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Simone Speziale

Publications and source records attributed to Simone Speziale.

At least 55 records · Page 3Linked to original sources
arXiv2016

Twisted geometries, twistors and conformal transformations

The twisted geometries of spin network states are described by simple twistors, isomorphic to null twistors with a time-like direction singled out. The isomorphism depends on the Immirzi parameter, and reduces to the identity when the parameter goes to infinity. Using this twistorial representation we study the action of the conformal group SU(2,2) on the classical phase space of loop quantum gravity, described by twisted geometry. The generators of translations and conformal boosts do not preserve the geometric structure, whereas the dilatation generator does. It corresponds to a 1-parameter family of embeddings of T*SL(2,C) in twistor space, and its action preserves the intrinsic geometry while changing the extrinsic one - that is the boosts among polyhedra. We discuss the implication of this action from a dynamical point of view, and compare it with a discretisation of the dilatation generator of the continuum phase space, given by the Lie derivative of the group character. At leading order in the continuum limit, the latter reproduces the same transformation of the extrinsic geometry, while also rescaling the areas and volumes and preserving the angles associated with the intrinsic geometry. Away from the continuum limit its action has an interesting non-linear structure, but is in general incompatible with the closure constraint needed for the geometric interpretation. As a side result, we compute the precise relation between the extrinsic geometry used in twisted geometries and the one defined in the gauge-invariant parametrization by Dittrich and Ryan, and show that the secondary simplicity constraints they posited coincide with those dynamically derived in the toy model of [1409.0836].

gr-qc↗
arXiv2016

Non-singular rotating black hole with a time delay in the center

As proposed by Bambi and Modesto, rotating non-singular black holes can be constructed via the Newman-Janis algorithm. Here we show that if one starts with a modified Hayward black hole with a time delay in the centre, the algorithm succeeds in producing a rotating metric, but curvature divergences reappear. To preserve finiteness, the time delay must be introduced directly at the level of the non-singular rotating metric. This is possible thanks to the deformation of the inner stationarity limit surface caused by the regularisation, and in more than one way. We outline three different possibilities, distinguished by the angular velocity of the event horizon. Along the way, we provide additional results on the Bambi-Modesto rotating Hayward metric, such as the structure of the regularisation occurring at the centre, the behaviour of the quantum gravity scale alike an electric charge in decreasing the angular momentum of the extremal black hole configuration, or details on the deformation of the ergosphere.

gr-qc↗
arXiv2015

A note on the secondary simplicity constraints in loop quantum gravity

A debate has appeared in the literature on loop quantum gravity and spin foams, over whether the secondary simplicity constraints, reducing the connection to be Levi-Civita, should imply the shape matching conditions, reducing twisted geometries to Regge geometries. We address the question using a simple model with a flat dynamics, in which secondary simplicity constraints arise from a dynamical preservation of the primary ones. We find that shape matching conditions arise, thus providing support to an affirmative question. The origin of these extra conditions is to be found in the different graph localisation of the Hamiltonian and primary simplicity constraints. Our results are consistent with previous claims by Dittrich and Ryan, and extend their validity to Lorentzian signature and arbitrary cellular decompositions. We show in particular how the (gauge-invariant version of the) twist angle xi featuring in twisted geometries equals on-shell the Regge dihedral angle multiplied by the Immirzi parameter, thus recovering the discrete extrinsic geometry from the Ashtekar-Barbero holonomy. Finally, we confirm that flatness implies both the Levi-Civita and the shape-matching conditions using twisted geometries and a 4-dimensional version of the vertex condition appearing in 't Hooft's polygon model.

gr-qc↗
arXiv2015

On the Effective Metric of a Planck Star

Spacetime metrics describing `non-singular' black holes are commonly studied in the literature as effective modification to the Schwarzschild solution that mimic quantum gravity effects removing the central singularity. Here we point out that to be physically plausible, such metrics should also incorporate the 1-loop quantum corrections to the Newton potential and a non-trivial time delay between an observer at infinity and an observer in the regular center. We present a modification of the well-known Hayward metric that features these two properties. We discuss bounds on the maximal time delay imposed by conditions on the curvature, and the consequences for the weak energy condition, in general violated by the large transversal pressures introduced by the time delay.

gr-qc↗
arXiv2015

First order gravity on the light front

We study the canonical structure of the real first order formulation of general relativity on a null foliation. We use a tetrad decomposition which allows to elegantly encode the nature of the foliation in the norm of a vector in the fibre bundle. The resulting constraint structure shows some peculiarities. In particular, the dynamical Einstein equations propagating the physical degrees of freedom appear in this formalism as second class tertiary constraints, which puts them on the same footing as the Hamiltonian constraint of the Ashtekar's connection formulation. We also provide a framework to address the issue of zero modes in gravity, in particular, to study the non-perturbative fate of the zero modes of the linearized theory. Our results give a new angle on the dynamics of general relativity and can be used to quantize null hypersurfaces in the formalism of loop quantum gravity or spin foams.

gr-qc↗
arXiv2014

Null twisted geometries

We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalims are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, abelian geometric picture. It can be described by an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is naturally decomposed into a conformal metric and scale factors, forming locally conjugate pairs. Proper action-angle variables on the gauge-invariant phase space are described by the eigenvectors of the Laplacian of the dual graph. We also identify the variables of the phase space amenable to characterize the extrinsic geometry of the foliation. Finally, we quantise the phase space and its algebra using Dirac's algorithm, obtaining a notion of spin networks for null hypersurfaces. Such spin networks are labelled by SO(2) quantum numbers, and are embedded non-trivially in the unitary, infinite-dimensional irreducible representations of the Lorentz group.

gr-qc↗
arXiv2013

Chiral description of ghost-free massive gravity

We propose and study a new first order version of the ghost-free massive gravity. Instead of metrics or tetrads, it uses a connection together with Plebanski's chiral 2-forms as fundamental variables, rendering the phase space structure similar to that of SU(2) gauge theories. The chiral description simplifies computations of the constraint algebra, and allows us to perform the complete canonical analysis of the system. In particular, we explicitly compute the secondary constraint and carry out the stabilization procedure, thus proving that in general the theory propagates 7 degrees of freedom, consistently with previous claims. Finally, we point out that the description in terms of 2-forms opens the door to an infinite class of ghost-free massive bi-gravity actions. Our results apply directly to Euclidean signature. The reality conditions to be imposed in the Lorentzian signature appear to be more complicated than in the usual gravity case and are left as an open issue.

hep-th↗
arXiv2012

The twistorial structure of loop-gravity transition amplitudes

The spin foam formalism provides transition amplitudes for loop quantum gravity. Important aspects of the dynamics are understood, but many open questions are pressing on. In this paper we address some of them using a twistorial description, which brings new light on both classical and quantum aspects of the theory. At the classical level, we clarify the covariant properties of the discrete geometries involved, and the role of the simplicity constraints in leading to SU(2) Ashtekar-Barbero variables. We identify areas and Lorentzian dihedral angles in twistor space, and show that they form a canonical pair. The primary simplicity constraints are solved by simple twistors, parametrized by SU(2) spinors and the dihedral angles. We construct an SU(2) holonomy and prove it to correspond to the (lattice version of the) Ashtekar-Barbero connection. We argue that the role of secondary constraints is to provide a non trivial embedding of the cotangent bundle of SU(2) in the space of simple twistors. At the quantum level, a Schroedinger representation leads to a spinorial version of simple projected spin networks, where the argument of the wave functions is a spinor instead of a group element. We rewrite the Liouville measure on the cotangent bundle of SL(2,C) as an integral in twistor space. Using these tools, we show that the Engle-Pereira-Rovelli-Livine transition amplitudes can be derived from a path integral in twistor space. We construct a curvature tensor, show that it carries torsion off-shell, and that its Riemann part is of Petrov type D. Finally, we make contact between the semiclassical asymptotic behaviour of the model and our construction, clarifying the relation of the Regge geometries with the original phase space.

gr-qc↗
arXiv2012

Discrete Gravity Models and Loop Quantum Gravity: a Short Review

We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the Plebanski action. We discuss the role of discrete geometries in the spin foam formalism, with particular attention to the definition of the simplicity constraints.

gr-qc↗
arXiv2012

On the Relations between Gravity and BF Theories

We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both self-dual and non-chiral formulations, their generalizations, and the MacDowell-Mansouri action.

gr-qc↗
arXiv2012

Spinors and Twistors in Loop Gravity and Spin Foams

Spinorial tools have recently come back to fashion in loop gravity and spin foams. They provide an elegant tool relating the standard holonomy-flux algebra to the twisted geometry picture of the classical phase space on a fixed graph, and to twistors. In these lectures we provide a brief and technical introduction to the formalism and some of its applications.

gr-qc↗
arXiv2012

Pauli-Fierz mass term in modified Plebanski gravity

We study SO(4) BF theory plus a general quadratic potential, which describes a bi- metric theory of gravity. We identify the profile of the potential leading to a Pauli-Fierz mass term for the massive graviton, thereby avoiding the linearized ghost. We include the Immirzi parameter in our analysis, and find that the mass of the second graviton depends on it. At the non-perturbative level, we find a situation similar to genuine bi-gravities: even choosing the Pauli-Fierz mass term, the ghost mode propagates through the interactions. We present some simple potentials leading to two and three degrees of freedom, and discuss the difficulties of finding a ghost-free bi-gravity with seven degrees of freedom. Finally, we discuss alternative reality conditions for the case of SO(3,1) BF theory, relevant for Lorentzian signature, and give a new solution to the compatibility equation.

hep-th↗
arXiv2012

Holomorphic Lorentzian Simplicity Constraints

We develop an Hamiltonian representation of the sl(2,C) algebra on a phase space consisting of N copies of twistors, or bi-spinors. We identify a complete set of global invariants, and show that they generate a closed algebra including gl(N,C) as a subalgebra. Then, we define the linear and quadratic simplicity constraints which reduce the spinor variables to (framed) 3d spacelike polyhedra embedded in Minkowski spacetime. Finally, we introduce a new version of the simplicity constraints which (i) are holomorphic and (ii) Poisson-commute with each other, and show their equivalence to the linear and quadratic constraints.

gr-qc↗
arXiv2012

Twistor Networks and Covariant Twisted Geometries

We study the symplectic reduction of the phase space of two twistors to the cotangent bundle of the Lorentz group. We provide expressions for the Lorentz generators and group elements in terms of the spinors defining the twistors. We use this to define twistor networks as a graph carrying the phase space of two twistors on each edge. We also introduce simple twistor networks, which provide a classical version of the simple projected spin networks living on the boundary Hilbert space of EPRL/FK spin foam models. Finally, we give an expression for the Haar measure in terms of spinors.

gr-qc↗
arXiv2011

Perturbative quantum gravity with the Immirzi parameter

We study perturbative quantum gravity in the first-order tetrad formalism. The lowest order action corresponds to Einstein-Cartan plus a parity-odd term, and is known in the literature as the Holst action. The coupling constant of the parity-odd term can be identified with the Immirzi parameter of loop quantum gravity. We compute the quantum effective action in the one-loop expansion. As in the metric second-order formulation, we find that in the case of pure gravity the theory is on-shell finite, and the running of Newton's constant and the Immirzi parameter is inessential. In the presence of fermions, the situation changes in two fundamental aspects. First, non-renormalizable logarithmic divergences appear, as usual. Second, the Immirzi parameter becomes a priori observable, and we find that it is renormalized by a four-fermion interaction generated by radiative corrections. We compute its beta function and discuss possible implications. The sign of the beta function depends on whether the Immirzi parameter is larger or smaller than one in absolute value, and the values plus or minus one are UV fixed-points (we work in Euclidean signature). Finally, we find that the Holst action is stable with respect to radiative corrections in the case of minimal coupling, up to higher order non-renormalizable interactions.

hep-th↗
arXiv2011

Lorentz covariance of loop quantum gravity

The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. K can be described in terms of a certain subset of the "projected" spin networks studied by Livine, Alexandrov and Dupuis. It is formed by SL(2,C) functions completely determined by their restriction on SU(2). These are square-integrable in the SU(2) scalar product, but not in the SL(2,C) one. Thus, SU(2)-spin-network states can be represented by Lorentz-covariant SL(2,C) functions, as two-component photons can be described in the Lorentz-covariant Gupta-Bleuler formalism. As shown by Wolfgang Wieland in a related paper, this manifestly Lorentz-covariant formulation can also be directly obtained from canonical quantization. We show that the spinfoam dynamics of loop quantum gravity is locally SL(2,C)-invariant in the bulk, and yields states that are preciseley in K on the boundary. This clarifies how the SL(2,C) spinfoam formalism yields an SU(2) theory on the boundary. These structures define a tidy Lorentz-covariant formalism for loop gravity.

gr-qc↗