arXiv subjects

Rodolfo Gambini

Publications and source records attributed to Rodolfo Gambini.

At least 37 records · Page 2Linked to original sources

arXiv2020

Critical collapse of a scalar field in semiclassical loop quantum gravity

We study the collapse in spherical symmetry of a massless scalar field minimally coupled to gravity using the semiclassical equations that are expected from loop quantum gravity. We find critical behavior of the mass as a function of the parameters of the initial data similar to that found by Choptuik in classical general relativity for a large set of initial data and values of the polymerization parameter. Contrary to wide expectations for quantum gravity, our semiclassical field equations have an exact scale invariance, as do the classical field equations. As one would then expect, we numerically find that the phase transition is second order, again as in the classical case.

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arXiv2020

Axisymmetric gravity in real Ashtekar variables: the quantum theory

In a previous paper we formulated axisymmetric general relativity in terms of real Ashtekar--Barbero variables. Here we proceed to quantize the theory. We are able to implement Thiemann's version of the Hamiltonian constraint. We discuss its action including the matrix elements and its solutions. This provides a 2+1 dimensional arena to test ideas for the dynamics of quantum gravity and opens the possibility of quantum studies of rotating black hole spacetimes.

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arXiv2019

Quantum fluctuating geometries and the information paradox II

In a previous paper we discussed corrections to Hawking radiation from a collapsing shell due to quantum fluctuations of the shell and the resulting horizon. For the computation of the quantum corrections we used several approximations. In this paper we take into account effects that were neglected in the previous one. We find important corrections including non-thermal contributions to the radiation at high frequencies and a frequency dependent time scale at which the emission of thermal radiation of frequency $ω$ cuts off. Such scale tends to infinity in the limit of a classical shell. The fact that one has almost from the outset non-thermal radiation has significant implications for the information paradox. In particular the amount of non-thermality is considerably larger than what we had estimated before. A naive estimate of the evaporation time leads to a much faster evaporation than in the usual Hawking analysis.

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arXiv2019

Covariance of the extended holonomy

It has been pointed out that the holonomy of generic extended loops is not gauge covariant. We show how to define a family of extended loops for which previous criticism does not apply. We also give sufficient conditions that extended loops must satisfy in order to yield covariant holonomies. This makes a quantum representation for Yang--Mills theories and gravity based on extended loops viable.

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arXiv2019

Classical axisymmetric gravity in real Ashtekar variables

We formulate axisymmetric general relativity in terms of real Ashtekar--Barbero variables. We study the constraints and equations of motion and show how the Kerr, Schwarzschild and Minkowski solutions arise. We also discuss boundary conditions. This opens the possibility of a midisuperspace quantization using loop quantum gravity techniques for spacetimes with axial symmetry and time dependence.

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arXiv2018

Gravitation in terms of observables

In the 1960's, Mandelstam proposed a new approach to gauge theories and gravity based on loops. The program for gauge theories was completed for Yang--Mills theories by Gambini and Trias in the 1980's. Gauge theories could be understood as representations of certain group: the group of loops. The same formalism could not be implemented at that time for the gravitational case. Here we would like to propose an extension to the case of gravity. The resulting theory is described in terms of loops and open paths and can provide the underpinning for a new quantum representation for gravity distinct from the one used in loop quantum gravity or string theory. In it, space-time points are emergent entities that would only have quasi-classical status. The formulation may be given entirely in terms of Dirac observables that form a complete set of gauge invariant functions that completely define the Riemannian geometry of the spacetime. At the quantum level this formulation will lead to a reduced phase space quantization free of any constraints.

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arXiv2018

A single-world consistent interpretation of quantum mechanics from fundamental time and length uncertainties

Within ordinary ---unitary--- quantum mechanics there exist global protocols that allow to verify that no definite event ---an outcome to which a probability can be associated--- occurs. Instead, states that start in a coherent superposition over possible outcomes always remain as a superposition. We show that, when taking into account fundamental errors in measuring length and time intervals, that have been put forward as a consequence of a conjunction of quantum mechanical and general relativity arguments, there are instances in which such global protocols no longer allow to distinguish whether the state is in a superposition or not. All predictions become identical as if one of the outcomes occurs, with probability determined by the state. We use this as a criteria to define events, as put forward in the Montevideo Interpretation of Quantum Mechanics. We analyze in detail the occurrence of events in the paradigmatic case of a particle in a superposition of two different locations. We argue that our approach provides a consistent (C) single-world (S) picture of the universe, thus allowing an economical way out of the limitations imposed by a recent theorem by Frauchiger and Renner showing that having a self-consistent single-world description of the universe is incompatible with quantum theory. In fact, the main observation of this paper may be stated as follows: If quantum mechanics is extended to include gravitational effects to a QG theory, then QG, S, and C are satisfied.

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arXiv2018

Quantum fluctuating CGHS geometries and the information paradox

We study Hawking radiation on the quantum spacetime generated by a quantum ingoing null shell in the 2d theory proposed by Callan-Giddings-Harvey-Strominger (CGHS). The quantum spacetime is a superposition of classical geometries with uncertainty in position and momentum of the collapsing shell. The Hawking radiation spectrum is computed, revealing a non-thermal behavior for finite time as well as a dependence on the shell's physical degrees of freedom. Hawking radiation's dependence on the collapsing shell becomes irrelevant in the late time approximation as we reach $i^+$ since the radiation's temperature depends exclusively on the cosmological constant. However, we argue that the information of the quantum state of a collapsing shell can be read from the Hawking radiation if we perform measurements at $\mathcal{I_R^+}$ taking into account backreaction effects.

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arXiv2018

The Montevideo Interpretation of Quantum Mechanics: a short review

The Montevideo interpretation of quantum mechanics, which consists in supplementing environmental decoherence with fundamental limitations in measurement stemming from gravity, has been described in several publications. However, some of them appeared before the full picture provided by the interpretation was developed. As such it can be difficult to get a good understanding via the published literature. Here we summarize it in a self contained brief presentation including all its principal elements.

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arXiv2017

Quantum fluctuating geometries and the information paradox

We study Hawking radiation on the quantum space-time of a collapsing null shell. We use the geometric optics approximation as in Hawking's original papers to treat the radiation. The quantum space-time is constructed by superposing the classical geometries associated with collapsing shells with uncertainty in their position and mass. We show that there are departures from thermality in the radiation even though we are not considering back reaction. One recovers the usual profile for the Hawking radiation as a function of frequency in the limit where the space-time is classical. However, when quantum corrections are taken into account, the profile of the Hawking radiation as a function of time contains information about the initial state of the collapsing shell. More work will be needed to determine if all the information can be recovered. The calculations show that non-trivial quantum effects can occur in regions of low curvature when horizons are involved, as for instance advocated in the firewall scenario.

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arXiv2016

Conformal loop quantum gravity coupled to the Standard Model

We argue that a conformally invariant extension of general relativity coupled to the Standard Model is the fundamental theory that needs to be quantized. We show that it can be treated by loop quantum gravity techniques. Through a gauge fixing and a modified Higgs mechanism particles acquire mass and one recovers general relativity coupled to the Standard Model. The theory suggests new views with respect to the definition of the Hamiltonian constraint in loop quantum gravity, the semi-classical limit and the issue of finite renormalization in quantum field theory in quantum space-time. It also gives hints about the elimination of ambiguities that arise in quantum field theory in quantum space-time in the calculation of back-reaction.

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arXiv2016

Event ontology in quantum mechanics and downward causation

We show that several interpretations of quantum mechanics admit an ontology of objects and events. This ontology reduces the breach between mind and matter. When humans act, their actions do not appear explainable in mechanical terms but through mental activity: motives, desires or needs that propel them to action. These are examples of what in the last few decades have come to be called "downward causation". Basically, downward causation is present when the disposition of the whole to behave in a certain way cannot be predicted from the dispositions of the parts. The event ontology of quantum mechanics allow us to show that systems in entangled states present emergent new properties and downward causation.

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arXiv2016

Schrödinger-like quantum dynamics in loop quantized black holes

We show, following a previous quantization of a vacuum spherically symmetric spacetime carried out in Ref. \cite{gop}, that this setting admits a Schrödinger-like picture. More precisely, the technique adopted there for the definition of parametrized Dirac observables (that codify local information of the quantum theory) can be extended in order to accommodate different pictures. In this new picture, the quantum states are parametrized in terms of suitable gauge parameters and the observables constructed out of the kinematical ones on this space of parametrized states.

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arXiv2016

Quantum self-gravitating collapsing matter in a quantum geometry

The problem of how space-time responds to gravitating quantum matter in full quantum gravity has been one of the main questions that any program of quantization of gravity should address. Here we analyze this issue by considering the quantization of a collapsing null shell coupled to spherically symmetric loop quantum gravity. We show that the constraint algebra of canonical gravity is Abelian both classically and when quantized using loop quantum gravity techniques. The Hamiltonian constraint is well defined and suitable Dirac observables characterizing the problem were identified at the quantum level. We can write the metric as a parameterized Dirac observable at the quantum level and study the physics of the collapsing shell and black hole formation. We show how the singularity inside the black hole is eliminated by loop quantum gravity and how the shell can traverse it. The construction is compatible with a scenario in which the shell tunnels into a baby universe inside the black hole or one in which it could emerge through a white hole.

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arXiv2015

Stress energy tensor renormalization for a spherically symmetric massive scalar field on a quantum space-time

We consider a massive scalar field living on the recently found exact quantum space-time corresponding to vacuum spherically symmetric loop quantum gravity. The discreteness of the quantum space time naturally regularizes the scalar field, eliminating divergences. However, the resulting finite theory depends on the details of the micro physics. We argue that such dependence can be eliminated through a finite renormalization and discuss its nature. This is an example of how quantum field theories on quantum space times deal with the issues of divergences in quantum field theories.

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arXiv2015

No fermion doubling in quantum geometry

In loop quantum gravity the discrete nature of quantum geometry acts as a natural regulator for matter theories. Studies of quantum field theory in quantum space-times in spherical symmetry in the canonical approach have shown that the main effect of the quantum geometry is to discretize the equations of matter fields. This raises the possibility that in the case of fermion fields one could confront the usual fermion doubling problem that arises in lattice gauge theories. We suggest, again based on recent results on spherical symmetry, that since the background space-times will generically involve superpositions of states associated with different discretizations the phenomenon may not arise. This opens a possibility of incorporating chiral fermions in the framework of loop quantum gravity.

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arXiv2015

Quantum mechanics, strong emergence and ontological non-reducibility

We show that a new interpretation of quantum mechanics, in which the notion of event is defined without reference to measurement or observers, allows to construct a quantum general ontology based on systems, states and events. Unlike the Copenhagen interpretation, it does not resort to elements of a classical ontology. The quantum ontology in turn allows us to recognize that a typical behavior of quantum systems exhibits strong emergence and ontological non-reducibility. Such phenomena are not exceptional but natural, and are rooted in the basic mathematical structure of quantum mechanics.

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arXiv2014

Quantum space-time of a charged black hole

We quantize spherically symmetric electrovacuum gravity. The algebra of Hamiltonian constraints can be made Abelian via a rescaling and linear combination with the diffeomorphism constraint. As a result the constraint algebra is a true Lie algebra. We complete the Dirac quantization procedure using loop quantum gravity techniques. We present explicitly the exact solutions of the physical Hilbert space annihilated by all constraints. The resulting quantum space-times resolve the singularity present in the classical theory inside charged black holes and allows to extend the space-time through where the singularity used to be into new regions. We show that quantum discreteness of space-time may also play a role in stabilizing the Cauchy horizons, though back reaction calculations are needed to confirm this point.

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