5,227 research outputs found
Stars creating a gravitational repulsion
In the framework of the Theory of General Relativity, models of stars with an
unusual equation of state where is the mass density
and is the pressure, are constructed. These objects create outside
themselves the forces of gravitational repulsion. The equilibrium of such stars
is ensured by a non-standard balance of forces. Negative mass density, acting
gravitationally on itself, creates an acceleration of the negative mass,
directed from the center. Therefore in the absence of pressure such an object
tends to expand. At the same time, the positive pressure, which falls just like
in ordinary stars from the center to the surface, creates a force directed from
the center. This force acts on the negative mass density, which causes
acceleration directed the opposite of the acting force, that is to the center
of the star. This acceleration balances the gravitational repulsion produced by
the negative mass. Thus, in our models gravity and pressure change roles: the
negative mass tends to create a gravitational repulsion, while the gradient of
the pressure acting on the negative mass tends to compress the star. In this
paper, we construct several models of such a star with various equations of
state.Comment: 6 pages, 4 figure
Topology of quasiperiodic functions on the plane
The article describes a topological theory of quasiperiodic functions on the
plane. The development of this theory was started (in different terminology) by
the Moscow topology group in early 1980s. It was motivated by the needs of
solid state physics, as a partial (nongeneric) case of Hamiltonian foliations
of Fermi surfaces with multivalued Hamiltonian function. The unexpected
discoveries of their topological properties that were made in 1980s and 1990s
have finally led to nontrivial physical conclusions along the lines of the
so-called geometric strong magnetic field limit. A very fruitful new point of
view comes from the reformulation of that problem in terms of quasiperiodic
functions and an extension to higher dimensions made in 1999. One may say that,
for single crystal normal metals put in a magnetic field, the semiclassical
trajectories of electrons in the space of quasimomenta are exactly the level
lines of the quasiperiodic function with three quasiperiods that is the
dispersion relation restricted to a plane orthogonal to the magnetic field.
General studies of the topological properties of levels of quasiperiodic
functions on the plane with any number of quasiperiods were started in 1999
when certain ideas were formulated for the case of four quasiperiods. The last
section of this work contains a complete proof of these results. Some new
physical applications of the general problem were found recently.Comment: latex2e, 27 pages, 7 figure
Time machines and the Principle of Self-Consistency as a consequence of the Principle of Stationary Action (II): the Cauchy problem for a self-interacting relativistic particle
We consider the action principle to derive the classical, relativistic motion
of a self-interacting particle in a 4-D Lorentzian spacetime containing a
wormhole and which allows the existence of closed time-like curves. In
particular, we study the case of a pointlike particle subject to a
`hard-sphere' self-interaction potential and which can traverse the wormhole an
arbitrary number of times, and show that the only possible trajectories for
which the classical action is stationary are those which are globally
self-consistent. Generically, the multiplicity of these trajectories (defined
as the number of self-consistent solutions to the equations of motion beginning
with given Cauchy data) is finite, and it becomes infinite if certain
constraints on the same initial data are satisfied. This confirms the previous
conclusions (for a non-relativistic model) by Echeverria, Klinkhammer and
Thorne that the Cauchy initial value problem in the presence of a wormhole
`time machine' is classically `ill-posed' (far too many solutions). Our results
further extend the recent claim by Novikov et al. that the `Principle of
self-consistency' is a natural consequence of the `Principle of minimal
action.'Comment: 39 pages, latex fil
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