74 research outputs found
Infinite slabs and other weird plane symmetric space-times with constant positive density
We present the exact solution of Einstein's equation corresponding to a
static and plane symmetric distribution of matter with constant positive
density located below . This solution depends essentially on two
constants: the density and a parameter . We show that this
space-time finishes down below at an inner singularity at finite depth. We
match this solution to the vacuum one and compute the external gravitational
field in terms of slab's parameters. Depending on the value of , these
slabs can be attractive, repulsive or neutral. In the first case, the
space-time also finishes up above at another singularity. In the other cases,
they turn out to be semi-infinite and asymptotically flat when .
We also find solutions consisting of joining an attractive slab and a
repulsive one, and two neutral ones. We also discuss how to assemble a
"gravitational capacitor" by inserting a slice of vacuum between two such
slabs.Comment: 8 page
Determination of "Best" Parameters in a General Linear Theory for Automatic Aircraft Control
Control Systems Laboratory changed its name to Coordinated Science LaboratoryContract DA-11-022-ORD-72
Reissner-Nordstrom and charged gas spheres
The main point of this paper is a suggestion about the proper treatment of
the photon gas in a theory of stellar structure and other plasmas. This problem
arises in the study of polytropic gas spheres, where we have already introduced
some innovations. The main idea, already advanced in the contextof neutral,
homogeneous, polytropic stellar models, is to base the theory firmly on a
variational principle. Another essential novelty is to let mass distribution
extend to infinity, the boundary between bulk and atmosphere being defined by
an abrupt change in the polytropic index, triggered by the density. The logical
next step in this program is to include the effect of radiation, which is a
very significant complication since a full treatment would have to include an
account of ionization, thus fieldsrepresenting electrons, ions, photons,
gravitons and neutral atoms as well. In way of preparation, we consider models
that are charged but homogeneous, involving only gravity, electromagnetism and
a single scalar field that represents both the mass and the electric charge; in
short, anon-neutral plasma. While this work only represents a stage in the
development of a theory of stars, without direct application to physical
systems, it does shed some light on the meaning of the Reissner-Nordstrom
solution of the modified Einstein-Maxwell equations., with an application to a
simple system.Comment: 19 pages, plain te
Ideal Stars and General Relativity
We study a system of differential equations that governs the distribution of
matter in the theory of General Relativity. The new element in this paper is
the use of a dynamical action principle that includes all the degrees of
freedom, matter as well as metric. The matter lagrangian defines a relativistic
version of non-viscous, isentropic hydrodynamics. The matter fields are a
scalar density and a velocity potential; the conventional, four-vector velocity
field is replaced by the gradient of the potential and its scale is fixed by
one of the eulerian equations of motion, an innovation that significantly
affects the imposition of boundary conditions. If the density is integrable at
infinity, then the metric approaches the Schwarzschild metric at large
distances. There are stars without boundary and with finite total mass; the
metric shows rapid variation in the neighbourhood of the Schwarzschild radius
and there is a very small core where a singularity indicates that the gas laws
break down. For stars with boundary there emerges a new, critical relation
between the radius and the gravitational mass, a consequence of the stronger
boundary conditions. Tentative applications are suggested, to certain Red
Giants, and to neutron stars, but the investigation reported here was limited
to polytropic equations of state. Comparison with the results of Oppenheimer
and Volkoff on neutron cores shows a close agreement of numerical results.
However, in the model the boundary of the star is fixed uniquely by the
required matching of the interior metric to the external Schwarzschild metric,
which is not the case in the traditional approach.Comment: 26 pages, 7 figure
Empty singularities in higher-dimensional Gravity
We study the exact solution of Einstein's field equations consisting of a
()-dimensional static and hyperplane symmetric thick slice of matter, with
constant and positive energy density and thickness , surrounded by
two different vacua. We explicitly write down the pressure and the external
gravitational fields in terms of and , the pressure is positive and
bounded, presenting a maximum at an asymmetrical position. And if
is small enough, the dominant energy condition is satisfied
all over the spacetime. We find that this solution presents many interesting
features. In particular, it has an empty singular boundary in one of the vacua.Comment: 13 page
Vacuum polarisation induced coupling between Maxwell and Kalb-Ramond Fields
We present here a manifestly gauge invariant calculation of vacuum
polarization to fermions in the presence of a constant Maxwell and a constant
Kalb-Ramond field in four dimensions. The formalism is a generalisation of the
one used by Schwinger in his famous paper on gauge invariance and vacuum
polarization. We get an explicit expression for the vacuum polarization induced
effective Lagrangian for a constant Maxwell field interacting with a constant
Kalb-Ramond field. In the weak field limit we get the coupling between the
Maxwell field and the Kalb-Ramond field to be , where
and is
the dual of .Comment: 16 pages, Revte
Lense-Thirring Precession in Pleba\'nski-Demia\'nski spacetimes
An exact expression of Lense-Thirring precession rate is derived for
non-extremal and extremal Pleba\'nski-Demia\'nski spacetimes. This formula is
used to find the exact Lense-Thirring precession rate in various axisymmetric
spacetimes, like: Kerr, Kerr-Newman, Kerr-de Sitter etc. We also show, if the
Kerr parameter vanishes in Pleba\'nski-Demia\'nski(PD) spacetime, the
Lense-Thirring precession does not vanish due to the existence of NUT charge.
To derive the LT precession rate in extremal Pleba\'nski-Demia\'nski we first
derive the general extremal condition for PD spacetimes. This general result
could be applied to get the extremal limit in any stationary and axisymmetric
spacetimes.Comment: 9 pages, Some special modifications are mad
On the Geometry of Planar Domain Walls
The Geometry of planar domain walls is studied. It is argued that the planar
walls indeed have plane symmetry. In the Minkowski coordinates the walls are
mapped into revolution paraboloids.Comment: 11 paghoj, Late
Evolution of high-frequency gravitational waves in some cosmological models
We investigate Isaacson's high-frequency gravitational waves which propagate
in some relevant cosmological models, in particular the FRW spacetimes. Their
time evolution in Fourier space is explicitly obtained for various metric forms
of (anti--)de Sitter universe. Behaviour of high-frequency waves in the
anisotropic Kasner spacetime is also described.Comment: 14 pages, 8 figures, to appear in Czech. J. Phy
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