Studies on Thermodynamics and No-hair Theorem in Black hole Spacetime

Department of Physics, Cochin University of Science and Technology

Conformal structures and twistors in the paravector model of spacetime

Some properties of the Clifford algebras Cl-3,Cl-0, Cl-1,Cl-3, Cl-4,Cl-1 similar or equal to C circle times Cl-1,Cl-3 and Cl-2,Cl-4 are presented, and three isomorphisms between the Dirac-Clifford algebra C circle times Cl-1,Cl-3 and Cl-4,Cl-1 are exhibited, in order to construct conformal maps and twistors, using the paravector model of spacetime. The isomorphism between the twistor space inner product isometry group SU( 2,2) and the group $pin(+)(2,4) is also investigated, in the light of a suitable isomorphism between C circle times Cl-1,Cl-3 and Cl-4,Cl-1. After reviewing the conformal spacetime structure, conformal maps are described in Minkowski spacetime as the twisted adjoint representation of $ pin(+)(2,4), acting on paravectors. Twistors are then presented via the paravector model of Clifford algebras and related to conformal maps in the Clifford algebra over the Lorentzian R-4,(1) spacetime.We construct twistors in Minkowski spacetime as algebraic spinors associated with the Dirac-Clifford algebra C circle times Cl-1,Cl-3 using one lower spacetime dimension than standard Clifford algebra formulations, since for this purpose, the Clifford algebra over R-4,R-1 is also used to describe conformal maps, instead of R-2,(4). Our formalism sheds some new light on the use of the paravector model and generalizations.

The catastrophic flash-flood event of 8–9 September 2002 in the Gard region, France: a first case study for the Cévennes–Vivarais Mediterranean Hydrometeorological Observatory

The Cévennes–Vivarais Mediterranean Hydrometeorological Observatory (OHM-CV) is a research initiative aimed at improving the understanding and modeling of the Mediterranean intense rain events that frequently result in devastating flash floods in southern France. A primary objective is to bring together the skills of meteorologists and hydrologists, modelers and instrumentalists, researchers and practitioners, to cope with these rather unpredictable events. In line with previously published flash-flood monographs, the present paper aims at documenting the 8–9 September 2002 catastrophic event, which resulted in 24 casualties and an economic damage evaluated at 1.2 billion euros (i.e., about 1 billion U.S. dollars) in the Gard region, France. A description of the synoptic meteorological situation is first given and shows that no particular precursor indicated the imminence of such an extreme event. Then, radar and rain gauge analyses are used to assess the magnitude of the rain event, which was particularly remarkable for its spatial extent with rain amounts greater than 200 mm in 24 h over 5500 km2. The maximum values of 600–700 mm observed locally are among the highest daily records in the region. The preliminary results of the postevent hydrological investigation show that the hydrologic response of the upstream watersheds of the Gard and Vidourle Rivers is consistent with the marked space–time structure of the rain event. It is noteworthy that peak specific discharges were very high over most of the affected areas (5–10 m3 s−1 km−2) and reached locally extraordinary values of more than 20 m3 s−1 km−2. A preliminary analysis indicates contrasting hydrological behaviors that seem to be related to geomorphological factors, notably the influence of karst in part of the region. An overview of the ongoing meteorological and hydrological research projects devoted to this case study within the OHM-CV is finally presented.

Sostanzialismo e relazionalismo dello spaziotempo alla luce della relatività generale

Until recently the debate on the ontology of spacetime had only a philosophical significance, since, from a physical point of view, General Relativity has been made "immune" to the consequences of the "Hole Argument" simply by reducing the subject to the assertion that solutions of Einstein equations which are mathematically different and related by an active diffeomorfism are physically equivalent. From a technical point of view, the natural reading of the consequences of the "Hole Argument” has always been to go further and say that the mathematical representation of spacetime in General Relativity inevitably contains a “superfluous structure” brought to light by the gauge freedom of the theory. This position of apparent split between the philosophical outcome and the physical one has been corrected thanks to a meticulous and complicated formal analysis of the theory in a fundamental and recent (2006) work by Luca Lusanna and Massimo Pauri entitled “Explaining Leibniz equivalence as difference of non-inertial appearances: dis-solution of the Hole Argument and physical individuation of point-events”. The main result of this article is that of having shown how, from a physical point of view, point-events of Einstein empty spacetime, in a particular class of models considered by them, are literally identifiable with the autonomous degrees of freedom of the gravitational field (the Dirac observables, DO). In the light of philosophical considerations based on realism assumptions of the theories and entities, the two authors then conclude by saying that spacetime point-events have a degree of "weak objectivity", since they, depending on a NIF (non-inertial frame), unlike the points of the homogeneous newtonian space, are plunged in a rich and complex non-local holistic structure provided by the “ontic part” of the metric field. Therefore according to the complex structure of spacetime that General Relativity highlights and within the declared limits of a methodology based on a Galilean scientific representation, we can certainly assert that spacetime has got "elements of reality", but the inevitably relational elements that are in the physical detection of point-events in the vacuum of matter (highlighted by the “ontic part” of the metric field, the DO) are closely dependent on the choice of the global spatiotemporal laboratory where the dynamics is expressed (NIF). According to the two authors, a peculiar kind of structuralism takes shape: the point structuralism, with common features both of the absolutist and substantival tradition and of the relationalist one. The intention of this thesis is that of proposing a method of approaching the problem that is, at least at the beginning, independent from the previous ones, that is to propose an approach based on the possibility of describing the gravitational field at three distinct levels. In other words, keeping the results achieved by the work of Lusanna and Pauri in mind and following their underlying philosophical assumptions, we intend to partially converge to their structuralist approach, but starting from what we believe is the "foundational peculiarity" of General Relativity, which is that characteristic inherent in the elements that constitute its formal structure: its essentially geometric nature as a theory considered regardless of the empirical necessity of the measure theory. Observing the theory of General Relativity from this perspective, we can find a "triple modality" for describing the gravitational field that is essentially based on a geometric interpretation of the spacetime structure. The gravitational field is now "visible" no longer in terms of its autonomous degrees of freedom (the DO), which, in fact, do not have a tensorial and, therefore, nor geometric nature, but it is analyzable through three levels: a first one, called the potential level (which the theory identifies with the components of the metric tensor), a second one, known as the connections level (which in the theory determine the forces acting on the mass and, as such, offer a level of description related to the one that the newtonian gravitation provides in terms of components of the gravitational field) and, finally, a third level, that of the Riemann tensor, which is peculiar to General Relativity only. Focusing from the beginning on what is called the "third level" seems to present immediately a first advantage: to lead directly to a description of spacetime properties in terms of gauge-invariant quantites, which allows to "short circuit" the long path that, in the treatises analyzed, leads to identify the "ontic part” of the metric field. It is then shown how to this last level it is possible to establish a “primitive level of objectivity” of spacetime in terms of the effects that matter exercises in extended domains of spacetime geometrical structure; these effects are described by invariants of the Riemann tensor, in particular of its irreducible part: the Weyl tensor. The convergence towards the affirmation by Lusanna and Pauri that the existence of a holistic, non-local and relational structure from which the properties quantitatively identified of point-events depend (in addition to their own intrinsic detection), even if it is obtained from different considerations, is realized, in our opinion, in the assignment of a crucial role to the degree of curvature of spacetime that is defined by the Weyl tensor even in the case of empty spacetimes (as in the analysis conducted by Lusanna and Pauri). In the end, matter, regarded as the physical counterpart of spacetime curvature, whose expression is the Weyl tensor, changes the value of this tensor even in spacetimes without matter. In this way, going back to the approach of Lusanna and Pauri, it affects the DOs evolution and, consequently, the physical identification of point-events (as our authors claim). In conclusion, we think that it is possible to see the holistic, relational, and non-local structure of spacetime also through the "behavior" of the Weyl tensor in terms of the Riemann tensor. This "behavior" that leads to geometrical effects of curvature is characterized from the beginning by the fact that it concerns extensive domains of the manifold (although it should be pointed out that the values of the Weyl tensor change from point to point) by virtue of the fact that the action of matter elsewhere indefinitely acts. Finally, we think that the characteristic relationality of spacetime structure should be identified in this "primitive level of organization" of spacetime.

CMB in a box: Causal structure and the Fourier-Bessel expansion

This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility gamma = e(-mu), where mu is the optical depth to Thomson scattering. We show that the contributions of order gamma(N) to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z >> 10(3), effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position (x) over right arrow = 0 and time t(0). Hence, for each multipole l there is a discrete tower of momenta k(il) (not a continuum) which can affect physical observables, with the smallest momenta being k(1l) similar to l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation-no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.

Spacetime algebraic skeleton

The cosmological constant is shown to have an algebraic meaning: it is essentially an eigenvalue of a Casimir invariant of the Lorentz group acting on the spaces tangent to every spacetime. This is found in the context of de Sitter spacetimes, for which the Einstein equation is a relation between operators. Nevertheless, the result brings, to the foreground the skeleton algebraic structure underlying the geometry of general physical spacetimes. which differ from one another by the fleshening of that structure by different tetrad fields.

On Clifford subalgebras, spacetime splittings and applications

Z(2)-gradings of Clifford algebras are reviewed and we shall be concerned with an alpha-grading based on the structure of inner automorphisms, which is closely related to the spacetime splitting, if we consider the standard conjugation map automorphism by an arbitrary, but fixed, splitting vector. After briefly sketching the orthogonal and parallel components of products of differential forms, where we introduce the parallel [orthogonal] part as the space [time] component, we provide a detailed exposition of the Dirac operator splitting and we show how the differential operator parallel and orthogonal components are related to the Lie derivative along the splitting vector and the angular momentum splitting bivector. We also introduce multivectorial-induced alpha-gradings and present the Dirac equation in terms of the spacetime splitting, where the Dirac spinor field is shown to be a direct sum of two quaternions. We point out some possible physical applications of the formalism developed.

Causal structure of the entanglement renormalization ansatz

We show that the multiscale entanglement renormalization ansatz (MERA) can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter space with a flat space-like boundary, where the volume of a spacetime region corresponds to the number of variational parameters it contains. This result clarifies the nature of the ansatz, and suggests a generalization to quantum field theory. It also constitutes an independent justification of the connection between MERA and hyperbolic geometry which was proposed as a concrete implementation of the AdS-CFT correspondence.

Changes In Chromatin Structure In Nih 3t3 Cells Induced By Valproic Acid And Trichostatin A.

Valproic acid (VPA) and trichostatin A (TSA) are known histone deacetylase inhibitors (HDACIs) with epigenetic activity that affect chromatin supra-organization, nuclear architecture, and cellular proliferation, particularly in tumor cells. In this study, chromatin remodeling with effects extending to heterochromatic areas was investigated by image analysis in non-transformed NIH 3T3 cells treated for different periods with different doses of VPA and TSA under conditions that indicated no loss of cell viability. Image analysis revealed chromatin decondensation that affected not only euchromatin but also heterochromatin, concomitant with a decreased activity of histone deacetylases and a general increase in histone H3 acetylation. Heterochromatin protein 1-α (HP1-α), identified immunocytochemically, was depleted from the pericentromeric heterochromatin following exposure to both HDACIs. Drastic changes affecting cell proliferation and micronucleation but not alteration in CCND2 expression and in ratios of Bcl-2/Bax expression and cell death occurred following a 48-h exposure of the NIH 3T3 cells particularly in response to higher doses of VPA. Our results demonstrated that even low doses of VPA (0.05 mM) and TSA (10 ng/ml) treatments for 1 h can affect chromatin structure, including that of the heterochromatin areas, in non-transformed cells. HP1-α depletion, probably related to histone demethylation at H3K9me3, in addition to the effect of VPA and TSA on histone H3 acetylation, is induced on NIH 3T3 cells. Despite these facts, alterations in cell proliferation and micronucleation, possibly depending on mitotic spindle defects, require a longer exposure to higher doses of VPA and TSA.

Matrix Metalloproteinases And Left Ventricular Function And Structure In Spinal Cord Injured Subjects.

Subjects with spinal cord injury (SCI) exhibit impaired left ventricular (LV) diastolic function, which has been reported to be attenuated by regular physical activity. This study investigated the relationship between circulating matrix metalloproteinases (MMPs) and tissue inhibitors of MMPs (TIMPs) and echocardiographic parameters in SCI subjects and the role of physical activity in this regard. Forty-two men with SCI [19 sedentary (S-SCI) and 23 physically-active (PA-SCI)] were evaluated by clinical, anthropometric, laboratory, and echocardiographic analysis. Plasmatic pro-MMP-2, MMP-2, MMP-8, pro-MMP-9, MMP-9, TIMP-1 and TIMP-2 levels were determined by enzyme-linked immunosorbent assay and zymography. PA-SCI subjects presented lower pro-MMP-2 and pro-MMP-2/TIMP-2 levels and improved markers of LV diastolic function (lower E/Em and higher Em and E/A values) than S-SCI ones. Bivariate analysis showed that pro-MMP-2 correlated inversely with Em and directly with E/Em, while MMP-9 correlated directly with LV mass index and LV end-diastolic diameter in the whole sample. Following multiple regression analysis, pro-MMP-2, but not physical activity, remained associated with Em, while MMP-9 was associated with LV mass index in the whole sample. These findings suggest differing roles for MMPs in LV structure and function regulation and an interaction among pro-MMP-2, diastolic function and physical activity in SCI subjects.

Growth Factor Stimulation Improves The Structure And Properties Of Scaffold-free Engineered Auricular Cartilage Constructs.

The reconstruction of the external ear to correct congenital deformities or repair following trauma remains a significant challenge in reconstructive surgery. Previously, we have developed a novel approach to create scaffold-free, tissue engineering elastic cartilage constructs directly from a small population of donor cells. Although the developed constructs appeared to adopt the structural appearance of native auricular cartilage, the constructs displayed limited expression and poor localization of elastin. In the present study, the effect of growth factor supplementation (insulin, IGF-1, or TGF-β1) was investigated to stimulate elastogenesis as well as to improve overall tissue formation. Using rabbit auricular chondrocytes, bioreactor-cultivated constructs supplemented with either insulin or IGF-1 displayed increased deposition of cartilaginous ECM, improved mechanical properties, and thicknesses comparable to native auricular cartilage after 4 weeks of growth. Similarly, growth factor supplementation resulted in increased expression and improved localization of elastin, primarily restricted within the cartilaginous region of the tissue construct. Additional studies were conducted to determine whether scaffold-free engineered auricular cartilage constructs could be developed in the 3D shape of the external ear. Isolated auricular chondrocytes were grown in rapid-prototyped tissue culture molds with additional insulin or IGF-1 supplementation during bioreactor cultivation. Using this approach, the developed tissue constructs were flexible and had a 3D shape in very good agreement to the culture mold (average error <400 µm). While scaffold-free, engineered auricular cartilage constructs can be created with both the appropriate tissue structure and 3D shape of the external ear, future studies will be aimed assessing potential changes in construct shape and properties after subcutaneous implantation.

Ssr-based Genetic Diversity And Structure Of Garlic Accessions From Brazil.

Garlic is a spice and a medicinal plant; hence, there is an increasing interest in 'developing' new varieties with different culinary properties or with high content of nutraceutical compounds. Phenotypic traits and dominant molecular markers are predominantly used to evaluate the genetic diversity of garlic clones. However, 24 SSR markers (codominant) specific for garlic are available in the literature, fostering germplasm researches. In this study, we genotyped 130 garlic accessions from Brazil and abroad using 17 polymorphic SSR markers to assess the genetic diversity and structure. This is the first attempt to evaluate a large set of accessions maintained by Brazilian institutions. A high level of redundancy was detected in the collection (50 % of the accessions represented eight haplotypes). However, non-redundant accessions presented high genetic diversity. We detected on average five alleles per locus, Shannon index of 1.2, HO of 0.5, and HE of 0.6. A core collection was set with 17 accessions, covering 100 % of the alleles with minimum redundancy. Overall FST and D values indicate a strong genetic structure within accessions. Two major groups identified by both model-based (Bayesian approach) and hierarchical clustering (UPGMA dendrogram) techniques were coherent with the classification of accessions according to maturity time (growth cycle): early-late and midseason accessions. Assessing genetic diversity and structure of garlic collections is the first step towards an efficient management and conservation of accessions in genebanks, as well as to advance future genetic studies and improvement of garlic worldwide.

The Atomic Structure Of A Bare Buffer Layer On Sic(0001) Chemically Resolved.

A chemical-specific photoelectron diffraction structure determination of a carbon rich buffer layer on SiC is reported. In addition to the long-range ripple of this surface, a local buckling in the hexagonal sublattice, which breaks the local range order symmetry, was unraveled.

Crystal Structure Of (3e)-3-[(4-nitro-phen-oxy)-meth-yl]-4-phenyl-but-3-en-2-one.

In the title compound, C17H15NO4, the conformation about the C=C double bond [1.348 (2) Å] is E with the ketone group almost co-planar [C-C-C-C torsion angle = 7.2 (2)°] but the phenyl group twisted away [C-C-C-C = 160.93 (17)°]. The terminal aromatic rings are almost perpendicular to each other [dihedral angle = 81.61 (9)°] giving the mol-ecule an overall U-shape. The crystal packing feature benzene-C-H⋯O(ketone) contacts that lead to supra-molecular helical chains along the b axis. These are connected by π-π inter-actions between benzene and phenyl rings [inter-centroid distance = 3.6648 (14) Å], resulting in the formation of a supra-molecular layer in the bc plane.