State independence for tunneling processes through black hole horizons and Hawking radiation

Tunneling processes through black hole horizons have recently been investigated in the framework of WKB theory discovering interesting interplay with the Hawking radiation. In this paper we instead adopt the point of view proper of QFT in curved spacetime, namely, we use a suitable scaling limit technique to obtain the leading order of the correlation function related with some tunneling process through a Killing horizon. The computation is done for certain large class of reference quantum states for scalar fields. In the limit of sharp localization either on the external side or on opposite sides of the horizon, the quantum correlation functions appear to have thermal nature, where in both cases the characteristic temperature is the Hawking one. Our approach is valid for every stationary charged rotating non extremal black hole, however, since the computation is completely local, it covers the case of a Killing horizon which just temporarily exists in some finite region too. These results give a strong support to the idea that the Hawking radiation, which is detected at future infinity and needs some global structures to be defined, is actually related to a local phenomenon taking place even for local geometric structures (local Killing horizons) existing just for a while.Comment: 19 pages, one figure, some comments added, minor errors corrected, accepted for publication in Communications in Mathematical Physic

Holography and Conformal Symmetry near black hole horizons

We show here how it is possible to build a QFT on the horizon of a Schwarzschild-like spacetime. That theory, found by restricting bulk quantum elds on the horizon, is equivalent to QFT on the bulk. That fact is called Holography. Moreover the hidden conformal symmetry (SL(2;R)) found for the bulk theory becomes manifest on the horizon in terms of some of its dieomorphisms. Then the extension of group of the generator of that symmetry to the Virasoro algebra is discussed

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

The discovery of the radiation properties of black holes prompted the search for a natural candidate quantum ground state for a massless scalar field theory on Schwarzschild spacetime, here considered in the Eddington-Finkelstein representation. Among the several available proposals in the literature, an important physical role is played by the so-called Unruh state which is supposed to be appropriate to capture the physics of a black hole formed by spherically symmetric collapsing matter. Within this respect, we shall consider a massless Klein-Gordon field and we shall rigorously and globally construct such state, that is on the algebra of Weyl observables localised in the union of the static external region, the future event horizon and the non-static black hole region. Eventually, out of a careful use of microlocal techniques, we prove that the built state fulfils, where defined, the so-called Hadamard condition; hence, it is perturbatively stable, in other words realizing the natural candidate with which one could study purely quantum phenomena such as the role of the back reaction of Hawking's radiation. From a geometrical point of view, we shall make a profitable use of a bulk-to-boundary reconstruction technique which carefully exploits the Killing horizon structure as well as the conformal asymptotic behaviour of the underlying background. From an analytical point of view, our tools will range from Hormander's theorem on propagation of singularities, results on the role of passive states, and a detailed use of the recently discovered peeling behaviour of the solutions of the wave equation in Schwarzschild spacetime.Comment: 63 pages, 3 figure

Hadamard States From Light-like Hypersurfaces

This book provides a rather self-contained survey of the construction of Hadamard states for scalar field theories in a large class of notable spacetimes, possessing a (conformal) light-like boundary. The first two sections focus on explaining a few introductory aspects of this topic and on providing the relevant geometric background material. The notions of asymptotically flat spacetimes and of expanding universes with a cosmological horizon are analysed in detail, devoting special attention to the characterization of asymptotic symmetries. In the central part of the book, the quantization of a real scalar field theory on such class of backgrounds is discussed within the framework of algebraic quantum field theory. Subsequently it is explained how it is possible to encode the information of the observables of the theory in a second, ancillary counterpart, which is built directly on the conformal (null) boundary. This procedure, dubbed bulk-to-boundary correspondence, has the net advantage of allowing the identification of a distinguished state for the theory on the boundary, which admits a counterpart in the bulk spacetime which is automatically of Hadamard form. In the last part of the book, some applications of these states are discussed, in particular the construction of the algebra of Wick polynomials. This book is aimed mainly, but not exclusively, at a readership with interest in the mathematical formulation of quantum field theory on curved backgrounds.Comment: 106 pages, 2 figures, to appear in SpringerBriefs in Mathematical Physics, references adde

Quantum Virasoro algebra with central charge c=1 on the horizon of a 2D-Rindler spacetime

Using the holographic machinery built up in a previous work, we show that the hidden SL(2,R) symmetry of a scalar quantum field propagating in a Rindler spacetime admits an enlargement in terms of a unitary positive-energy representation of Virasoro algebra, with central charge c=1, defined in the Fock representation. The Virasoro algebra of operators gets a manifest geometrical meaning if referring to the holographically associated QFT on the horizon: It is nothing but a representation of the algebra of vector fields defined on the horizon equipped with a point at infinity. All that happens provided the Virasoro ground energy h vanishes and, in that case, the Rindler Hamiltonian is associated with a certain Virasoro generator. If a suitable regularization procedure is employed, for h=1/2, the ground state of that generator corresponds to thermal states when examined in the Rindler wedge, taking the expectation value with respect to Rindler time. This state has inverse temperature 1/(2beta), where beta is the parameter used to define the initial SL(2,R) unitary representation. (As a consequence the restriction of Minkowski vacuum to Rindler wedge is obtained by fixing h=1/2 and 2beta=beta_U, the latter being Unruh's inverse temperature). Finally, under Wick rotation in Rindler time, the pair of QF theories which are built up on the future and past horizon defines a proper two-dimensional conformal quantum field theory on a cylinder.Comment: 35 pages, 1 figure .eps, LaTeX 2e, minor changes, accepted for publication in J.Math.Phy

Black Hole Horizons and Thermodynamics: A Quantum Approach

We focus on quantization of the metric of a black hole restricted to the Killing horizon with universal radius $r_0$. After imposing spherical symmetry and after restriction to the Killing horizon, the metric is quantized employing the chiral currents formalism. Two ``components of the metric'' are indeed quantized: The former behaves as an affine scalar field under changes of coordinates, the latter is instead a proper scalar field. The action of the symplectic group on both fields is realized in terms of certain horizon diffeomorphisms. Depending on the choice of the vacuum state, such a representation is unitary. If the reference state of the scalar field is a coherent state rather than a vacuum, spontaneous breaking of conformal symmetry arises and the state contains a Bose-Einstein condensate. In this case the order parameter fixes the actual size of the black hole with respect to $r_0$. Both the constructed state together with the one associated with the affine scalar are thermal states (KMS) with respect to Schwarzschild Killing time when restricted to half horizon. The value of the order parameter fixes the temperature at the Hawking value as well. As a result, it is found that the quantum energy and entropy densities coincide with the black hole mass and entropy, provided the universal parameter $r_0$ is suitably chosen, not depending on the size of the actual black hole in particular.Comment: 21 pages, revised and published version, title change

Holography and SL(2,\bR) symmetry in 2D Rindler spacetime

It is shown that it is possible to define quantum field theory of a massless scalar free field on the Killing horizon of a 2D-Rindler spacetime. Free quantum field theory on the horizon enjoys diffeomorphism invariance and turns out to be unitarily and algebraically equivalent to the analogous theory of a scalar field propagating inside Rindler spacetime, nomatter the value of the mass of the field in the bulk. More precisely, there exists a unitary transformation that realizes the bulk-boundary correspondence under an appropriate choice for Fock representation spaces. Secondly, the found correspondence is a subcase of an analogous algebraic correspondence described by injective *-homomorphisms of the abstract algebras of observables generated by abstract quantum free-field operators. These field operators are smeared with suitable test functions in the bulk and exact 1-forms on the horizon. In this sense the correspondence is independent from the chosen vacua. It is proven that, under that correspondence the ``hidden'' SL(2,\bR) quantum symmetry found in a previous work gets a clear geometric meaning, it being associated with a group of diffeomorphisms of the horizon itself.Comment: Title changed, further minor changes, references added, accepted for publication in J. Math. Phy

Streamlined management of the built environment: the district and the building logbook as risk prevention tools

Management of information related to the real properties is a key topic both in private and public sector. In the Italian context, can be spotted an overall lack of organisation of the information concerning the real estate assets, from the building scale, to the neighbourhood, until the city and the territory. Moreover, management of the urban environment is characterised by the presence of different players asking for common needs in management and use of data. This research aims at proposing the Building Logbook and the District Logbook as tools for collection, organisation and management of information, in a perspective of streamlined real estate management process. Moreover, the Logbooks can be conceived as tools for risk management. They should be exploited especially in technical management phase of assets, as well as in the verification of compliance with laws, authorisations and licenses, since these issues often bear to disputes between public and private players. Often disputes concern that areas where the competences and responsibilities among different players are not clear (connections to system, property boundaries, licenses, occupation of public land etc.). In this situations, information management assumes a key role, since it could be a powerful mean to clarify responsibilities among players. Therefore, the scope of the research concerns the investigation on the relationships and related information flows among stakeholders in the real estate field. Altogether, it can be stated that the logbooks can streamline processes in the use phase of assets, despite they could be intended as rigid control tools. Through this paper these issues will deepened and clarified. The paper concludes with some considerations concerning the possible integration of the Logbooks in a digital environment, following the BIM approach

Hospitalization for COPD in Puglia: the role of hospital discharge database to estimate prevalence and incidence

Background and aim. Chronic Obstructive Pulmonary Disease (COPD), although largely preventable, is a great health burden in all the countries worldwide. Statistics of morbidity and mortality of COPD show the need for correct management of the disease. Chronic Obstructive Respiratory Diseases (DRG 88) are in 9th place for discharge in in-patient hospital admission. It is necessary to establish specific indicators which are efficacious and relevant for the patient, the doctor and the health manager. This study will analyse the information in respect of hospital admissions (Hospital discharge database) in Puglia for the period 2000-2005. Methods. The analysis was carried out utilising the Puglia Region hospital patient discharge database, selecting those patients with admission for chronic respiratory disease as principal or secondary diagnosis. Results. Chronic respiratory diseases are more frequent in males and in people over 45 years old with frequency increasing with age. Geographical distribution shows that there are greater rates of hospitalisation in big cities and in the neighbourhood of industrial areas. Although the trend over time is slight. A higher percentage of re-admission has been found for patients with COPD, and the interval between the two admissions occurs within one or two months; the diagnosis at the second admission is the same as for the first. 10.6% of discharge forms report one diagnosis, especially in patients older than 65 years of age. Little could be said about diagnostic procedures because these are not reported on the discharge form. Conclusion. Hospitalisation data confirms expectations regarding age and sex of patients. The high hospitalisation rates indicate that in-patients care still remains the only viable treatment for COPD and other chronic respiratory diseases. The high number of exacerbations reflect the absence of out-patients service or community care, and the same diagnosis in more than one episode shows the lack of efficiency of health services and disease management. This data is necessary to understand disease distribution and the modification of disease management in order to reduce health care costs, to increase efficacy in disease control and to limit repeated exacerbation and so to obtain the maximum benefit for the patients