102 research outputs found
Symmetric hyperbolic systems for a large class of fields in arbitrary dimension
Symmetric hyperbolic systems of equations are explicitly constructed for a
general class of tensor fields by considering their structure as r-fold forms.
The hyperbolizations depend on 2r-1 arbitrary timelike vectors. The importance
of the so-called "superenergy" tensors, which provide the necessary symmetric
positive matrices, is emphasized and made explicit. Thereby, a unified
treatment of many physical systems is achieved, as well as of the sometimes
called "higher order" systems. The characteristics of these symmetric
hyperbolic systems are always physical, and directly related to the null
directions of the superenergy tensor, which are in particular principal null
directions of the tensor field solutions. Generic energy estimates and
inequalities are presented too.Comment: 24 pages, no figure
Algorithmic construction of static perfect fluid spheres
Perfect fluid spheres, both Newtonian and relativistic, have attracted
considerable attention as the first step in developing realistic stellar models
(or models for fluid planets). Whereas there have been some early hints on how
one might find general solutions to the perfect fluid constraint in the absence
of a specific equation of state, explicit and fully general solutions of the
perfect fluid constraint have only very recently been developed. In this
article we present a version of Lake's algorithm [Phys. Rev. D 67 (2003)
104015; gr-qc/0209104] wherein: (1) we re-cast the algorithm in terms of
variables with a clear physical meaning -- the average density and the locally
measured acceleration due to gravity, (2) we present explicit and fully general
formulae for the mass profile and pressure profile, and (3) we present an
explicit closed-form expression for the central pressure. Furthermore we can
then use the formalism to easily understand the pattern of inter-relationships
among many of the previously known exact solutions, and generate several new
exact solutions.Comment: Uses revtex4. V2: Minor clarifications, plus an additional section on
how to turn the algorithm into a solution generalization technique. This
version accepted for publication in Physical Review D. Now 7 page
Time transfer and frequency shift to the order 1/c^4 in the field of an axisymmetric rotating body
Within the weak-field, post-Newtonian approximation of the metric theories of
gravity, we determine the one-way time transfer up to the order 1/c^4, the
unperturbed term being of order 1/c, and the frequency shift up to the order
1/c^4. We adapt the method of the world-function developed by Synge to the
Nordtvedt-Will PPN formalism. We get an integral expression for the
world-function up to the order 1/c^3 and we apply this result to the field of
an isolated, axisymmetric rotating body. We give a new procedure enabling to
calculate the influence of the mass and spin multipole moments of the body on
the time transfer and the frequency shift up to the order 1/c^4. We obtain
explicit formulas for the contributions of the mass, of the quadrupole moment
and of the intrinsic angular momentum. In the case where the only PPN
parameters different from zero are beta and gamma, we deduce from these results
the complete expression of the frequency shift up to the order 1/c^4. We
briefly discuss the influence of the quadrupole moment and of the rotation of
the Earth on the frequency shifts in the ACES mission.Comment: 17 pages, no figure. Version 2. Abstract and Section II revised. To
appear in Physical Review
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
Absolute Stability Limit for Relativistic Charged Spheres
We find an exact solution for the stability limit of relativistic charged
spheres for the case of constant gravitational mass density and constant charge
density. We argue that this provides an absolute stability limit for any
relativistic charged sphere in which the gravitational mass density decreases
with radius and the charge density increases with radius. We then provide a
cruder absolute stability limit that applies to any charged sphere with a
spherically symmetric mass and charge distribution. We give numerical results
for all cases. In addition, we discuss the example of a neutral sphere
surrounded by a thin, charged shell.Comment: 25 pages, 1 figure 1 June 07: Replaced with added citations to prior
work along same line
On static shells and the Buchdahl inequality for the spherically symmetric Einstein-Vlasov system
In a previous work \cite{An1} matter models such that the energy density
and the radial- and tangential pressures and
satisfy were considered in the context of
Buchdahl's inequality. It was proved that static shell solutions of the
spherically symmetric Einstein equations obey a Buchdahl type inequality
whenever the support of the shell, satisfies
Moreover, given a sequence of solutions such that then the
limit supremum of was shown to be bounded by
In this paper we show that the hypothesis
that can be realized for Vlasov matter, by constructing a
sequence of static shells of the spherically symmetric Einstein-Vlasov system
with this property. We also prove that for this sequence not only the limit
supremum of is bounded, but that the limit is
since for Vlasov matter.
Thus, static shells of Vlasov matter can have arbitrary close to
which is interesting in view of \cite{AR2}, where numerical evidence is
presented that 8/9 is an upper bound of of any static solution of the
spherically symmetric Einstein-Vlasov system.Comment: 20 pages, Late
On Higher Order Gravities, Their Analogy to GR, and Dimensional Dependent Version of Duff's Trace Anomaly Relation
An almost brief, though lengthy, review introduction about the long history
of higher order gravities and their applications, as employed in the
literature, is provided. We review the analogous procedure between higher order
gravities and GR, as described in our previous works, in order to highlight its
important achievements. Amongst which are presentation of an easy
classification of higher order Lagrangians and its employment as a
\emph{criteria} in order to distinguish correct metric theories of gravity. For
example, it does not permit the inclusion of only one of the second order
Lagrangians in \emph{isolation}. But, it does allow the inclusion of the
cosmological term. We also discuss on the compatibility of our procedure and
the Mach idea. We derive a dimensional dependent version of Duff's trace
anomaly relation, which in \emph{four}-dimension is the same as the usual Duff
relation. The Lanczos Lagrangian satisfies this new constraint in \emph{any}
dimension. The square of the Weyl tensor identically satisfies it independent
of dimension, however, this Lagrangian satisfies the previous relation only in
three and four dimensions.Comment: 30 pages, added reference
New Black Hole Solutions in Brans-Dicke Theory of Gravity
Existence check of non-trivial, stationary axisymmetric black hole solutions
in Brans-Dicke theory of gravity in different direction from those of Penrose,
Thorne and Dykla, and Hawking is performed. Namely, working directly with the
known explicit spacetime solutions in Brans-Dicke theory, it is found that
non-trivial Kerr-Newman-type black hole solutions different from general
relativistic solutions could occur for the generic Brans-Dicke parameter values
-5/2\leq \omega <-3/2. Finally, issues like whether these new black holes carry
scalar hair and can really arise in nature and if they can, what the associated
physical implications would be are discussed carefully.Comment: 20 pages, no figure, Revtex, version to appear in Phys. Rev.
General Static Solutions of 2-dimensional Einstein-Dilaton-Maxwell-Scalar Theories
General static solutions of effectively 2-dimensional
Einstein-Dilaton-Maxwell-Scalar theories are obtained. Our model action
includes a class of 2-d dilaton gravity theories coupled with a gauge
field and a massless scalar field. Therefore it also describes the spherically
symmetric reduction of -dimensional Einstein-Scalar-Maxwell theories. The
properties of the analytic solutions are briefly discussed.Comment: 16 pages, Latex fil
Compact anisotropic spheres with prescribed energy density
New exact interior solutions to the Einstein field equations for anisotropic
spheres are found. We utilise a procedure that necessitates a choice for the
energy density and the radial pressure. This class contains the constant
density model of Maharaj and Maartens (Gen. Rel. Grav., Vol 21, 899-905, 1989)
and the variable density model of Gokhroo and Mehra (Gen. Rel. Grav., Vol 26,
75-84, 1994) as special cases. These anisotropic spheres match smoothly to the
Schwarzschild exterior and gravitational potentials are well behaved in the
interior. A graphical analysis of the matter variables is performed which
points to a physically reasonable matter distribution.Comment: 22 pages, 3 figures, to appear in Gen. Rel. Gra
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