67 research outputs found
Charge Fluctuations of a Schwarzschild Black-Hole
In this paper we calculate charge fluctuations of a Schwarzschild black-hole
of mass in thermal equilibrium with radiation and an electron-positron
plasma confined within a vessel of radius R. We show that charge fluctuations
are always present, even if the black-hole is neutral and the overall charge of
the system vanishes. Furthermore, if the system becomes unstable
under charge fluctuations. Surprisingly enough, besides the expected
thermodynamical black hole charge fluctuation that result from the fluctuations
on the number of charge carriers, there are other contributions to the overall
charge fluctuation of the black-hole which, against our intuition, do not
depend upon the charge of the particles. We conjecture that one of the
contributions is an intrinsic purely quantum mechanical fluctuation of the
black-hole itself as it does not depend on any of the control parameters,
namely the radius of the confining cavity nor the temperature of the system,
and even not upon the mass or charge of the particles
Quantum Limitations on the Storage and Transmission of Information
Information must take up space, must weigh, and its flux must be limited.
Quantum limits on communication and information storage leading to these
conclusions are here described. Quantum channel capacity theory is reviewed for
both steady state and burst communication. An analytic approximation is given
for the maximum signal information possible with occupation number signal
states as a function of mean signal energy. A theorem guaranteeing that these
states are optimal for communication is proved. A heuristic "proof" of the
linear bound on communication is given, followed by rigorous proofs for signals
with specified mean energy, and for signals with given energy budget. And
systems of many parallel quantum channels are shown to obey the linear bound
for a natural channel architecture. The time--energy uncertainty principle is
reformulated in information language by means of the linear bound. The quantum
bound on information storage capacity of quantum mechanical and quantum field
devices is reviewed. A simplified version of the analytic proof for the bound
is given for the latter case. Solitons as information caches are discussed, as
is information storage in one dimensional systems. The influence of signal
self--gravitation on communication is considerd. Finally, it is shown that
acceleration of a receiver acts to block information transfer.Comment: Published relatively inaccessible review on a perennially interesting
subject. Plain TeX, 47 pages, 5 jpg figures (not embedded
Hamiltonian Map to Conformal Modification of Spacetime Metric: Kaluza-Klein and TeVeS
It has been shown that the orbits of motion for a wide class of
nonrelativistic Hamiltonian systems can be described as geodesic flows on a
manifold and an associated dual. This method can be applied to a four
dimensional manifold of orbits in spacetime associated with a relativistic
system. We show that a relativistic Hamiltonian which generates Einstein
geodesics, with the addition of a world scalar field, can be put into
correspondence with another Hamiltonian with conformally modified metric. Such
a construction could account for part of the requirements of Bekenstein for
achieving the MOND theory of Milgrom in the post-Newtonian limit. The
constraints on the MOND theory imposed by the galactic rotation curves, through
this correspondence, would then imply constraints on the structure of the world
scalar field. We then use the fact that a Hamiltonian with vector gauge fields
results, through such a conformal map, in a Kaluza-Klein type theory, and
indicate how the TeVeS structure of Bekenstein and Sanders can be put into this
framework. We exhibit a class of infinitesimal gauge transformations on the
gauge fields which preserve the Bekenstein-Sanders condition
. The underlying quantum structure giving rise
to these gauge fields is a Hilbert bundle, and the gauge transformations induce
a non-commutative behavior to the fields, i.e., they become of Yang-Mills type.
Working in the infinitesimal gauge neighborhood of the initial Abelian theory,
we show that in the Abelian limit the Yang-Mills field equations provide
nonlinear terms which may avoid the caustic singularity found by Contaldi, et
al.Comment: Plain TeX, 8 pages. Proceedings of Conference of International
Association for Relativistic Dynamics, Thessaloniki, Greece, June 2008.
Revision includes discussion of field norm preserving gauge on Hilbert bundle
and nonlinear contributions to field equations in Abelian limi
The gravitational Vavilov-Cherenkov effect
In this essay we show that an uncharged black-hole moving superluminally in a
transparent dielectric medium violates Hawking's area theorem. The violation is
overcome through the emission of radiation. Since modes cannot emerge from the
black hole itself, this radiation must originate from a collective effect in
the medium, in complete analogy with the Vavilov-Cherenkov effect. However,
because the black-hole is uncharged, the emission mechanism must be different.
We discuss the physical origin of the effect and obtain a Newtonian estimative.
Then we obtain the appropriate equations in the relativistic case and show that
the field which is radiated away is a combination of gravitational and
electromagnetic degrees of freedom. Possible astrophysical relevance for the
detection of primordial black-holes and binary systems is discussed.Comment: 9 pages, Honorable Mention from the Gravity Research Foundation, 199
On the geometry of Hamiltonian chaos
We show that Gutzwiller's characterization of chaotic Hamiltonian systems in
terms of the curvature associated with a Riemannian metric tensor in the
structure of the Hamiltonian can be extended to a wide class of potential
models of standard form through definition of a conformal metric. The geodesic
equations reproduce the Hamilton equations of the original potential model when
a transition is made to the dual manifold, and the geodesics in the dual space
coincide with the orbits of the Hamiltonian potential model. We therefore find
a direct geometrical description of the time development of a Hamiltonian
potential model. The second covariant derivative of the geodesic deviation in
this dual manifold generates a dynamical curvature, resulting in (energy
dependent) criteria for unstable behavior different from the usual Lyapunov
criteria. We discuss some examples of unstable Hamiltonian systems in two
dimensions giving, in particular, detailed results for a potential obtained
from a fifth order expansion of a Toda lattice Hamiltonian.Comment: 7 pages TeX, Figure captions, 4 figures (eps). Some clarifications,
added reference
Bound states due to an accelerated mirror
We discuss an effect of accelerated mirrors which remained hitherto
unnoticed, the formation of a field condensate near its surface for massive
fields. From the view point of an observer attached to the mirror, this is
effect is rather natural because a gravitational field is felt there. The
novelty here is that since the effect is not observer dependent even inertial
observers will detect the formation of this condensate. We further show that
this localization is in agreement with Bekenstein's entropy bound.Comment: Final version to appear in PR
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