About the Statistical Properties of Cosmological Billiards
We summarize some recent progress in the understanding of the statistical properties of cosmological billiards.
gr-qc↗
arXiv subjects
Orchidea Maria Lecian
Publications and source records attributed to Orchidea Maria Lecian.
Statistical Properties of Cosmological Billiards
Belinski, Khalatnikov and Lifshitz (BKL) pioneered the study of the statistical properties of the never-ending oscillatory behavior (among successive Kasner epochs) of the geometry near a space-like singularity. We show how the use of a "cosmological billiard" description allows one to refine and deepen the understanding of these statistical properties. Contrary to previous treatments, we do not quotient the dynamics by its discrete symmetry group (of order 6), thereby uncovering new phenomena, such as correlations between the successive billiard corners in which the oscillations take place. Starting from the general integral invariants of Hamiltonian systems, we show how to construct invariant measures for various projections of the cosmological-billiard dynamics. In particular, we exhibit, for the first time, a (non-normalizable) invariant measure on the "Kasner circle" which parametrizes the exponents of successive Kasner epochs. Finally, we discuss the relation between: (i) the unquotiented dynamics of the Bianchi IX (a, b, c or mixmaster) model; (ii) its quotienting by the group of permutations of (a, b, c); and (iii) the billiard dynamics that arose in recent studies suggesting the hidden presence of Kac-Moody symmetries in cosmological billiards.
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On the gravitational polarizability of black holes
The gravitational polarizability properties of black holes are compared and contrasted with their electromagnetic polarizability properties. The "shape" or "height" multipolar Love numbers h_l of a black hole are defined and computed. They are then compared to their electromagnetic analogs h_l^{EM}. The Love numbers h_l give the height of the l-th multipolar "tidal bulge" raised on the horizon of a black hole by faraway masses. We also discuss the shape of the tidal bulge raised by a test mass m, in the limit where m gets very close to the horizon.
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Fermion Dynamics by Internal and Space-Time Symmetries
This manuscript is devoted to introduce a gauge theory of the Lorentz Group based on the ambiguity emerging in dealing with isometric diffeo-morphism-induced Lorentz transformations. The behaviors under local transformations of fermion fields and spin connections (assumed to be ordinary world vectors) are analyzed in flat space-time and the role of the torsion field, within the generalization to curved space-time, is briefly discussed. The fermion dynamics is then analyzed including the new gauge fields and assuming time-gauge. Stationary solutions of the problem are also analyzed in the non-relativistic limit, to study the spinor structure of an hydrogen-like atom.
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GUP vs polymer quantum cosmology: the Taub model
The fate of the cosmological singularity in the Taub model is discussed within the two frameworks. An internal time variable is ruled out and the only remaining degree of freedom (the anisotropy) of the Universe is quantized according to such schemes. The resulting GUP Taub Universe is singularity-free, differently from the second case, where the classical singularity is not tamed by the polymer-loop quantum effects.
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Polymer Quantum Dynamics of the Taub Universe
Within the framework of non-standard (Weyl) representations of the canonical commutation relations, we investigate the polymer quantization of the Taub cosmological model. The Taub model is analyzed within the Arnowitt-Deser-Misner reduction of its dynamics, by which a time variable arises. While the energy variable and its conjugate momentum are treated as ordinary Heisenberg operators, the anisotropy variable and its conjugate momentum are represented by the polymer technique. The model is analyzed at both classical and quantum level. As a result, classical trajectories flatten with respect to the potential wall, and the cosmological singularity is not probabilistically removed. In fact, the dynamics of the wave packets is characterized by an interference phenomenon, which, however, is not able to stop the evolution towards the classical singularity.
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Lorentz Gauge Theory and Spinor Interaction
A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is briefly discussed. The spinor interaction with the new gauge field is then analyzed assuming the time gauge and stationary solutions, in the non-relativistic limit, are treated to generalize the Pauli equation.
hep-th↗
Macroscopic and Microscopic Paradigms for the Torsion Field: from the Test-Particle Motion to a Lorentz Gauge Theory
Torsion represents the most natural extension of General Relativity and it attracted interest over the years in view of its link with fundamental properties of particle motion. The bulk of the approaches concerning the torsion dynamics focus their attention on their geometrical nature and they are naturally led to formulate a non-propagating theory. Here we review two different paradigms to describe the role of the torsion field, as far as a propagating feature of the resulting dynamics is concerned. However, these two proposals deal with different pictures, i.e., a macroscopic approach, based on the construction of suitable potentials for the torsion field, and a microscopic approach, which relies on the identification of torsion with the gauge field associated with the local Lorentz symmetry. We analyze in some detail both points of view and their implications on the coupling between torsion and matter will be investigated. In particular, in the macroscopic case, we analyze the test-particle motion to fix the physical trajectory, while, in the microscopic approach, a natural coupling between torsion and the spin momentum of matter fields arises.
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Electro-weak Model within a 5-dimensional Lorentz group theory
The Electroweak model will be geometrized in a 5-D Riemann-Cartan framework: U(1) weak hyper-charge group will be worked out in a Klauza-Klein scheme, while SU(2) weak isospin group will be identified to suitable bein projections of the contortion field. The possibility of introducing Ashtekar formalism in 5-D Klauza-Klein theories will be investigated.
gr-qc↗
Is Torsion a Fundamental Physical Field?
The local Lorentz group is introduced in flat space-time, where the resulting Dirac and Yang-Mills equations are found, and then generalized to curved space-time: if matter is neglected, the Lorentz connection is identified with the contortion field, while, if matter is taken into account, both the Lorentz connection and the spinor axial current are illustrated to contribute to the torsion of space-time.
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Electro-weak Model within the framework of Lorentz gauge theory: Ashtekar variables?
The Electroweak (EW) model is geometrized in the framework of a 5D gauge theory of the Lorentz group, after the implementation of the Kaluza-Klein (KK) paradigm. The possibility of introducing Ashtekar variables on a 5D KK manifold is considered on the ground of its geometrical structure.
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E.C.G. Stueckelberg: a forerunner of modern physics
The pioneering work of E.C.G. Stueckelberg is briefly analyzed: the formalism of the Stueckelberg field, able to describe a massive vector field, is reviewed, and some applications are presented. In particular, starting from his very first application, devoted to describe nuclear phenomena known in the Thirties, later attempts to demonstrate the renormalizability of the model are considered. Finally, also string theory and LQG are illustrated to be a suitable scenario for the Stueckelberg field.
physics.hist-ph↗