Michele Arzano

Hawking radiation as tunneling through the quantum horizon

Planck-scale corrections to the black-hole radiation spectrum in the Parikh-Wilczek tunneling framework are calculated. The corrective terms arise from modifications in the expression of the surface gravity in terms of the mass-energy of the black hole-emitted particle system. The form of the new spectrum is discussed together with the possible consequences for the fate of black holes in the late stages of evaporation.

Severe constraints on the loop-quantum-gravity energy-momentum dispersion relation from the black-hole area-entropy law

We explore a possible connection between two aspects of loop quantum gravity which have been extensively studied in the recent literature: the black-hole area-entropy law and the energy-momentum dispersion relation. We observe that the original Bekenstein argument for the area-entropy law implicitly requires information on the energy-momentum dispersion relation and on the position-momentum uncertainty relation. Recent results show that in first approximation black-hole entropy in loop quantum gravity depends linearly on the area, with small correction terms which have logarithmic or inverse-power dependence on the area. And it has been argued that in loop quantum gravity the dispersion relation should include terms that depend linearly on the Planck length, while no evidence of modification of the position-momentum uncertainty relation has been found. We observe that this scenario with Planck-length-linear modification of the dispersion relation and unmodified position-momentum uncertainty relation is incompatible with the black-hole-entropy results, since it would give rise to a term in the entropy formula going like the square root of the area.

GENERALIZING THE NOETHER THEOREM FOR HOPF-ALGEBRA SPACETIME SYMMETRIES

Over these past few years several quantum-gravity research groups have been exploring the possibility that in some Planck-scale nonclassical descriptions of spacetime one or another form of nonclassical spacetime symmetries might arise. One of the most studied scenarios is based on the use of Hopf algebras, but previous attempts were not successful in deriving constructively the properties of the conserved charges one would like to obtain from the Hopf structure, and this in turn did not allow a crisp physical characterization of the new concept of spacetime symmetry. Working within the example of κ-Minkowski noncommutative spacetime, known to be particularly troublesome from this perspective, we observe that these past failures in the search of the charges originated from not recognizing the crucial role that the noncommutative transformation parameters play in the symmetry analysis. We show that, if indeed one introduces appropriate noncommutative transformation parameters, all the steps of the Noether analysis can be easily performed, obtaining an explicit formula for the charges carried by fields that are solutions of the equation of motion.

Implications of spacetime quantization for the Bahcall–Waxman neutrino bound

There is growing interest in quantum-spacetime models in which small departures from Lorentz symmetry are governed by the Planck scale. In particular, several studies have considered the possibility that these small violations of Lorentz symmetry may affect various astrophysical observations, such as the evaluation of the GZK limit for cosmic rays, the interaction of TeV photons with the far infrared background and the arrival time of photons with different energies from cosmological sources. We show that the same Planck-scale departures from Lorentz symmetry that led to a modification of the GZK limit also have significant implications for the evaluation of the Bahcall–Waxman bound on the flux of high-energy neutrinos produced by photo–meson interactions.

Fractional and noncommutative spacetimes

We establish a mapping between fractional and noncommutative spacetimes in configuration space. Depending on the scale at which the relation is considered, there arise two possibilities. For a fractional spacetime with log-oscillatory measure, the effective measure near the fundamental scale determining the log-period coincides with the nonrotation-invariant but cyclicity-preserving measure of -Minkowski spacetime. At scales larger than the log-period, the fractional measure is averaged and becomes a power law with real exponent. This can be also regarded as the cyclicity-inducing measure in a noncommutative spacetime defined by a certain nonlinear algebra of the coordinates, which interpolates between -Minkowski and canonical spacetime. These results are based upon a braiding formula valid for any nonlinear algebra which can be mapped onto the Heisenberg algebra.

A GLIMPSE AT THE FLAT-SPACETIME LIMIT OF QUANTUM GRAVITY USING THE BEKENSTEIN ARGUMENT IN REVERSE

An insightful argument for a linear relation between the entropy and the area of a black hole was given by Bekenstein using only the energy–momentum dispersion relation, the uncertainty principle, and some properties of classical black holes. Recent analyses within String Theory and Loop Quantum Gravity describe black-hole entropy in terms of a dominant contribution, which indeed depends linearly on the area, and a leading log-area correction. We argue that, by reversing the Bekenstein argument, the log-area correction can provide insight on the energy–momentum dispersion relation and the uncertainty principle of a quantum-gravity theory. As examples, we consider the energy–momentum dispersion relations that recently emerged in the Loop Quantum Gravity literature and the Generalized Uncertainty Principle that is expected to hold in String Theory.

Tunneling through the quantum horizon

The emergence of quantum-gravity induced corrective terms for the probability of emission of a particle from a black hole in the Parikh–Wilczek tunneling framework is studied. It is shown, in particular, how corrections might arise from modifications of the surface gravity due to near horizon Planck-scale effects. Our derivation provides an example of the possible linking between Planck-scale departures from Lorentz invariance and the appearance of higher order quantum gravity corrections in the black-hole entropy-area relation.

Dimensional reduction in the sky

We explore the cosmological implications of a mechanism found in several approaches to quantum gravity, whereby the spectral dimension of spacetime runs from the standard value of 4 in the infrared (IR) to a smaller value in the ultraviolet (UV). Specifically, we invoke the picture where the phenomenon is associated with modified dispersion relations. With minimal assumptions, we find that UV behavior leading to 2 spectral dimensions results in an exactly scale-invariant spectrum of vacuum scalar and tensor fluctuations, regardless of the equation of state. The fluctuation production mechanism is analogous to the one known for varying speed of sound/light models and, unlike in inflation, the spectrum is already scale invariant before leaving the horizon, remaining so after freeze-in. In the light of Plancks recent results we also discuss scenarios that break exact scale invariance, such as the possibility that the spectral dimension runs down to a value slightly higher than 2, or runs down to 2 but with an extremely slow transient. We further show that the tensor to scalar ratio is fixed by the UV ratio between the speed of gravity and the speed of light. Not only does our model not require inflation, but at its most minimal it seems incompatible with it. In contrast, we find that running spectral dimensions can improve the outlook of the cyclic/ekpyrotic scenario, solving the main problems present in its simplest and most appealing realizations.

Relative-locality distant observers and the phenomenology of momentum-space geometry

We study the translational invariance of the relative-locality framework proposed in Amelino-Camelia et al (2011 Phys. Rev. D 84 084010), which had been previously established only for the case of a single interaction. We provide an explicit example of boundary conditions at endpoints of worldlines, which indeed ensures the desired translational invariance for processes involving several interactions, even when some of the interactions are causally connected (particle exchange). We illustrate the properties of the associated relativistic description of distant observers within the example of a ?-Poincar?-inspired momentum-space geometry, with de Sitter metric and parallel transport governed by a non-metric and torsionful connection. We find that in such a theory, simultaneously emitted massless particles do not reach simultaneously a distant detector, as expected in light of the findings of Freidel and Smolin (2011 arXiv:1103.5626) on the implications of non-metric connections. We also show that the theory admits a free-particle limit, where the relative-locality results of Amelino-Camelia et al (2011 Phys. Lett. B 700 150) are reproduced. We establish that the torsion of the ?-Poincar? connection introduces a small (but observably large) dependence of the time of detection, for simultaneously emitted particles, on some properties of the interactions producing the particles at the source.

Anomalous dimension in three-dimensional semiclassical gravity

Abstract The description of the phase space of relativistic particles coupled to three-dimensional Einstein gravity requires momenta which are coordinates on a group manifold rather than on ordinary Minkowski space. The corresponding field theory turns out to be a non-commutative field theory on configuration space and a group field theory on momentum space. Using basic non-commutative Fourier transform tools we introduce the notion of non-commutative heat-kernel associated with the Laplacian on the non-commutative configuration space. We show that the spectral dimension associated to the non-commutative heat kernel varies with the scale reaching a non-integer value smaller than three for Planckian diffusion scales.