arXiv subjects

Gianluca Mandanici

Publications and source records attributed to Gianluca Mandanici.

18 recordsLinked to original sources

arXiv2016

Rainbow's Stars

In recent years, a growing interest on the equilibrium of compact astrophysical objects like white dwarf and neutron stars has been manifested. In particular, various modifications due to Planck scale energy effects have been considered. In this paper we analyze the modification induced by Gravity's Rainbow on the equilibrium configurations described by the Tolman-Oppenheimer-Volkoff (TOV) equation. Our purpose is to explore the possibility that the Rainbow Planck-scale deformation of space-time could support the existence of different compact stars.

gr-qc↗

arXiv2015

Gravity's Rainbow and Compact Stars

A number of recent studies has focused on the implications of new physics at the Planck scale on the equilibrium of compact astrophysical objects such as white dwarf and neutron stars. Here we analyze the modification of the equilibrium configurations induced by the so-called Gravity's Rainbow that account for Planck scale deformation of the space-time.

physics.gen-ph↗

arXiv2013

A map between Galilean relativity and special relativity

A map is discussed that connects, in 1+1 dimensions, Galilei's relativity to Einstein's special relativity. By means of this map it is possible to derive special-relativistic formulas from the corresponding Galilean ones. Beyond being interesting on its own, this map is also significant with respect to a recent debate on the extension of relativistic symmetries to the Planck scale (especially in the framework of the so-called doubly special relativity). The map in fact provides an explicit example of how can be misleading to interpret a mathematical correspondence between two relativity schemes as an argument in favor of their physical equivalence.

gr-qc↗

arXiv2013

On the invariance of the relative rest in doubly special relativity

In the framework of the most-studied doubly special relativity models the use of the naive formula $v=dE/dp$ has been argued to lead to inconsistencies connected to different rules of transformation, under boosts, of particles with the same energy but with different masses. In this paper we show that, at least in 1+1 dimensions, doubly special relativity can be formulated in such a way that the formula $v=dE/dp$ is fully consistent with the invariance of the relative rest, easily fitting to the relativity principle. It is also argued that, always in 1+1d, is not necessary to renounce to the usual (commutative) Minkowski space-time endowed with energy-independent boost transformations. The compatibility of the approach with superluminal propagation, with linear addition rule for energy, and possible extensions to 3+1 dimensions are also discussed.

gr-qc↗

arXiv2013

Finite Zero Point Gravitational Energy in the context of Modified Dispersion Relations

We compute the Zero Point Energy in a spherically symmetric background distorted at high energy as predicted by Gravity's Rainbow. In this context we setup a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The eigenvalue equation is a reformulation of the Wheeler-DeWitt equation. We find that the ordinary divergences can here be handled by an appropriate choice of the rainbow's functions, in contrast to what happens in other conventional approaches.

gr-qc↗

arXiv2011

UV and IR quantum-spacetime effects for the Chandrasekhar model

We modify the Chandrasekhar model of white dwarfs by introducing novel momentum-space features that characterize the analysis of some quantum-spacetime scenarios. We find that the rather standard ultraviolet effects of spacetime quantization can only be significant in a regime where the Chandrasekhar model anyway lacks any contact with observations. But a new class of quantum-spacetime effects inspired by the mechanism of "ultraviolet/infrared mixing" could be relevant for white dwarfs whose mass is roughly half the mass of the Sun, some of which are described in the literature as "strange white dwarfs". We also offer a preliminary argument suggesting that Planck-scale (ultraviolet) effects could be significant in cases where ultra-high densities are present, even when the relevant star is still gigantic in Planck-length units.

gr-qc↗

arXiv2011

Particle propagation and effective space-time in Gravity's Rainbow

Basing on the results obtained in a our previous study on Gravity's Rainbow, we determine the quantum corrections to the space-time metric for the Schwarzschild and the de Sitter background, respectively. We analyze how quantum fluctuations alter these metrics inducing modifications on the propagation of test particles. Significantly enough we find that quantum corrections can become relevant not only for particles approaching the Planck energy but, due to the one loop contribution, even for low-energy particles as far as Planckian length scales are considered. We briefly compare our results with others obtained in similar studies and with the recent experimental OPERA announcement of superluminal neutrino propagation.

gr-qc↗

arXiv2011

Modified Dispersion Relations lead to a finite Zero Point Gravitational Energy

We compute the Zero Point Energy in a spherically symmetric background distorted at high energy as predicted by \textit{Gravity's Rainbow}. In this context we setup a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The eigenvalue equation is a reformulation of the Wheeler-DeWitt equation. With the help of a canonical decomposition, we find that the relevant contribution to one loop is given by the graviton quantum fluctuations around the given background. By means of a variational approach based on gaussian trial functionals, we find that the ordinary divergences can here be handled by an appropriate choice of the rainbow's functions, in contrast to what happens in other conventional approaches. A final discussion on the connection of our result with the observed cosmological constant is also reported.

gr-qc↗

arXiv2010

Gravity in quantum spacetime

The literature on quantum-gravity-inspired scenarios for the quantization of spacetime has so far focused on particle-physics-like studies. This is partly justified by the present limitations of our understanding of quantum-gravity theories, but we here argue that valuable insight can be gained through semi-heuristic analyses of the implications for gravitational phenomena of some results obtained in the quantum-spacetime literature. In particular, we show that the types of description of particle propagation that emerged in certain quantum-spacetime frameworks have striking implications for gravitational collapse and for the behaviour of gravity at large distances.

gr-qc↗

arXiv2010

Interplay between curvature and Planck-scale effects in astrophysics and cosmology

Several recent studies have considered the implications for astrophysics and cosmology of some possible nonclassical properties of spacetime at the Planck scale. The new effects, such as a Planck-scale-modified energy-momentum (dispersion) relation, are often inferred from the analysis of some quantum versions of Minkowski spacetime, and therefore the relevant estimates depend heavily on the assumption that there could not be significant interplay between Planck-scale and curvature effects. We here scrutinize this assumption, using as guidance a quantum version of de Sitter spacetime with known Inonu-Wigner contraction to a quantum Minkowski spacetime. And we show that, contrary to common (but unsupported) beliefs, the interplay between Planck-scale and curvature effects can be significant. Within our illustrative example, in the Minkowski limit the quantum-geometry deformation parameter is indeed given by the Planck scale, while in the de Sitter picture the parameter of quantization of geometry depends both on the Planck scale and the curvature scalar. For the much-studied case of Planck-scale effects that intervene in the observation of gamma-ray bursts we can estimate the implications of "quantum spacetime curvature" within robust simplifying assumptions. For cosmology at the present stage of the development of the relevant mathematics one cannot go beyond semiheuristic reasoning, and we here propose a candidate approximate description of a quantum FRW geometry, obtained by patching together pieces (with different spacetime curvature) of our quantum de Sitter. This semiheuristic picture, in spite of its limitations, provides rather robust evidence that in the early Universe the interplay between Planck-scale and curvature effects could have been particularly significant.

gr-qc↗

arXiv2008

Undeformed (additive) energy conservation law in Doubly Special Relativity

All the Doubly Special Relativity (DSR) models studied in literature so far involve a deformation of the energy conservation rule that forces us to release the hypothesis of the additivity of the energy for composite systems. In view of the importance of the issue for a consistent formulation of a DSR statistical mechanics and a DSR thermodynamics, we show that DSR models preserving the usual (i.e. additive) energy conservation rule can be found. These models allow the construction of a DSR-covariant extensive energy. The implications of the analysis for the dynamics of DSR-covariant multiparticle systems are also briefly discussed.

gr-qc↗

arXiv2005

Black-hole thermodynamics with modified dispersion relations and generalized uncertainty principles

In several approaches to the quantum-gravity problem evidence has emerged of the validity of a "GUP" (a Generalized position-momentum Uncertainty Principle) and/or a "MDR" (a modification of the energy-momentum dispersion relation), but very little is known about the implications of GUPs and MDRs for black-hole thermodynamics, another key topic for quantum-gravity research. We investigate an apparent link, already suggested in an earlier exploratory study involving two of us, between the possibility of a GUP and/or a MDR and the possibility of a log term in the area-entropy black-hole formula. We then obtain, from that same perspective, a modified relation between the mass of a black hole and its temperature, and we examine the validity of the "Generalized Second Law of black-hole thermodynamics" in theories with a GUP and/or a MDR. After an analysis of GUP- and MDR-modifications of the black-body radiation spectrum, we conclude the study with a description of the black-hole evaporation process.

gr-qc↗

arXiv2004

Heisenberg Evolution in a Quantum Theory of Noncommutative Fields

A quantum theory of noncommutative fields was recently proposed by Carmona, Cortez, Gamboa and Mendez (hep-th/0301248). The implications of the noncommutativity of the fields, intended as the requirements $[ϕ,ϕ^{+}]=θδ^{3}(x-x^{\prime}), [π,π^{+}]=Bδ^{3}(x-x^{\prime}) $, were analyzed on the basis of an analogy with previous results on the so-called ``noncommutative harmonic oscillator construction". Some departures from Lorentz symmetry turned out to play a key role in the emerging framework. We first consider the same hamiltonian proposed in hep-th/0301248, and we show that the theory can be analyzed straightforwardly within the framework of Heisenberg evolution equation without any need of making reference to the ``noncommutative harmonic oscillator construction". We then consider a rather general class of alternative hamiltonians, and we observe that violations of Lorentz invariance are inevitably encountered. These violations must therefore be viewed as intrinsically associated with the proposed type of noncommutativity of fields, rather than as a consequence of a specific choice of Hamiltonian.

hep-th↗

arXiv2003

Wave Propagation and IR/UV Mixing in Noncommutative Spacetimes

In this thesis I study various aspects of theories in the two most studied examples of noncommutative spacetimes: canonical spacetime ($[x_μ,x_ν]=θ_{μν}$) and $κ$-Minkowski spacetime ($[x_{i},t]=κ^{-1} x_{i}$). In the first part of the thesis I consider the description of the propagation of "classical" waves in these spacetimes. In the case of $κ$-Minkowski this description is rather nontrivial, and its phenomenological implications are rather striking. In the second part of the thesis I examine the structure of quantum field theory in noncommutative spacetime, with emphasis on the simple case of the canonical spacetime. I find that the so-called IR/UV mixing can affect significantly the phase structure of a quantum field theory and also forces us upon a certain revision of the strategies used in particle-physics phenomenology to constrain the parameters of a model.

hep-th↗

arXiv2003

Phenomenology of Doubly Special Relativity

Investigations of the possibility that some novel ``quantum" properties of spacetime might induce a modification dispersion relation focused at first on scenarios with Planck-scale violations of Lorentz symmetry. More recently several studies have considered the possibility of a ``doubly special relativity", in which the modification of the dispersion relation emerges from a framework with both the Planck scale and the speed-of-light scale as characteristic scales of a deformation of the Lorentz transformations. For the schemes with broken Lorentz symmetry at the Planck scale there is a large literature on the derivation of experimental limits. We provide here a corresponding analysis for the doubly-special-relativity framework. We find that the analyses of photon stability, synchrotron radiation, and threshold conditions for particle production in collision processes, the three contexts which are considered as most promising for constraining the broken-Lorentz-symmetry scenario, cannot provide significant constraints on doubly-special-relativity parameter space. However, certain types of analyses of gamma-ray bursts are sensitive to the symmetry deformation. A key element of our study is an observation that removes a possible sign ambiguity for the doubly-special-relativity framework. This result also allows us to characterize more sharply the differences between the doubly-special-relativity framework and the framework of k-Poincare Hopf algebras, two frameworks which are often confused with each other in the literature.

gr-qc↗

arXiv2003

Cornwall-Jackiw-Tomboulis effective potential for canonical noncommutative field theories

We apply the Cornwall-Jackiw-Tomboulis (CJT) formalism to the scalar $λϕ^{4}$ theory in canonical-noncommutative spacetime. We construct the CJT effective potential and the gap equation for general values of the noncommutative parameter $θ_{μν}$. We observe that under the hypothesis of translational invariance, which is assumed in the effective potential construction, differently from the commutative case ($θ_{μν}= 0$), the renormalizability of the gap equation is incompatible with the renormalizability of the effective potential. We argue that our result, is consistent with previous studies suggesting that a uniform ordered phase would be inconsistent with the infrared structure of canonical noncommutative theories.

hep-th↗

arXiv2002

Group velocity in noncommutative spacetime

The realization that forthcoming experimental studies, such as the ones planned for the GLAST space telescope, will be sensitive to Planck-scale deviations from Lorentz symmetry has increased interest in noncommutative spacetimes in which this type of effects is expected. We focus here on $κ$-Minkowski spacetime, a much-studied example of Lie-algebra noncommutative spacetime, but our analysis appears to be applicable to a more general class of noncommutative spacetimes. A technical controversy which has significant implications for experimental testability is the one concerning the $κ$-Minkowski relation between group velocity and momentum. A large majority of studies adopted the relation $v = dE(p)/dp$, where $E(p)$ is the $κ$-Minkowski dispersion relation, but recently some authors advocated alternative formulas. While in these previous studies the relation between group velocity and momentum was introduced through ad hoc formulas, we rely on a direct analysis of wave propagation in $κ$-Minkowski. Our results lead conclusively to the relation $v = dE(p)/dp$. We also show that the previous proposals of alternative velocity/momentum relations implicitly relied on an inconsistent implementation of functional calculus on $κ$-Minkowski and/or on an inconsistent description of spacetime translations.

hep-th↗

arXiv2002

On the IR/UV mixing and experimental limits on the parameters of canonical noncommutative spacetimes

We investigate some issues that are relevant for the derivation of experimental limits on the parameters of canonical noncommutative spacetimes. By analyzing a simple Wess-Zumino-type model in canonical noncommutative spacetime with soft supersymmetry breaking we explore the implications of ultraviolet supersymmetry on low-energy phenomenology. The fact that new physics in the ultraviolet can modify low-energy predictions affects significantly the derivation of limits on the noncommutativity parameters based on low-energy data. These are, in an appropriate sense here discussed, ``conditional limits''. We also find that some standard techniques for an effective low-energy description of theories with non-locality at short distance scales are only applicable in a regime where theories in canonical noncommutative spacetime lack any predictivity, because of the strong sensitivity to unknown UV physics. It appears useful to combine high-energy data, from astrophysics, with the more readily available low-energy data.

hep-th↗