RECENT DEVELOPMENTS IN GRAVITATION AND COSMOLOGY: 3rd Mexican Meeting on Mathematicaland Experimental Physics

On the incompatibility between General Relativity and Quantum Theory
View Description Hide DescriptionThe aim of this work is to review the concepts of time in quantum mechanics and general relativity to show their incompatibility. We show that the absolute character of Newtonian time is present in quantum mechanics and also partially in quantum field theories which consider the Minkowski metric as the background spacetime. We discuss the problems which this non‐dynamical concept of time causes in general relativity that is characterized by a dynamical spacetime.

Noncommutative Geometries and Gravity
View Description Hide DescriptionWe briefly review ideas about “noncommutativity of space‐time” and approaches toward a corresponding theory of gravity.

Non‐commutative models in gravity
View Description Hide DescriptionWe discuss two examples of geometries within the framework of non‐commutative geometry. Both geometries are of interest due to their appearance in General Relativity and other fields in physics.

Noncommutative Solitons
View Description Hide DescriptionSolitonic objects play a central role in gauge and string theory (as, e.g., monopoles, black holes, D‐branes, etc.). Certain string backgrounds produce a noncommutative deformation of the low‐energy effective field theory, which allows for new types of solitonic solutions. I present the construction, moduli spaces and dynamics of Moyal‐deformed solitons, exemplified in the dimensional Yang‐Mills‐Higgs theory and its Bogomolny system, which is gauge‐fixed to an integrable chiral sigma model (the Ward model). Noncommutative solitons for various dimensional integrable systems (such as sine‐Gordon) easily follow by dimensional and algebraic reduction. Supersymmetric extensions exist as well and are related to twistor string theory.

Loop quantization of spherically symmetric midi‐superspaces : the interior problem
View Description Hide DescriptionWe continue the study of spherically symmetric vacuum space‐times in loop quantum gravity by treating the interior of a black hole. We start from a midi‐superspace approach, but a simple gauge fixing leads to a Kantowski–Sachs form for the variables. We show that one can solve the quantum theory exactly in the (periodic) connection representation, including the inner product. The evolution can be solved exactly by de‐parameterizing the theory and can be easily interpreted as a semi‐classical evolution plus quantum corrections. A relational evolution can also be introduced in a precise manner, suggesting what may happen in situations where it is not possible to de‐parameterize. We show that the singularity is replaced by a bounce at which quantum effects are important and that the extent of the region at the bounce where one departs from classical general relativity depends on the initial data.

On a Continuum Limit for Loop Quantum Cosmology
View Description Hide DescriptionThe use of non‐regular representations of the Heisenberg‐Weyl commutation relations has proved to be useful for studying conceptual and technical issues in quantum gravity. Of particular relevance is the study of Loop Quantum Cosmology (LQC), symmetry reduced theory that is related to Loop Quantum Gravity, and that is based on a non‐regular, polymeric representation. Recently, a soluble model was used by Ashtekar, Corichi and Singh to study the relation between Loop Quantum Cosmology and the standard Wheeler‐DeWitt theory and, in particular, the passage to the limit in which the auxiliary parameter (interpreted as “quantum geometry discreetness”) is sent to zero in hope to get rid of this ‘regulator’ that dictates the LQC dynamics at each ‘scale’. In this note we outline the first steps toward reformulating this question within the program developed by the authors for studying the continuum limit of polymeric theories, which was successfully applied to simple systems such as a Simple Harmonic Oscillator.

ENERGY EXTRACTION FROM BLACK HOLES
View Description Hide DescriptionIn this lecture I give an introduction to the rotational energy extraction of black holes by the electromagnetic Blandford‐Znajek process and the generation of relativistic jets. After some basic material on the electrodynamics of black hole magnetospheres, we derive the most important results of Blandford and Znajek by making use of Kerr‐Schild coordinates, which are regular on the horizon. In a final part we briefly describe results of recent numerical simulations of accretion flows on rotating black holes, the resulting large‐scale outflows, and the formation of collimated relativistic jets with high Lorentz factors.

Rotating Black Holes in Higher Dimensions
View Description Hide DescriptionThe properties of higher‐dimensional black holes can differ significantly from those of black holes in four dimensions, since neither the uniqueness theorem, nor the staticity theorem or the topological censorship theorem generalize to higher dimensions. We first discuss black holes of Einstein‐Maxwell theory and Einstein‐Maxwell‐Chern‐Simons theory with spherical horizon topology. Here new types of stationary black holes are encountered. We then discuss nonuniform black strings and present evidence for a horizon topology changing transition.

Geodesic equation and theta–divisor
View Description Hide DescriptionThe complete set of analytic solutions of the geodesic equation in Schwarzschild–(anti)de Sitter space–times is presented. The solutions are derived from the Jacobi inversion problem restricted to the set of zeros of the theta function, called the theta–divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sigma functions. The different types of the resulting orbits are characterized in terms of the conserved energy and angular momentum as well as the cosmological constant. An elaboration of the necessary steps of the explicit computation of the solutions is given.

BRST and the pure spinor formalism
View Description Hide DescriptionThe aim of this talk is to show the relation between the standard BRST approach of the GS superstring with the quantization technics used in the pure spinor approach to superstring. To that end we will use the Batalin‐Fradkin‐Tyutin (BFT) conversion program of second class constraints to first class constraints in the GS superstring using light cone coordinates. By applying this systematic procedure we were able to obtain a gauge system that is equivalent to the recent model proposed in [1] to relate the GS superstring to the pure spinor formalism.

Quantum Stress Tensor Fluctuations and their Physical Effects
View Description Hide DescriptionWe summarize several aspects of recent work on quantum stress tensor fluctuations and their role in driving fluctuations of the gravitational field. The role of correlations and anticorrelations is emphasized. We begin with a review of the properties of the stress tensor correlation function. We next consider some illuminating examples of non‐gravitational effects of stress tensors fluctuations, specifically fluctuations of the Casimir force and radiation pressure fluctuations. We next discuss passive fluctuations of spacetime geometry and some of their operational signatures. These include luminosity fluctuations, line broadening, and angular blurring of a source viewed through a fluctuating gravitational field. Finally, we discuss the possible role of quantum stress tensor fluctuations in the early universe, especially in inflation. The fluctuations of the expansion of a congruence of comoving geodesics grows during the inflationary era, due to non‐cancellation of anticorrelations that would have occurred in flat spacetime. This results in subsequent non‐Gaussian density perturbations and allows one to infer an upper bound on the duration of inflation. This bound is consistent with adequate inflation to solve the horizon and flatness problems.

Heat in general relativity: a controversy in irreversible thermodynamics
View Description Hide DescriptionInterest in relativistic irreversible thermodynamics has been revived due to several new experiments, such as relativistic heavy ion collisions, now feasible with modern technology. Also, old unsolved problems such as the derivation of a causal heat equation have witnessed novel approaches. This work presents an account of the controversy that arises when one wants to include heat in relativistic irreversible thermodynamics formalisms. An experiment which may throw light on this problem is emphasized.

The geometry of thermodynamics
View Description Hide DescriptionWe present a review of the main aspects of geometrothermodynamics, an approach which allows us to associate a specific Riemannian structure to any classical thermodynamic system. In the space of equilibrium states, we consider a Legendre invariant metric, which is given in terms of the fundamental equation of the corresponding thermodynamic system, and analyze its geometric properties in the case of the van der Waals gas, and black holes. We conclude that the geometry of this particular metric reproduces the thermodynamic behavior of the van der Waals gas, and the Reissner‐Nordström black hole, but it is not adequate for the thermodynamic description of Kerr black holes.

Bose–Einstein condensation in gravitational field
View Description Hide DescriptionThe thermodynamics of a massive bosonic gas, under the presence of a gravitational field is analyzed. The possibility of using these results as an experimental proposal to have a direct test, of the usually assumed equivalence between a gravitation field and an accelerated coordinate system in a Minkowskian manifold, will also be addressed. This will be done calculating the modifications upon the condensation temperature provoked by the gravitational field.

Small‐Scale Structure of Spacetime: Bounds and Conjectures
View Description Hide DescriptionThis review consists of two parts. The first part establishes certain astrophysical bounds on the smoothness of classical spacetime.
Some of the best bounds to date are based on the absence of vacuum Cherenkov radiation in ultrahigh‐energy cosmic rays. The second part discusses possible implications of these bounds for the quantum structure of spacetime. One conjecture is that the fundamental length scale of quantum spacetime may be different from the Planck length.

Perspectives of the use of Statistical Mechanics Methods in Quantum Gravity Phenomenology
View Description Hide DescriptionThe possible benefits of the use of the methods of statistical mechanics in the context of gravity are analyzed. Two directions will be explored, i.e., Bose–Einstein condensation under the presence of a gravitational field, and the possible emergence of phase transitions due to the breakdown of Lorentz symmetry.

The scalar sector in the Myers‐Pospelov model
View Description Hide DescriptionWe construct a perturbative expansion of the scalar sector in the Myers‐Pospelov model, up to second order in the Lorentz violating parameter and taking into account its higher‐order time derivative character. This expansion allows us to construct an hermitian positive‐definite Hamiltonian which provides a correct basis for quantization. Demanding that the modified normal frequencies remain real requires the introduction of an upper bound in the magnitude of the momentum, which is a manifestation of the effective character of the model. The free scalar propagator, including the corresponding modified dispersion relations, is also calculated to the given order, thus providing the starting point to consider radiative corrections when interactions are introduced.

Phase transitions in a relativistic bosonic gas induced by the breakdown of Lorentz symmetry
View Description Hide DescriptionIt is well known that phase transitions arise if the interaction among particles embodies an attractive as well as a repulsive contribution. In this work it will be shown that the breakdown of Lorentz symmetry can be interpreted as a repulsive pseudo‐interaction, the one appears as a counterpart to the effects produced by the bosonic statistics, which can be contemplated as an attractive interaction. Afterwards, it will be proved that the breakdown of the Lorentz symmetry predicts, for some cases, the emergence of phase transitions and critical phenomena, which could be used as a test for those theories entailing this kind of violations.

Experimental Efforts in Space for Fundamental Physics Tests
View Description Hide DescriptionTests of fundamental concepts and theories in physics are more and more based on space experiments. Along many studies, various satellite experiments have been proposed and some already been carried out. Fundamental physics experiments usually have to be performed with very high accuracy. It is evident that the sensitivity of measuring devices and the sensing resolution increase if the experiments can be performed under conditions of free fall, that is, under conditions of weightlessness. Although in many precision experiments on Earth gravitation might have a negligible influence and seismic noise is either irrelevant or at least can be shielded sufficiently enough, the more accurate the measuring devices are, the more terrestrial influences become the dominant disturbing effect. More than that, many experiments need an interaction–free environment and the absence of any linear or rotational acceleration. It indicates, that it might be of great advantage to perform precision experiments in space.