# Saeed RastgooUniversity of Alberta | UAlberta · Department of Physics

Saeed Rastgoo

Ph.D.

## About

53

Publications

4,176

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686

Citations

Citations since 2017

Introduction

Saeed Rastgoo is currently an assistant professor of physics at the School of Sciences and Engineering, at Monterrey Institute of Technology (ITESM), Campus Leon, Guanajuato, Mexico.
Saeed's research is in theoretical and mathematical physics, classical and quantum gravity, and black hole physics. His current projects include "Quantum black holes: interior, exterior, and matter fields", "Quantum gravity in terms of observables" and "Emergence of smooth spacetime".

## Publications

Publications (53)

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundament...

We compute the expected response of detector arms of gravitational wave observatories to polymerized gravitational waves. The mathematical and theoretical features of these waves were discussed in our previous work. In the present manuscript, we find both perturbative analytical, and full nonperturbative numerical solutions to the equations of moti...

It is widely accepted that curvature singularity resolution should be a feature of quantum gravity. We present a class of time-dependent asymptotically flat spherically symmetric metrics that model gravitational collapse in quantum gravity. The metrics capture intuitions associated with the dynamics of singularity resolution, and horizon formation...

We compute the expected response of detector arms of gravitational wave observatories to polymerized gravitational waves. The mathematical and theoretical features of these waves were discussed in our previous work. In the present manuscript, we find both perturbative analytical, and full nonperturbative numerical solutions to the equations of moti...

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundament...

We review, as well as provide some new results regarding the study of the structure of spacetime and the singularity in the interior of the Schwarzschild black hole in both loop quantum gravity and generalized uncertainty principle approaches, using congruences and their associated expansion scalar and the Raychaudhuri equation. We reaffirm previou...

It is widely accepted that curvature singularity resolution should be a feature of quantum gravity. We present a class of time-dependent asymptotically flat spherically symmetric metrics that model gravitational collapse in quantum gravity. The metrics capture intuitions associated with the dynamics of singularity resolution, and horizon formation...

We review, as well as provide some new results regarding the study of the structure of spacetime and the singularity in the interior of the Schwarzschild black hole in both loop quantum gravity and generalized uncertainty principle approaches, using congruences and their associated expansion scalar and the Raychaudhuri equation. We reaffirm previou...

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundament...

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological app...

Inspirals of an intermediate mass black hole (IMBH) and a solar mass type object will be observable by space based gravitational wave detectors such as the Laser Interferometer Space Antenna. A dark matter overdensity around an IMBH—a dark matter spike—can affect the orbital evolution of the system. We consider here such intermediate mass ratio ins...

The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give u...

Inspirals of an Intermediate Mass Black Hole (IMBH) and a solar mass type object will be observable by space based gravitational wave detectors such as The Laser Interferometer Space Antenna (LISA). A dark matter overdensity around an IMBH - a dark matter spike - can affect the orbital evolution of the system. We consider here such Intermediate Mas...

The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give u...

We propose a polymer quantization scheme to derive the effective propagation of gravitational waves on a classical Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. These waves, which may originate from a high energy source, are a consequence of the dynamics of the gravitational field in a linearized low-energy regime. A novel method of derivin...

We show that loop quantum gravity effects leads to the finiteness of expansion and its rate of change in the effective regime in the interior of the Schwarzschild black hole. As a consequence the singularity is resolved.

A bstract
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...

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 res...

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 Ray...

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-Lemaître-Robertson-Walker space...

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 the...

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 the...

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 related to two parameters δb,δc associated to the minimum length in the radial and angular directions, that enter Thiemann’s trick for quantum inverse tr...

The linearized Einstein field equations provide a low energy wave equation for propagation of gravitational fields which may be originated from a high energy source. Motivated by loop quantum gravity (LQG), we propose the polymer quantization scheme to derive the effective propagation of such waves on a classical FLRW spacetime. To overcome the cha...

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 res...

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 the...

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...

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...

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 back...

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 back...

The study of the interior of black holes in the quantum regime is important, not only with regard to the singularity avoidance, but also to get more insight into their behavior in connection with quantum gravity. We introduce several extensions and new improvements regarding the previous works on the effective behavior of the interior of the Schwar...

We study the interior of the Schwarzschild black hole in the presence of further inverse triad quantum corrections, using loop quantum gravity techniques. Although this model has been studied using loop quantization before, so far, inverse triad corrections have been neglected, mostly to simplify the analysis. Due to the noncompact spatial topology...

Within Loop Quantum Gravity, the polymer representation has been suggested as a possible matter field quantization scheme. Here we apply a version of the polymer quantization to the electromagnetic field, in a reduced phase space setting, and derive the corresponding effective (i.e., semiclassical) Hamiltonian. In this limit the theory is nonlinear...

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 corr...

We study here a complete quantization of a Callan-Giddings-Harvey-Strominger 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...

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 pa...

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...

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 s...

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 models, with and
without matter, one can perform a series of cano...

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 can not be applied directly. This is due to the fact that their action evaluated on...

Starting from the working hypothesis that both physics and the corresponding
mathematics 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. We regard these cont...

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...

This is a summary of the talk presented by one of us in Loops 2011. We discuss the application of the uniform discretization approach to spherically symmetric gravity coupled to a spherically symmetric scalar field.

We respond to a comment by Joseph Polchinski on: 'Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?'

We discuss the applicability of the argument of Collins, P\'erez, 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 f...

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 f...

We reconsider the argument of Collins, Perez, Sudarsky, Urrutia and
Vucetich concerning violations of Lorentz invariance in the context of
loop quantum gravity. We show that even if one introduces a lattice that
violates Lorentz invariance at the Planck scale, this does not translate
itself into large violations that would conflict with experiment.

We show that the canonical formulation of a generic action for (1 + 1)-dimensional models of gravity coupled to matter admits a description in terms of Ashtekar-type variables. This opens the possibility of discussing models of black hole evaporation using loop representation techniques and verifying which paradigm emerges for the possible eliminat...

We study gravity coupled to a scalar field in spherical symmetry using loop quantum gravity techniques. Since this model has local degrees of freedom, one has to face ``the problem of dynamics'', that is, diffeomorphism and Hamiltonian constraints that do not form a Lie algebra. We tackle the problem using the ``uniform discretization'' technique....

This new approach, suggests that the nature and the mathematics that describe it, are discrete at and below the planck scale. Also it assumes that the physical world, has several levels and each level has its own structure, laws and eective theories based on these laws. These laws, structures and theories, emerge from the ones of the previous level...

## Projects

Projects (3)

We are working towards finding a new quantum representation for gravity based on a certain group of loops. This is a representation that is distinct from the one used in loop quantum gravity or string theory.
This approach has several interesting aspects: In it, space-time points are emergent entities that would only have quasi-classical status. The formulation is given entirely in terms of Dirac observables forming a set of gauge invariant quantities that completely define the Riemannian geometry of the spacetime. Also, at the quantum level this formulation will lead to a reduced phase space quantization free of any constraints.
Historically, this can be considered as the continuation and extension of Mandelstam's program to represent gauge theories based on loops, that was completed for Yang–Mills theories by Gambini and Trias in the 1980s.

We study the behavior of black holes in the regime where both their spacetime and the matter field on it are quantized. This also serves as the study of the two-way relationship between the black holes and quantum gravity in general, to get insight about both, from the study of both subjects.

Understanding the quantum/fine structure of spacetime and investigating whether/how it may emerge from a more fundamental substrate