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

Black Hole Entropy is Noether Charge

We consider a general, classical theory of gravity in $n$ dimensions, arising from a diffeomorphism invariant Lagrangian. In any such theory, to each vector field, $\xi^a$, on spacetime one can associate a local symmetry and, hence, a Noether current $(n-1)$-form, ${\bf j}$, and (for solutions to the field equations) a Noether charge $(n-2)$-form, ${\bf Q}$. 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 $2 \pi$ times the integral over $\Sigma$ of the Noether charge $(n-2)$-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

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

Eternal Black Holes in AdS

We propose a dual non-perturbative description for maximally extended Schwarzschild Anti-de-Sitter spacetimes. The description involves two copies of the conformal field theory associated to the AdS spacetime and an initial entangled state. In this context we also discuss a version of the information loss paradox and its resolution.Comment: v4: New section added on black holes with only one asymptotic boundary, v5,6: More references adde

Wnt signalling and cancer stem cells

[Abstract] Intracellular signalling mediated by secreted Wnt proteins is essential for the establishment of cell fates and proper tissue patterning during embryo development and for the regulation of tissue homeostasis and stem cell function in adult tissues. Aberrant activation of Wnt signalling pathways has been directly linked to the genesis of different tumours. Here, the components and molecular mechanisms implicated in the transduction of Wnt signal, along with important results supporting a central role for this signalling pathway in stem cell function regulation and carcinogenesis will be briefly reviewed.Ministerio de Ciencia e Innovación; SAF2008-0060