arXiv subjects

Alejandro Corichi

Publications and source records attributed to Alejandro Corichi.

At least 37 records · Page 2Linked to original sources

arXiv2015

Energy of test objects on black hole spacetimes: A brief review

In this paper, we review the issue of defining energy for test particles on a background stationary spacetime. We revisit the different notions of energy as defined by different observers. As is well known, the existence of a time-like isometry allows for the notion of total conserved energy to be well defined. We use this well known quantity to show that a gravitational potential energy can be consistently defined. As examples, we study the case of the exterior regions of an asymptotically flat black hole and of the $Λ>0$ Schwarzschild de Sitter case, where an asymptotic region is not available. We then consider the situation in which the test particle is absorbed by the black hole, and analyze the energetics in detail. In particular, we show that the notion of horizon energy as defined by the isolated horizons formalism provides a satisfactory notion of energy compatible with the particle's total conserved energy. With these choices, there is a global conservation of energy. Finally, we comment on a recent proposal to define energy of the black hole as seen by a nearby observer at rest, for which this feature is lost.

gr-qc↗

arXiv2015

Constraint Lie algebra and local physical Hamiltonian for a generic 2D dilatonic model

We consider a class of two dimensional dilatonic models, and revisit them from the perspective of a new set of "polar type" variables. These are motivated by recently defined variables within the spherically symmetric sector of 4D general relativity. We show that for a large class of dilatonic models, including the case \emph{with} matter, one can perform a series of canonical transformations in such a way that the Poisson algebra of the constraints becomes a Lie algebra. Furthermore, we construct Dirac observables and a reduced Hamiltonian that accounts for the time evolution of the system. Thus, with our formulation, the systems under consideration are amenable to be quantized with loop quantization methods.

gr-qc↗

arXiv2015

Energy in first order 2+1 gravity

We consider $Λ$=0 three dimensional gravity with asymptotically flat boundary conditions. This system was studied by Ashtekar and Varadarajan within the second order formalism -with metric variables- who showed that the Regge-Teitelboim formalism yields a consistent Hamiltonian description where, surprisingly, the energy is bounded from below and from above. The energy of the spacetime is, however, determined up to an arbitrary constant. The natural choice was to fix that freedom such that Minkowski spacetime has zero energy. More recently, Marolf and Patiño started from the Einstein-Hilbert action supplemented with the Gibbons-Hawking term and showed that, in the 2+1 decomposition of the theory, the energy is shifted from the Ashtekar-Varadarajan analysis in such a way that Minkowski spacetime possesses a negative energy. In this contribution we consider the first order formalism, where the fundamental variables are a so(2,1) connection $ω_a{^I}_J$ and a triad $e_a^I$. We consider two actions. A natural extension to 3 dimensions of the consistent action in 4D Palatini gravity is shown to be finite and differentiable. For this action, the 2+1 decomposition (that we perform using two methods) yields a Hamiltonian boundary term that corresponds to energy. It assigns zero energy to Minkowski spacetime. We then put forward a totally gauge invariant action, and show that it is also well defined and differentiable. Interestingly, it turns out to be related, on shell, to the 3D Palatini action by an additive constant in such a way that its associated energy is given by the Marolf-Patiño expression. Thus, we conclude that, from the perspective of the first order formalism, Minkowski spacetime can consistently have either, zero, or a negative energy equal to -1/4G, depending on the choice of consistent action employed as starting point.

gr-qc↗

arXiv2014

Inflationary Attractors and their Measures

Several recent misconceptions about the measure problem in inflation and the nature of inflationary attractors are addressed. We show that within the Hamiltonian system of flat Friedmann-Lemaître-Robertson-Walker cosmology coupled to a massive scalar field, the focussing of the Liouville measure on attractor solutions is brought about by a spread in a gauge degree of freedom - the spatial volume. Using this we show how the Liouville measure formulated on a surface of constant Hubble rate induces a probability distribution function on surfaces of other Hubble rates, and the attractor behaviour is seen through the focussing of this function on a narrow range of physical observables. One can conclude then that standard techniques from Hamiltonian dynamics suffice to provide a satisfactory description of attractor solutions and the measure problem. Updated to match published version.

gr-qc↗

arXiv2013

Loop quantum cosmology of k=1 FLRW: Effects of inverse volume corrections

We consider the k=1 Friedman-Lemaitre-Robertson-Walker (FLRW) model within loop quantum cosmology (LQC), from the perspective of the two available quantization prescriptions. We focus our attention on the existence of the so called `inverse corrections' in the quantization process. We derive the corresponding quantum constraint operators, and study in detail the issue of the self-adjointness of the quantum Hamiltonian constraint for two different quantizations based on open holonomies. Furthermore, we analize in detail the resulting effective theories, paying special attention to issues such as the boundedness of different scalar observables such as energy density and expansion. We show that the inclusion of the inverse corrections solves one of the main undesirable features of the previous formalism, namely the unboundedness of the energy density and expansion near the bounce on the full (effective) phase space. We briefly comment on possible consequences of this new feature.

gr-qc↗

arXiv2013

Loop Quantum Cosmology

This Chapter provides an up to date, pedagogical review of some of the most relevant advances in loop quantum cosmology. We review the quantization of homogeneous cosmological models, their singularity resolution and the formulation of effective equations that incorporate the main quantum corrections to the dynamics. We also summarize the theory of quantized metric perturbations propagating in those quantum backgrounds. Finally, we describe how this framework can be applied to obtain a self-consistent extension of the inflationary scenario to incorporate quantum aspects of gravity, and to explore possible phenomenological consequences.

gr-qc↗

arXiv2012

Loop Quantum Cosmology: Anisotropy and singularity resolution

In this contribution we consider the issue of singularity resolution within loop quantum cosmology (LQC) for different homogeneous models. We present results of numerical evolutions of effective equations for both isotropic as well as anisotropic cosmologies, with and without spatial curvature. To address the issue of singularity resolution we examine the time evolution of geometrical and curvature invariants that yield information about the semiclassical spacetime geometry. We discuss generic behavior found for a variety of initial conditions. Finally, we show that the modifications which come from Loop Quantum Cosmology imply a non-chaotic effective behavior in the vacuum Bianchi IX model.

gr-qc↗

arXiv2012

On the choice of time in the continuum limit of polymeric effective theories

In polymeric quantum theories, a natural question pertains to the so called continuum limit, corresponding to the limit where the `discreteness parameter' $λ$ approaches zero. In particular one might ask whether the limit exists and, in that case, what the limiting theory is. Here we review recent results on the classical formulation of the problem for a soluble model in loop quantum cosmology. We show that it is only through the introduction of a particular $λ$-dependent internal time function that the limit $λ\to 0$ can be well defined. We then compare this result with the existing analysis in the quantum theory, where the dynamics was cast in terms of an internal ($λ$-independent) parameter for which the limit does not exist. We briefly comment on the steps needed to define the corresponding time parameter in the quantum theory for which the limit was shown to exist classically.

gr-qc↗

arXiv2012

On the Semiclassical Limit of Loop Quantum Cosmology

We consider a k=0 Friedman-Robertson-Walker (FRW) model within loop quantum cosmology (LQC) and explore the issue of its semiclassical limit. The model is exactly solvable and allows us to construct analytical (Gaussian) coherent-state solutions for each point on the space of classical states. We propose physical criteria that select from these coherent states, those that display semiclassical behavior, and study their properties in the deep Planck regime. Furthermore, we consider generalized squeezed states and compare them to the Gaussian states. The issue of semiclassicality preservation across the bounce is studied and shown to be generic for all the states considered. Finally, we comment on some implications these results have, depending on the topology of the spatial slice. In particular we consider the issue of the recovery, within our class of states, of a scaling symmetry present in the classical description of the system when the spatial topology is non-compact.

gr-qc↗

arXiv2012

Effective constrained polymeric theories and their continuum limit

The classical limit of polymer quantum theories yields a one parameter family of `effective' theories labeled by λ. Here we consider such families for constrained theories and pose the problem of taking the `continuum limit', λ-> 0. We put forward criteria for such question to be well posed, and propose a concrete strategy based in the definition of appropriately constructed Dirac observables. We analyze two models in detail, namely a constrained oscillator and a cosmological model arising from loop quantum cosmology. For both these models we show that the program can indeed be completed, provided one makes a particular choice of λ-dependent internal time with respect to which the dynamics is described and compared. We show that the limiting theories exist and discuss the corresponding limit. These results might shed some light in the problem of defining a renormalization group approach, and its associated continuum limit, for quantum constrained systems.

gr-qc↗

arXiv2012

Effective Dynamics in Bianchi Type II Loop Quantum Cosmology

We numerically investigate the solutions to the effective equations of the Bianchi II model within the "improved" Loop Quantum Cosmology (LQC) dynamics. The matter source is a massless scalar field. We perform a systematic study of the space of solutions, and focus on the behavior of several geometrical observables. We show that the big-bang singularity is replaced by a bounce and the point-like singularities do not saturate the energy density bound. There are up to three directional bounces in the scale factors, one global bounce in the expansion, the shear presents up to four local maxima and can be zero at the bounce. This allows for solutions with density larger than the maximal density for the isotropic and Bianchi I cases. The asymptotic behavior is shown to behave like that of a Bianchi I model, and the effective solutions connect anisotropic solutions even when the shear is zero at the bounce. All known facts of Bianchi I are reproduced. In the "vacuum limit", solutions are such that almost all the dynamics is due to the anisotropies. Since Bianchi II plays an important role in the Bianchi IX model and the Belinskii, Khalatnikov, Lifshitz (BKL) conjecture, our results can provide an intuitive understanding of the behavior in the vicinity of general space-like singularities, when loop-geometric corrections are present.

gr-qc↗

arXiv2011

Coherent semiclassical states for loop quantum cosmology

The spatially flat Friedman-Robertson-Walker (FRW) cosmological model with a massless scalar field in loop quantum cosmology admits a description in terms of a completely solvable model. This has been used to prove that: i) the quantum bounce that replaces the big bang singularity is generic; ii) there is an upper bound on the energy density for all states and iii) semiclassical states at late times had to be semiclassical before the bounce. Here we consider a family of exact solutions to the theory, corresponding to generalized coherent Gaussian and squeezed states. We analyze the behavior of basic physical observables and impose restrictions on the states based on physical considerations. These turn out to be enough to select, from all the generalized coherent states, those that behave semiclassical at late times. We study then the properties of such states near the bounce where the most `quantum behavior' is expected. As it turns out, the states remain sharply peaked and semiclassical at the bounce and the dynamics is very well approximated by the `effective theory' throughout the time evolution. We compare the semiclassicality properties of squeezed states to those of the Gaussian semiclassical states and conclude that the Gaussians are better behaved. In particular, the asymmetry in the relative fluctuations before and after the bounce are negligible, thus ruling out claims of so called `cosmic forgetfulness'.

gr-qc↗

arXiv2011

Loop quantum cosmology of k=1 FRW: A tale of two bounces

We consider the k=1 Friedman-Robertson-Walker (FRW) model within loop quantum cosmology, paying special attention to the existence of an ambiguity in the quantization process. In spatially non-flat anisotropic models such as Bianchi II and IX, the standard method of defining the curvature through closed holonomies is not admissible. Instead, one has to implement the quantum constraints by approximating the connection via open holonomies. In the case of flat k=0 FRW and Bianchi I models, these two quantization methods coincide, but in the case of the closed $k$=1 FRW model they might yield different quantum theories. In this manuscript we explore these two quantizations and the different effective descriptions they provide of the bouncing cyclic universe. In particular, as we show in detail, the most dramatic difference is that in the theory defined by the new quantization method, there is not one, but two different bounces through which the cyclic universe alternates. We show that for a `large' universe, these two bounces are very similar and, therefore, practically indistinguishable, approaching the dynamics of the holonomy based quantum theory.

gr-qc↗

arXiv2011

On the measure problem in slow roll inflation and loop quantum cosmology

We consider the measure problem in standard slow-roll inflationary models from the perspective of loop quantum cosmology (LQC). Following recent results by Ashtekar and Sloan, we study the probability of having enough e-foldings and focus on its dependence on the quantum gravity scale, including the transition of the theory to the limit where general relativity (GR) is recovered. Contrary to the standard expectation, the probability of having enough inflation, that is close to one in LQC, grows and tends to 1 as one approaches the GR limit. We study the origin of the tension between these results with those by Gibbons and Turok, and offer an explanation that brings these apparent contradictory results into a coherent picture. As we show, the conflicting results stem from different choices of initial conditions for the computation of probability. The singularity free scenario of loop quantum cosmology offers a natural choice of initial conditions, and suggests that enough inflation is generic.

gr-qc↗

arXiv2010

Surface terms, Asymptotics and Thermodynamics of the Holst Action

We consider a first order formalism for general relativity derived from the Holst action. This action is obtained from the standard Palatini-Hilbert form by adding a topological-like term and can be taken as the starting point for loop quantum gravity and spin foam models. The equations of motion derived from the Holst action are, nevertheless, the same as in the Palatini formulation. Here we study the form of the surface terms of the action for general boundaries as well as the symplectic current in the covariant formulation of the theory. Furthermore, we analyze the behavior of the surface terms in asymptotically flat space-times. We show that the contribution to the symplectic structure from the Holst term vanishes and one obtains the same asymptotic expressions as in the Palatini action. It then follows that the asymptotic Poincare symmetries and conserved quantities such as energy, linear momentum and relativistic angular momentum found here are equivalent to those obtained from the standard Arnowitt, Deser and Misner formalism. Finally, we consider the Euclidean approach to black hole thermodynamics and show that the on-shell Holst action, when evaluated on some static solutions containing horizons, yields the standard thermodynamical relations.

gr-qc↗

arXiv2010

Robustness of key features of loop quantum cosmology

Loop quantum cosmology of the k=0 FRW model (with a massless scalar field) is shown to be exactly soluble if the scalar field is used as the internal time already in the classical Hamiltonian theory. Analytical methods are then used i) to show that the quantum bounce is generic; ii) to establish that the matter density has an absolute upper bound which, furthermore, equals the critical density that first emerged in numerical simulations and effective equations; iii) to bring out the precise sense in which the Wheeler DeWitt theory approximates loop quantum cosmology and the sense in which this approximation fails; and iv) to show that discreteness underlying LQC is fundamental. Finally, the model is compared to analogous discussions in the literature and it is pointed out that some of their expectations do not survive a more careful examination. An effort has been made to make the underlying structure transparent also to those who are not familiar with details of loop quantum gravity.

gr-qc↗

arXiv2009

A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology

We re-examine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From their behavior in the effective constraint surface and in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate is absolutely bounded only for the so called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear are bounded for only one regularization of the quantum constraint. It turns out that only for this choice, the theory exhibits quantum gravity corrections at a unique scale, and is physically viable.

gr-qc↗

arXiv2009

Semiclassical Quantum Gravity: Obtaining Manifolds from Graphs

We address the "inverse problem" for discrete geometry, which consists in determining whether, given a discrete structure of a type that does not in general imply geometrical information or even a topology, one can associate with it a unique manifold in an appropriate sense, and constructing the manifold when it exists. This problem arises in a variety of approaches to quantum gravity that assume a discrete structure at the fundamental level; the present work is motivated by the semiclassical sector of loop quantum gravity, so we will take the discrete structure to be a graph and the manifold to be a spatial slice in spacetime. We identify a class of graphs, those whose vertices have a fixed valence, for which such a construction can be specified. We define a procedure designed to produce a cell complex from a graph and show that, for graphs with which it can be carried out to completion, the resulting cell complex is in fact a PL-manifold. Graphs of our class for which the procedure cannot be completed either do not arise as edge graphs of manifold cell decompositions, or can be seen as cell decompositions of manifolds with structure at small scales (in terms of the cell spacing). We also comment briefly on how one can extend our procedure to more general graphs.

gr-qc↗