771 research outputs found
Static spherically symmetric perfect fluid solutions in theories of gravity
Static spherically symmetric perfect fluid solutions are studied in metric
theories of gravity. We show that pressure and density do not uniquely
determine ie. given a matter distribution and an equation state, one
cannot determine the functional form of . However, we also show that
matching the outside Schwarzschild-de Sitter-metric to the metric inside the
mass distribution leads to additional constraints that severely limit the
allowed fluid configurations.Comment: 5 page
Degrees and segments
I make two related proposals, one about directed scale segments and the other about the nature of degrees. Bale (2007, 2011) argued that degrees should be analyzed as sets of individuals and that degree arguments are created in the syntax from relational predicates. Schwarz (2010) showed that Bale’s construction runs into problems when the required degree relation is complex, denoted by an LF constituent that contains more than just a gradable adjective. I modify Bale’s proposal so that it overcomes Schwarz’s objection. But first I propose a semantics for comparatives based on quantification over directed scale segments, triples consisting of two degrees and a measure function. The modification of Bale’s proposal depends upon this. Segments are of independent interest as they permit a conjunctive semantics for extended adjectival phrases, the way events do for verb phrases. Potential benefits of ‘degree-conjunctivism’ are explored
Partitives and duratives
Champollion detects similarities in the interpretation of three seemingly unrelated forms: partitives, measure adverbials and distributivity operators.
Stratified reference is a high level description of the unique meaning component that lies at the core of these similarities. It was helpful for me to think of ‘stratified reference’ as having the same type of status as ‘maximality’ which is implicated in the interpretation of definite descriptions, degree constructions, interrogatives and elsewhere. Converging on a single statement with which to describe the meanings of diverse forms enables us, as Champollion puts it, to link problems.
Mereological parts make up the domains of quantification for stratified
reference statements. I inquire here about the nature of the quantification:
what kind of quantificational force do we want?, how might the parthood
relation be restricted? and are there constraints on the size of the domain of quantification? I’ve come to appreciate Champollion’s mechanism by taking it apart and trying to put it back together with a few pieces missing. I hope the reader is able to learn something from this exercise. My comments are exclusively directed toward Section 2 Aspect and Section 3 Measurement (sometimes referred to below with the symbols ‘C.§2’, ‘C.§3’ respectively)
Dynamics of the Fisher Information Metric
We present a method to generate probability distributions that correspond to
metrics obeying partial differential equations generated by extremizing a
functional , where is the
Fisher metric. We postulate that this functional of the dynamical variable
is stationary with respect to small variations of these
variables. Our approach enables a dynamical approach to Fisher information
metric. It allows to impose symmetries on a statistical system in a systematic
way. This work is mainly motivated by the entropy approach to nonmonotonic
reasoning.Comment: 11 page
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
Removing black-hole singularities with nonlinear electrodynamics
We propose a way to remove black hole singularities by using a particular
nonlinear electrodynamics Lagrangian that has been recently used in various
astrophysics and cosmological frameworks. In particular, we adapt the
cosmological analysis discussed in a previous work to the black hole physics.
Such analysis will be improved by applying the Oppenheimer-Volkoff equation to
the black hole case. At the end, fixed the radius of the star, the final
density depends only on the introduced quintessential density term
and on the mass.Comment: In this last updated version we correct two typos which were present
in Eqs. (21) and (22) in the version of this letter which has been published
in Mod. Phys. Lett. A 25, 2423-2429 (2010). In the present version, both of
Eqs. (21) and (22) are dimensionally and analytically correc
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
Gravity of a static massless scalar field and a limiting Schwarzschild-like geometry
We study a set of static solutions of the Einstein equations in presence of a
massless scalar field and establish their connection to the Kantowski-Sachs
cosmological solutions based on some kind of duality transformations. The
physical properties of the limiting case of an empty hyperbolic spacetime
(pseudo-Schwarzschild geometry) are analyzed in some detail.Comment: 13 pages, 4 figure
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