings will remain unaltered and can be extended to any other
sequence of pure SQM. This study explicitly show that although the strange
quark matter might exist in the state of zero pressure and temperature, but the
models of pure strange quark `stars' can not exist in the state of hydrostatic
equilibrium on the basis of General Relativity Theory. This study can affect
the results which are claiming that various objects like - RX J1856.5-3754, SAX
J1808.4-3658, 4U 1728-34, PSR 0943+10 etc. might be strange stars.Comment: 7 pages (including 6 tables and 1 figure) in MNRAS styl
Hydrostatic equilibrium of insular, static, spherically symmetric, perfect fluid solutions in general relativity
An analysis of insular solutions of Einstein's field equations for static,
spherically symmetric, source mass, on the basis of exterior Schwarzschild
solution is presented. Following the analysis, we demonstrate that the {\em
regular} solutions governed by a self-bound (that is, the surface density does
not vanish together with pressure) equation of state (EOS) or density variation
can not exist in the state of hydrostatic equilibrium, because the source mass
which belongs to them, does not represent the `actual mass' appears in the
exterior Schwarzschild solution. The only configuration which could exist in
this regard is governed by the homogeneous density distribution (that is, the
interior Schwarzschild solution). Other structures which naturally fulfill the
requirement of the source mass, set up by exterior Schwarzschild solution (and,
therefore, can exist in hydrostatic equilibrium) are either governed by
gravitationally-bound regular solutions (that is, the surface density also
vanishes together with pressure), or self-bound singular solutions (that is,
the pressure and density both become infinity at the centre).Comment: 16 pages (including 1 table); added section 5; accepted for
publication in Modern Physics Letters
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