arXiv subjects

Rodolfo Gambini

Publications and source records attributed to Rodolfo Gambini.

At least 55 records · Page 3Linked to original sources

arXiv2014

Casimir effect in a quantum space-time

We apply quantum field theory in quantum space-time techniques to study the Casimir effect for large spherical shells. As background we use the recently constructed exact quantum solution for spherically symmetric vacuum space-time in loop quantum gravity. All calculations are finite and one recovers the usual results without the need of regularization or renormalization. This is an example of how loop quantum gravity provides a natural resolution to the infinities of quantum field theories.

gr-qc↗

arXiv2014

Quantum shells in a quantum space-time

We study the quantum motion of null shells in the quantum space-time of a black hole in loop quantum gravity. We treat the shells as test fields and use an effective dynamics for the propagation equations. The shells propagate through the region where the singularity was present in the classical black hole space-time, but is absent in the quantum space-time, eventually emerging through a white hole to a new asymptotic region of the quantum space-time. The profiles of the shells get distorted due to the quantum fluctuations in the Planckian region that replaces the singularity. The evolution of the shells is unitary throughout the whole process.

gr-qc↗

arXiv2014

A scenario for black hole evaporation on a quantum geometry

We incorporate elements of the recently discovered exact solutions of the quantum constraints of loop quantum gravity for vacuum spherically symmetric space-times into the paradigm of black hole evaporation due to Ashtekar and Bojowald. The quantization of the area of the surfaces of symmetry of the solutions implies that the number of nice slices that can be fit inside the black hole is finite. The foliation eventually moves through the region where the singularity in the classical theory used to be and all the particles that fell into the black hole due to Hawking radiation emerge finally as a white hole. This yields a variant of a scenario advocated by Arkani-Hamed {\em et al.} Fluctuations in the horizon that naturally arise in the quantum space time allow radiation to emerge during the evaporation process due to stimulated emission allowing evaporation to proceed beyond Page time without reaching the maximum entanglement limit until the formation of the white hole. No firewalls nor remnants arise in this scenario.

gr-qc↗

arXiv2014

The SL(2,R) totally constrained model: three quantization approaches

We provide a detailed comparison of the different approaches available for the quantization of a totally constrained system with a constraint algebra generating the non-compact $SL(2,\mathbb{R})$ group. In particular, we consider three schemes: the Refined Algebraic Quantization, the Master Constraint Programme and the Uniform Discretizations approach. For the latter, we provide a quantum description where we identify semiclassical sectors of the kinematical Hilbert space. We study the quantum dynamics of the system in order to show that it is compatible with the classical continuum evolution. Among these quantization approaches, the Uniform Discretizations provides the simpler description in agreement with the classical theory of this particular model, and it is expected to give new insights about the quantum dynamics of more realistic totally constrained models such as canonical general relativity.

gr-qc↗

arXiv2014

Emergence of string-like physics from Lorentz invariance in loop quantum gravity

We consider a quantum field theory on a spherically symmetric quantum space time described by loop quantum gravity. The spin network description of space time in such a theory leads to equations for the quantum field that are discrete. We show that to avoid significant violations of Lorentz invariance one needs to consider specific non-local interactions in the quantum field theory similar to those that appear in string theory. This is the first sign that loop quantum gravity places restrictions on the type of matter considered, and points to a connection with string theory physics.

gr-qc↗

arXiv2014

Hawking radiation from a spherical loop quantum gravity black hole

We introduce quantum field theory on quantum space-times techniques to characterize the quantum vacua as a first step towards studying black hole evaporation in spherical symmetry in loop quantum gravity and compute the Hawking radiation. We use as quantum space time the recently introduced exact solution of the quantum Einstein equations in vacuum with spherical symmetry and consider a spherically symmetric test scalar field propagating on it. The use of loop quantum gravity techniques in the background space-time naturally regularizes the matter content, solving one of the main obstacles to back reaction calculations in more traditional treatments. The discreteness of area leads to modifications of the quantum vacua, eliminating the trans-Planckian modes close to the horizon, which in turn eliminates all singularities from physical quantities, like the expectation value of the stress energy tensor. Apart from this, the Boulware, Hartle--Hawking and Unruh vacua differ little from the treatment on a classical space-time. The asymptotic modes near scri are reproduced very well. We show that the Hawking radiation can be computed, leading to an expression similar to the conventional one but with a high frequency cutoff. Since many of the conclusions concern asymptotic behavior, where the spherical mode of the field behaves in a similar way as higher multipole modes do, the results can be readily generalized to non spherically symmetric fields.

gr-qc↗

arXiv2014

Quantum black holes in Loop Quantum Gravity

We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and that the singularity inside black holes is resolved. Moreover, we consider an alternative quantization based on a slightly different kinematical Hilbert space. The ambiguity in kinematical spaces stems from how one treats the periodicity of one of the classical variables in these models. The corresponding physical Hilbert spaces solve the diffeomorphism and Hamiltonian constraint but their intrinsic structure is radically different depending on the kinematical Hilbert space one started from. In both cases there are quantum observables that do not have a classical counterpart. However, one can show that at the end of the day, by examining Dirac observables, both quantizations lead to the same physical predictions.

gr-qc↗

arXiv2013

An introduction to spherically symmetric loop quantum gravity black holes

We review recent developments in the treatment of spherically symmetric black holes in loop quantum gravity. In particular, we discuss an exact solution to the quantum constraints that represents a black hole and is free of singularities. We show that new observables that are not present in the classical theory arise in the quantum theory. We also discuss Hawking radiation by considering the quantization of a scalar field on the quantum spacetime.

gr-qc↗

arXiv2013

Loop quantization of the Schwarzschild black hole

We quantize spherically symmetric vacuum gravity without gauge fixing the diffeomorphism constraint. Through a rescaling, we make the algebra of Hamiltonian constraints Abelian and therefore the constraint algebra is a true Lie algebra. This allows the completion of the Dirac quantization procedure using loop quantum gravity techniques. We can construct explicitly the exact solutions of the physical Hilbert space annihilated by all constraints. New observables living in the bulk appear at the quantum level (analogous to spin in quantum mechanics) that are not present at the classical level and are associated with the discrete nature of the spin network states of loop quantum gravity. The resulting quantum space-times resolve the singularity present in the classical theory inside black holes.

gr-qc↗

arXiv2012

Spherically symmetric gravity coupled to a scalar field with a local Hamiltonian: the complete initial-boundary value problem using metric variables

We discuss a gauge fixing of gravity coupled to a scalar field in spherical symmetry such that the Hamiltonian is an integral over space of a local density. In a previous paper we had presented it using Ashtekar's new variables. Here we study it in metric variables. We specify completely the initial-boundary value problem for ingoing Gaussian pulses.

gr-qc↗

arXiv2012

Self-adjointness in the Hamiltonians of deparameterized totally constrained theories: a model

Several proposals to deal with the dynamics of general relativity involve gauge fixings or the introduction matter fields in terms of which the theory is deparameterized. The resulting theories have true Hamiltonians for their evolution that usually involve square roots, and this poses certain challenges for their implementation as self-adjoint quantum operators. We show in the context of a simple model of totally constrained theory that one can introduce related, well defined operators that reproduce semiclassically the same physics as the original ones, at least for states peaked in the regions of phase space where their associated classical quantities are well defined.

gr-qc↗

arXiv2012

A local Hamiltonian for spherically symmetric gravity coupled to a scalar field

We present a gauge fixing of gravity coupled to a scalar field in spherical symmetry such that the Hamiltonian is an integral over space of a local density. Such a formulation had proved elusive over the years. As in any gauge fixing, it works for a restricted set of initial data. We argue that the set could be large enough to attempt a quantization the could include the important case of an evaporating black hole.

gr-qc↗

arXiv2012

Discretisations, Constraints and Diffeomorphisms in Quantum Gravity

In this review we discuss the interplay between discretization, constraint implementation, and diffeomorphism symmetry in Loop Quantum Gravity and Spin Foam models. To this end we review the Consistent Discretizations approach, which is an application of the master constraint program to construct the physical Hilbert space of the canonical theory, as well as the Perfect Actions approach, which aims at finding a path integral measure with the correct symmetry behavior under diffeomorphisms.

gr-qc↗

arXiv2011

An axiomatic formulation of the Montevideo interpretation of quantum mechanics

We make a first attempt to axiomatically formulate the Montevideo interpretation of quantum mechanics. In this interpretation environmental decoherence is supplemented with loss of coherence due to the use of realistic clocks to measure time to solve the measurement problem. The resulting formulation is framed entirely in terms of quantum objects without having to invoke the existence of measurable classical quantities like the time in ordinary quantum mechanics. The formulation eliminates any privileged role to the measurement process giving an objective definition of when an event occurs in a system.

quant-ph↗

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.

gr-qc↗

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.

gr-qc↗

arXiv2010

A realist interpretation of quantum mechanics based on undecidability due to gravity

We summarize several recent developments suggesting that solving the problem of time in quantum gravity leads to a solution of the measurement problem in quantum mechanics. This approach has been informally called "the Montevideo interpretation". In particular we discuss why definitions in this approach are not "for all practical purposes" (fapp) and how the problem of outcomes is resolved.

quant-ph↗

arXiv2010

Undecidability as solution to the problem of measurement: fundamental criterion for the production of events

In recent papers we put forth a new interpretation of quantum mechanics, colloquially known as ``the Montevideo interpretation''. This interpretation is based on taking into account fundamental limits that gravity imposes on the measurement process. As a consequence one has that situations develop where a reduction process is undecidable from an evolution operator. When such a situation is achieved, an event has taken place. In this paper we sharpen the definition of when and how events occur, more precisely we give sufficient conditions for the occurrence of events. We probe the new definition in an example. In particular we show that the concept of undecidability used is not ``FAPP'' (for all practical purposes), but fundamental.

quant-ph↗