arXiv subjects

Saeed Rastgoo

Publications and source records attributed to Saeed Rastgoo.

At least 37 records · Page 2Linked to original sources

arXiv2021

Effective GUP-modified Raychaudhuri equation and black hole singularity: four models

The classical Raychaudhuri equation predicts the formation of conjugate points for a congruence of geodesics, in a finite proper time. This in conjunction with the Hawking-Penrose singularity theorems predicts the incompleteness of geodesics and thereby the singular nature of practically all spacetimes. We compute the generic corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole, arising from modifications to the algebra inspired by the generalized uncertainty principle (GUP) theories. Then we study four specific models of GUP, compute their effective dynamics as well as their expansion and its rate of change using the Raychaudhuri equation. We show that the modification from GUP in two of these models, where such modifications are dependent of the configuration variables, lead to finite Kretchmann scalar, expansion and its rate, hence implying the resolution of the singularity. However, the other two models for which the modifications depend on the momenta still retain their singularities even in the effective regime.

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arXiv2021

Deformed algebra and the effective dynamics of the interior of black holes

We consider the classical Hamiltonian of the interior of the Schwarzschild black hole in Ashtekar-Barbero connection formalism. Then, inspired by generalized uncertainty principle models, we deform the classical canonical algebra and derive the effective dynamics of the model under this modification. We show that such a deformation leads to the resolution of the singularity of the black hole and a minimum nonzero radius for the infalling 2-spheres, provided that the deformation parameters are chosen to be negative.

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arXiv2021

Propagation of quantum gravity-modified gravitational waves on a classical FLRW spacetime

The linearized Einstein field equations provide a low-energy wave equation for the propagation of gravitational fields which may originate from a high energy source. Motivated by loop quantum gravity, we propose the polymer quantization scheme to derive the effective propagation of such waves on a classical Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. To overcome the challenge of polymer quantizing a time-dependent Hamiltonian, we rewrite such a Hamiltonian in a time-independent manner in the extended phase space, polymerize it, and then transform it back to the usual phase space. In this way we obtain a time-dependent polymer Hamiltonian for the gravitational waves. We then derive the effective equations of motion and show that (i) the form of the waves is modified, (ii) the speed of the waves depends on their frequencies, and (iii) quantum effects become more apparent as waves traverse longer distances.

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arXiv2021

Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity

We derive loop quantum gravity corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole and near the classical singularity. We show that the resulting effective equation implies defocusing of geodesics due to the appearance of repulsive terms. This prevents the formation of conjugate points, renders the singularity theorems inapplicable, and leads to the resolution of the singularity for this spacetime.

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arXiv2021

Effective dynamics of the Schwarzschild black hole interior with inverse triad corrections

We reconsider the study of the interior of the Schwarzschild black hole now including inverse triad quantum corrections within loop quantization. We derive these corrections and show that they are are related to two parameters $δ_b, δ_c$ associated to the minimum length in the radial and angular directions, that enter Thiemann's trick for quantum inverse triads. Introduction of such corrections may lead to non-invariance of physical results under rescaling of the fiducial volume needed to compute the dynamics, due to noncompact topology of the model. So, we put forward two prescriptions to resolve this issue. These prescriptions amount to interchange $δ_b, δ_c$ in classical computations in Thiemann's trick. By implementing the inverse triad corrections we found, previous results such as singularity resolution and black-to-white hole bounce hold with different values for the minimum radius-at-bounce, and the mass of the white hole.

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arXiv2020

Gravitation in terms of observables 2: the algebra of fundamental observables

In a previous paper, we showed how to use the techniques of the group of loops to formulate the loop approach to gravity proposed by Mandelstam in the 1960's. Those techniques allow to overcome some of the difficulties that had been encountered in the earlier treatment. In this approach, gravity is formulated entirely in terms of Dirac observables without constraints, opening attractive new possibilities for quantization. In this paper we discuss the Poisson algebra of the resulting Dirac observables, associated with the intrinsic components of the Riemann tensor. This provides an explicit realization of the non-local algebra of observables for gravity that several authors have conjectured.

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arXiv2020

Phenomenology of a massive quantum field in a cosmological quantum spacetime

We revisit the quantum theory of a massive, minimally coupled scalar field, propagating on the Planck-era isotropic cosmological quantum spacetime which transitions to a classical spacetime in later times. The quantum effects modify the isotropic spacetime such that effectively it exhibits anisotropies. Thus, the interplay between this quantum background and modes of the field, when disregarding the backreactions, gives rise to a theory of a quantum field on an anisotropic, dressed spacetime. Different solutions are found whose components depend on the quantum fluctuations of the background geometry. We construct a formal expression for the power spectrum of the scalar field fluctuations on such anisotropic background. It is shown that the anisotropy of this power spectrum is due to the modified frequency of the propagating quantum modes. This provides a quantitative estimate for the deviations from the isotropic power spectrum which can lead to the potential observational signatures on the cosmic microwave background. In addition, the problem of particle production when transitioning from such an effective spacetime to a classical one is reexamined. It is shown that particles are created, and the expectation value of their number operator depends on the quantum geometry fluctuations.

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arXiv2017

Bounds on the Polymer Scale from Gamma Ray Bursts

The polymer representations, which are partially motivated by loop quantum gravity, have been suggested as alternative schemes to quantize the matter fields. Here we apply a version of the polymer representations to the free electromagnetic field, in a reduced phase space setting, and derive the corresponding effective (i.e., semiclassical) Hamiltonian. We study the propagation of an electromagnetic pulse and we confront our theoretical results with gamma ray burst observations. This comparison reveals that the dimensionless polymer scale must be smaller than $4\times 10^{-35}$, casting doubts on the possibility that the matter fields are quantized with the polymer representation we employed.

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arXiv2017

Path integral polymer propagator of relativistic and non-relativistic particles

A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The mechanical models we consider are deparametrized and thus the group averaging technique is used to deal with the corresponding constraints. The transition amplitudes are written in a vertex expansion form used in the spin foam models, where here a vertex is actually a jump in position. Polymer propagators previously obtained by spectral methods for a nonrelativistic polymer particle, both free and in a box, are regained with this method and as a new result we obtain the polymer propagator of the relativistic particle. All of them reduce to their standard form in the continuum limit for which the length scale parameter of the polymer quantization is taken to be small. Our results are robust thanks to their analytic and exact character which in turn come from the fact that presented models are solvable. They lend support to the vertex expansion scheme of the polymer path integral explored before in a formal way for cosmological models. Some possible future developments are commented upon in the discussion.

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arXiv2016

Emergent Space-Time via a Geometric Renormalization Method

We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of quasi-isometry, which yields a sequence of discrete coarse grained spaces each having a continuum limit under the rescaling operation. We provide criteria under which such sequences do converge within a superspace of metric spaces, or may constitute the basin of attraction of a common continuum limit, which hopefully, may represent our space-time continuum. We discuss some of the properties of these coarse grained spaces as well as their continuum limits, such as scale invariance and metric similarity, and show that different layers of spacetime can carry different distance functions while being homeomorphic. Important tools in this analysis are the Gromov-Hausdorff distance functional for general metric spaces and the growth degree of graphs or networks. The whole construction is in the spirit of the Wilsonian renormalization group. Furthermore we introduce a physically relevant notion of dimension on the spaces of interest in our analysis, which e.g. for regular lattices reduces to the ordinary lattice dimension. We show that this dimension is stable under the proposed coarse graining procedure as long as the latter is sufficiently local, i.e. quasi-isometric, and discuss the conditions under which this dimension is an integer. We comment on the possibility that the limit space may turn out to be fractal in case the dimension is non-integer. At the end of the paper we briefly mention the possibility that our network carries a translocal far-order which leads to the concept of wormhole spaces and a scale dependent dimension if the coarse graining procedure is no longer local.

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arXiv2016

Callan-Giddings-Harvey-Strominger vacuum in loop quantum gravity and singularity resolution

We study here a complete quantization of a Callan-Giddings-Harvey-Strominger (CGHS) vacuum model following loop quantum gravity techniques. Concretely, we adopt a formulation of the model in terms of a set of new variables that resemble the ones commonly employed in spherically symmetric loop quantum gravity. The classical theory consists of two pairs of canonical variables plus a scalar and diffeomorphism (first class) constraints. We consider a suitable redefinition of the Hamiltonian constraint such that the new constraint algebra (with structure constants) is well adapted to the Dirac quantization approach. For it, we adopt a polymeric representation for both the geometry and the dilaton field. On the one hand, we find a suitable invariant domain of the scalar constraint operator, and we construct explicitly its solution space. There, the eigenvalues of the dilaton and the metric operators cannot vanish locally, allowing us to conclude that singular geometries are ruled out in the quantum theory. On the other hand, the physical Hilbert space is constructed out of them, after group averaging the previous states with the diffeomorphism constraint. In turn, we identify the standard observable corresponding to the mass of the black hole at the boundary, in agreement with the classical theory. We also construct an additional observable on the bulk associated with the square of the dilaton field, with no direct classical analog.

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arXiv2016

Polymerization, the Problem of Access to the Saddle Point Approximation, and Thermodynamics

The saddle point approximation to the partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical models for which this method can not be applied directly. This is due to the fact that their action evaluated on a classical solution is not finite and its first variation does not vanish for all consistent boundary conditions. These problems can be dealt with by adding a counter-term to the classical action, which is a solution of the corresponding Hamilton-Jacobi equation. In this work however, we seek an alternative solution to this problem via the polymer quantization which is motivated by the loop quantum gravity.

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arXiv2015

Polymer quantization and the saddle point approximation of partition functions

The saddle point approximation of the path integral partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical models for which this method cannot be applied directly. This is due to the fact that their action evaluated on a classical solution is not finite and its first variation does not vanish for all consistent boundary conditions. These problems can be dealt with by adding a counterterm to the classical action, which is a solution of the corresponding Hamilton-Jacobi equation. In this work we study the effects of polymer quantization on a mechanical model presenting the aforementioned difficulties and contrast it with the above counterterm method. This type of quantization for mechanical models is motivated by the loop quantization of gravity which is known to play a role in the thermodynamics of black hole systems. The model we consider is a nonrelativistic particle in an inverse square potential, and analyze two polarizations of the polymer quantization in which either the position or the momentum is discrete. In the former case, Thiemann's regularization is applied to represent the inverse power potential but we still need to incorporate the Hamilton-Jacobi counterterm which is now modified by polymer corrections. In the latter, momentum discrete case however, such regularization could not be implemented. Yet, remarkably, owing to the fact that the position is bounded, we do not need a Hamilton-Jacobi counterterm in order to have a well-defined saddle point approximation. Further developments and extensions are commented upon in the discussion.

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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.

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arXiv2015

The Structurally Dynamic Cellular Network and Quantum Graphity Approaches to Quantum Gravity and Quantum Geometry - A Review and Comparison

Starting from the working hypothesis that both physics and the corresponding mathematics and in particular geometry have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the discrete protoforms of the building blocks of our ordinary continuum physics and mathematics living on a smooth background, and perhaps more importantly find a way how this continuum limit emerges from the mentioned discrete structure. We model this underlying substratum as a structurally dynamic cellular network (basically a generalisation of a cellular automaton). We regard these continuum concepts and continuum spacetime in particular as being emergent, coarse-grained and derived relative to this underlying erratic and disordered microscopic substratum, which we would like to call quantum geometry and which is expected to play by quite different rules, namely generalized cellular automaton rules. A central role in our analysis is played by a geometric renormalization group which creates (among other things) a kind of sparse translocal network of correlations between the points in classical continuous space-time and underlies, in our view, such mysterious phenomena as holography and the black hole entropy-area law. The same point of view holds for quantum theory which we also regard as a low-energy, coarse-grained continuum theory, being emergent from something more fundamental. In this paper we review our approach and compare it to the quantum graphity framework.

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arXiv2013

A local true Hamiltonian for the CGHS model in new variables

Following our previous work, a complete classical solution of the CGHS model in Hamiltonian formulation in new variables is given. We preform a series of analyses and transformations to get to the CGHS Hamiltonian in new variables from a generic class of two dimensional dilatonic gravitational systems coupled to matter. This gives us a second class system, a total Hamiltonian consisting of a Hamiltonian constraint, a diffeomorphism constraint and two second class constraints. We calculate the Dirac brackets, bring them to a standard form similar to the Poisson brackets by introducing a new variable. Then by rescaling lapse and shift, the Hamiltonian constraint is transformed into a form where it has an strong Abelian algebra with itself. This property holds both in vacuum case and in case with matter coupling. Then for each of the vacuum and the coupled-to-matter cases, we preform two gauge fixings, one set for each case, and solve the classical system completely in both cases. The gauge fixing of the case coupled to matter is done by implementing a method based on canonical transformation to a new set of variables and leads to a true local Hamiltonian. We also show that our formalism is consistent with the original CGHS paper by showing that the equations of motion are the same in both cases. Finally we derive the relevant surface term of the model.

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arXiv2011

Quantum scalar field in quantum gravity: the propagator and Lorentz invariance in the spherically symmetric case

We recently studied gravity coupled to a scalar field in spherical symmetry using loop quantum gravity techniques. Since there are local degrees of freedom one faces the "problem of dynamics". We attack it using the "uniform discretization technique". We find the quantum state that minimizes the value of the master constraint for the case of weak fields and curvatures. The state has the form of a direct product of Gaussians for the gravitational variables times a modified Fock state for the scalar field. In this paper we do three things. First, we verify that the previous state also yields a small value of the master constraint when one polymerizes the scalar field in addition to the gravitational variables. We then study the propagators for the polymerized scalar field in flat space-time using the previously considered ground state in the low energy limit. We discuss the issue of the Lorentz invariance of the whole approach. We note that if one uses real clocks to describe the system, Lorentz invariance violations are small. We discuss the implications of these results in the light of Horava's Gravity at the Lifshitz point and of the argument about potential large Lorentz violations in interacting field theories of Collins et. al.

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arXiv2011

Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?

We discuss the applicability of the argument of Collins, Pérez, Sudarsky, Urrutia and Vucetich to loop quantum gravity. This argument suggests that Lorentz violations, even ones that only manifest themselves at energies close to the Planck scale, have significant observational consequences at low energies when one considers perturbative quantum field theory and renormalization. We show that non-perturbative treatments like those of loop quantum gravity may generate deviations of Lorentz invariance of a different type than those considered by Collins et al. that do not necessarily imply observational consequences at low energy.

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