170 research outputs found
Pseudo-Schwarzschild Spherical Accretion as a Classical Black Hole Analogue
We demonstrate that a spherical accretion onto astrophysical black holes,
under the influence of Newtonian or various post-Newtonian pseudo-Schwarzschild
gravitational potentials, may constitute a concrete example of classical
analogue gravity naturally found in the Universe. We analytically calculate the
corresponding analogue Hawking temperature as a function of the minimum number
of physical parameters governing the accretion flow. We study both the
polytropic and the isothermal accretion. We show that unlike in a general
relativistic spherical accretion, analogue white hole solutions can never be
obtained in such post-Newtonian systems. We also show that an isothermal
spherical accretion is a remarkably simple example in which the only one
information--the temperature of the fluid, is sufficient to completely describe
an analogue gravity system. For both types of accretion, the analogue Hawking
temperature may become higher than the usual Hawking temperature. However, the
analogue Hawking temperature for accreting astrophysical black holes is
considerably lower compared with the temperature of the accreting fluid.Comment: Final Version to appear in the journal General Relativity &
Gravitation, Volume 27, Issue 11, 2005. 17 pages, Two colour and one black
and white figures. Typos corrected. Recent reference on analogue effect in
relativistic accretion disc adde
Black holes and Hawking radiation in spacetime and its analogues
These notes introduce the fundamentals of black hole geometry, the thermality
of the vacuum, and the Hawking effect, in spacetime and its analogues.
Stimulated emission of Hawking radiation, the trans-Planckian question, short
wavelength dispersion, and white hole radiation in the setting of analogue
models are also discussed. No prior knowledge of differential geometry, general
relativity, or quantum field theory in curved spacetime is assumed.Comment: 31 pages, 9 figures; to appear in the proceedings of the IX SIGRAV
School on 'Analogue Gravity', Como (Italy), May 2011, eds. D. Faccio et. al.
(Springer
The Irreducible Spine(s) of Undirected Networks
Using closure concepts, we show that within every undirected network, or
graph, there is a unique irreducible subgraph which we call its "spine". The
chordless cycles which comprise this irreducible core effectively characterize
the connectivity structure of the network as a whole. In particular, it is
shown that the center of the network, whether defined by distance or
betweenness centrality, is effectively contained in this spine. By counting the
number of cycles of length 3 <= k <= max_length, we can also create a kind of
signature that can be used to identify the network. Performance is analyzed,
and the concepts we develop are illurstrated by means of a relatively small
running sample network of about 400 nodes.Comment: Submitted to WISE 201
Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
We consider a general, classical theory of gravity with arbitrary matter
fields in dimensions, arising from a diffeomorphism invariant Lagrangian,
\bL. We first show that \bL always can be written in a ``manifestly
covariant" form. We then show that the symplectic potential current
-form, , and the symplectic current -form, \om, for the
theory always can be globally defined in a covariant manner. Associated with
any infinitesimal diffeomorphism is a Noether current -form, \bJ, and
corresponding Noether charge -form, \bQ. We derive a general
``decomposition formula" for \bQ. Using this formula for the Noether charge,
we prove that the first law of black hole mechanics holds for arbitrary
perturbations of a stationary black hole. (For higher derivative theories,
previous arguments had established this law only for stationary perturbations.)
Finally, we propose a local, geometrical prescription for the entropy,
, of a dynamical black hole. This prescription agrees with the Noether
charge formula for stationary black holes and their perturbations, and is
independent of all ambiguities associated with the choices of \bL, , and
\bQ. However, the issue of whether this dynamical entropy in general obeys a
``second law" of black hole mechanics remains open. In an appendix, we apply
some of our results to theories with a nondynamical metric and also briefly
develop the theory of stress-energy pseudotensors.Comment: 30 pages, LaTe
Black Hole Entropy is Noether Charge
We consider a general, classical theory of gravity in dimensions, arising
from a diffeomorphism invariant Lagrangian. In any such theory, to each vector
field, , on spacetime one can associate a local symmetry and, hence, a
Noether current -form, , and (for solutions to the field
equations) a Noether charge -form, . Assuming only that the
theory admits stationary black hole solutions with a bifurcate Killing horizon,
and that the canonical mass and angular momentum of solutions are well defined
at infinity, we show that the first law of black hole mechanics always holds
for perturbations to nearby stationary black hole solutions. The quantity
playing the role of black hole entropy in this formula is simply times
the integral over of the Noether charge -form associated with
the horizon Killing field, normalized so as to have unit surface gravity.
Furthermore, we show that this black hole entropy always is given by a local
geometrical expression on the horizon of the black hole. We thereby obtain a
natural candidate for the entropy of a dynamical black hole in a general theory
of gravity. Our results show that the validity of the ``second law" of black
hole mechanics in dynamical evolution from an initially stationary black hole
to a final stationary state is equivalent to the positivity of a total Noether
flux, and thus may be intimately related to the positive energy properties of
the theory. The relationship between the derivation of our formula for black
hole entropy and the derivation via ``Euclidean methods" also is explained.Comment: 16 pages, EFI 93-4
A synthesis of carbon dioxide emissions from fossil-fuel combustion
This synthesis discusses the emissions of carbon dioxide from fossil-fuel combustion and cement production. While much is known about these emissions, there is still much that is unknown about the details surrounding these emissions. This synthesis explores our knowledge of these emissions in terms of why there is concern about them; how they are calculated; the major global efforts on inventorying them; their global, regional, and national totals at different spatial and temporal scales; how they are distributed on global grids (i.e., maps); how they are transported in models; and the uncertainties associated with these different aspects of the emissions. The magnitude of emissions from the combustion of fossil fuels has been almost continuously increasing with time since fossil fuels were first used by humans. Despite events in some nations specifically designed to reduce emissions, or which have had emissions reduction as a byproduct of other events, global total emissions continue their general increase with time. Global total fossil-fuel carbon dioxide emissions are known to within 10 % uncertainty (95 % confidence interval). Uncertainty on individual national total fossil-fuel carbon dioxide emissions range from a few percent to more than 50 %. This manuscript concludes that carbon dioxide emissions from fossil-fuel combustion continue to increase with time and that while much is known about the overall characteristics of these emissions, much is still to be learned about the detailed characteristics of these emissions
Linking the trans-Planckian and the information loss problems in black hole physics
The trans-Planckian and information loss problems are usually discussed in
the literature as separate issues concerning the nature of Hawking radiation.
Here we instead argue that they are intimately linked, and can be understood as
"two sides of the same coin" once it is accepted that general relativity is an
effective field theory.Comment: 10 pages, 2 figures. Replaced with the version to be published in
General Relativity and Gravitatio
Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems
We determine explicit orbit representatives of reducible Jordan algebras and
of their corresponding Freudenthal triple systems. This work has direct
application to the classification of extremal black hole solutions of N = 2, 4
locally supersymmetric theories of gravity coupled to an arbitrary number of
Abelian vector multiplets in D = 4, 5 space-time dimensions.Comment: 18 pages. Updated to match published versio
Lorentz breaking Effective Field Theory and observational tests
Analogue models of gravity have provided an experimentally realizable test
field for our ideas on quantum field theory in curved spacetimes but they have
also inspired the investigation of possible departures from exact Lorentz
invariance at microscopic scales. In this role they have joined, and sometime
anticipated, several quantum gravity models characterized by Lorentz breaking
phenomenology. A crucial difference between these speculations and other ones
associated to quantum gravity scenarios, is the possibility to carry out
observational and experimental tests which have nowadays led to a broad range
of constraints on departures from Lorentz invariance. We shall review here the
effective field theory approach to Lorentz breaking in the matter sector,
present the constraints provided by the available observations and finally
discuss the implications of the persisting uncertainty on the composition of
the ultra high energy cosmic rays for the constraints on the higher order,
analogue gravity inspired, Lorentz violations.Comment: 47 pages, 4 figures. Lecture Notes for the IX SIGRAV School on
"Analogue Gravity", Como (Italy), May 2011. V.3. Typo corrected, references
adde
Density correlations and dynamical Casimir emission of Bogoliubov phonons in modulated atomic Bose-Einstein condensates
We present a theory of the density correlations that appear in an atomic
Bose-Einstein condensate as a consequence of the dynamical Casimir emission of
pairs of Bogoliubov phonons when the atom-atom scattering length is modulated
in time. Different regimes as a function of the temporal shape of the
modulation are identified and a simple physical picture of the phenomenon is
discussed. Analytical expressions for the density correlation function are
provided for the most significant limiting cases. This theory is able to
explain some unexpected features recently observed in numerical calculations of
Hawking radiation from analog black holes
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