arXiv subjects

Alessandro Pesci

Publications and source records attributed to Alessandro Pesci.

32 records · Page 2Linked to original sources

arXiv2019

Spacetime atoms and extrinsic curvature of equi-geodesic surfaces

A recently-introduced function $ρ$ of spacetime event $P$ expressing spacetime as made of 'spacetime atoms' of quantum origin is considered. Using its defining relation, we provide an exact expression for $ρ$ involving the van Vleck biscalar, and show it can be recast in terms of the extrinsic curvature of suitable equi-geodesic surfaces centered at $P$. Moreover, looking at the role $ρ$ plays in the statistical description of spacetime, we point out that this quantity should actually be understood as counting the quantum states of the collection of spacetime atoms rather than counting directly the spacetime atoms themselves (or the degrees of freedom associated to them), and would correspond to the ratio of the number of quantum states 'at $P$' for an assigned spacetime configuration to the number of quantum states for flat spacetime.

gr-qc↗

arXiv2018

Effective null Raychaudhuri equation

The effects on Raychaudhuri's equation of an intrinsically-discrete or particle nature of spacetime are investigated. This is done through the consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e. in geometric circumstances somehow prototypical of singularity issues. We do this from an effective point of view, that is through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, this adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point. Further, this results in a non-vanishing of the limiting cross-sectional area itself of the congruence.

gr-qc↗

arXiv2018

Looking at spacetime atoms from within the Lorentz sector

Recently, a proposal has been made to figure out the expected discrete nature of spacetime at the smallest scales in terms of atoms of spacetime, capturing their effects through a scalar $ρ$, function of the point $P$ and the vector $v^a$ at $P$, expressing their density. This has been done in the Euclideanized space one obtains through analytic continuation from Lorentzian sector at $P$. $ρ$ is defined in terms of a peculiar `effective' metric $q_{ab}$, also recently introduced, which stems from a careful request that $q_{ab}$ coincides with $g_{ab}$ at large (space/time) distances, but gives finite distance in the coincidence limit. This work reports on an attempt to introduce a definition of $ρ$ directly in the Lorentz sector. This turns out to be not a so trivial task, essentially because of the null case, i.e. when $v^a$ is null, as in this case we lack even a concept of $q_{ab}$. A notion for $q_{ab}$ in the null case is here proposed and an expression for it is derived. In terms of it, an expression for $ρ$ can be derived, which turns out to coincide with what obtained from analytic continuation. This, joined with the consideration of timelike/spacelike cases, potentially completes a description of $q_{ab}$ and $ρ$ within Lorentz spacetimes.

gr-qc↗

arXiv2016

Null-null components of the generalized Einstein tensor for Lovelock models

For spherical symmetry, we provide expressions for the radial null-null components of the generalized Einstein tensor $E_{ab}$ for Lovelock models for diagonal $E_{ab}$ in terms of the metric and of the radial null-null components of the Ricci tensor. We show they can be usefully employed for example in obtaining the Birkhoff-like theorem for Lovelock models, as well as in providing a relation between the null energy and null convergence conditions for the same models.

gr-qc↗

arXiv2015

Entropy bounds and field equations

For general metric theories of gravity, we compare the approach that describes-derives the field equations of gravity as a thermodynamic identity with the one which looks at them from entropy bounds. The comparison is made through the consideration of the matter entropy flux across (Rindler) horizons, studied by making use of the notion of a limiting thermodynamic scale $l^*$ of matter, previously introduced in the context of entropy bounds. In doing this: i) a bound for the entropy of any lump of matter with a given energy-momentum tensor $T_{ab}$ is considered, in terms of a quantity which is independent of the theory of gravity we use; this quantity is the variation of the Clausius entropy of a suitable horizon when the element of matter crosses it; ii) by making use of the equations of motion of the theory, the same quantity is then expressed as the variation of Wald's entropy of that horizon (and this leads to a generalized form of the generalized covariant entropy bound, applicable to general diffeomorphism-invariant theories of gravity); iii) a notion of $l^*$ for horizons, and an expression for it, is given.

gr-qc↗

arXiv2011

The existence of a minimum wavelength for photons

The holographic property of entropy plays a key role in the thermodynamic description of gravitational field equations. It remains unclear, we argue, whether this property is necessarily interwoven with gravity itself or can be understood instead as a manifestation of physics outside gravity. It is pointed out that if the latter is the case, so that the holographic property of entropy could be considered as completely rooted on some microscopic, non-gravitational, intrinsic property of matter, gravity could merely be understood as the necessary macroscopic manifestation of this microscopic property of matter, being simply the expression of the thermodynamic conservation of energy. A quite peculiar status of Einstein's gravity in this context (as compared to generalized metric theories of gravity) is apparent. A successful microscopic property of matter, is found to necessarily mean in particular the existence of an absolute minimum wavelength for photons, of orders of Planck length.

gr-qc↗

arXiv2011

Gravity from the entropy of light

The holographic principle, considered in a semiclassical setting, is shown to have direct consequences on physics at a fundamental level. In particular, a certain relation is pointed out to be the expression of holography in basic thermodynamics. It is argued moreover that through this relation holography can be recognized to induce gravity, and an expression for the gravitational lensing is obtained in terms of entropy over wavelength of black-body radiation, or, at a deeper level, in terms of maximum entropy over associated space to the elementary bit of information.

gr-qc↗

arXiv2010

A proof of the Bekenstein bound for any strength of gravity through holography

The universal entropy bound of Bekenstein is considered, at any strength of the gravitational interaction. A proof of it is given, provided the considered general-relativistic spacetimes allow for a meaningful and inequivocal definition of the quantities which partecipate to the bound (such as system's energy and radius). This is done assuming as starting point that, for assigned statistical-mechanical local conditions, a lower-limiting scale l* to system's size definitely exists, being it required by holography through its semiclassical formulation as given by the generalized covariant entropy bound. An attempt is made also to draw some possible general consequences of the l* assumption with regards to the proliferation of species problem and to the viscosity to entropy density ratio. Concerning the latter, various fluids are considered including systems potentially relevant, to some extent, to the quark-gluon plasma case.

gr-qc↗

arXiv2009

A semiclassical approach to η/s bound through holography

We consider the holographic principle, in its lightsheet formulation, in the semiclassical context of statistical-mechanical systems in classical Einstein spacetimes. A local condition, in terms of entropy and energy local densities of the material medium under consideration, is discussed, which turns out to be necessary and sufficient for the validity of the closely-related generalized covariant entropy bound. This condition is apparently a general consequence or expression of flat-spacetime quantum mechanics alone, without any reference to gravity. Using it, a lower bound η/s >= 1/4πcan be derived, with the limit attained (in certain circumstances) by systems hydrodynamically dominated by radiation quanta.

hep-th↗

arXiv2009

A note on the connection between the universal relaxation bound and the covariant entropy bound

A recently proposed universal lower-bound to the characteristic relaxation times of perturbed thermodynamic systems, derived from quantum information theory and (classical) thermodynamics and known to be saturated for (certain) black holes, is investigated in the light of the gravity/thermodynamics connection. A statistical-mechanical property, unrelated to gravity, essential for the validity of the generalized covariant entropy bound, namely the existence of a lower-limiting value l* for the size of thermodynamic systems, is found to provide a way to understand the universal relaxation bound, thus regardless of the kind of foundations (i.e. whether conventional or information-based) of the statistical-mechanical description. As a by-product an example of a conventional system (i.e. not a black hole) seemingly saturating the universal relaxation bound is provided.

gr-qc↗

arXiv2008

On the statistical-mechanical meaning of the Bousso bound

The Bousso entropy bound, in its generalized form, is investigated for the case of perfect fluids at local thermodynamic equilibrium and evidence is found that the bound is satisfied if and only if a certain local thermodynamic property holds, emerging when the attempt is made to apply the bound to thin layers of matter. This property consists in the existence of an ultimate lower limit l* to the thickness of the slices for which a statistical-mechanical description is viable, depending l* on the thermodynamical variables which define the state of the system locally. This limiting scale, found to be in general much larger than the Planck scale (so that no Planck scale physics must be necessarily invoked to justify it), appears not related to gravity and this suggests that the generalized entropy bound is likely to be rooted on conventional flat-spacetime statistical mechanics, with the maximum admitted entropy being however actually determined also by gravity. Some examples of ideal fluids are considered in order to identify the mechanisms which can set a lower limit to the statistical-mechanical description and these systems are found to respect the lower limiting scale l*. The photon gas, in particular, appears to seemingly saturate this limiting scale and the consequence is drawn that for systems consisting of a single slice of a photon gas with thickness l*, the generalized Bousso bound is saturated. It is argued that this seems to open the way to a peculiar understanding of black hole entropy: if an entropy can meaningfully (i.e. with a second law) be assigned to a black hole, the value A/4 for it (where A is the area of the black hole) is required simply by (conventional) statistical mechanics coupled to general relativity.

gr-qc↗

arXiv2007

From Unruh temperature to generalized Bousso bound

In a classical spacetime satisfying Einstein's equation and the null convergence condition, the same quantum mechanical effects that cause black holes to have a temperature are found to imply, if joined to the macroscopic nature of entropy, the covariant entropy bound in its generalized form. This is obtained from thermodynamics, as applied across the local Rindler causal horizon through every point p of the null hypersurfaces L the covariant entropy bound refers to, in the direction of the null geodesics generating L.

gr-qc↗

arXiv2007

Entropy of gravitating systems: scaling laws versus radial profiles

Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which it is no longer an extensive quantity (it does not scale with system's size). To accomplish this, the methods introduced by Oppenheim [1] to characterize non-extensivity are used, suitably generalized to the case of gravitating systems subject to an external pressure. In particular when, far from the system's Schwarzschild limit, both area scaling for conventional entropy and inverse radius law for the temperature set in (i.e. the same properties of the corresponding black hole thermodynamical quantities), the entropy profile is found to behave like 1/r, being r the area radius inside the system. In such circumstances thus entropy heavily resides in internal layers, in opposition to what happens when area scaling is gained while approaching the Schwarzschild mass, in which case conventional entropy lies at the surface of the system. The information content of these systems, even if it globally scales like the area, is then stored in the whole volume, instead of packed on the boundary.

gr-qc↗

arXiv2006

Mass and temperature limits for blackbody radiation

A spherically symmetric distribution of classical blackbody radiation is considered, at conditions in which gravitational self-interaction effects become not negligible. Static solutions to Einstein field equations are searched for, for each choice of the assumed central energy density. Spherical cavities at thermodynamic equilibrium, i.e. filled with blackbody radiation, are then studied, in particular for what concerns the relation among the mass M of the ball of radiation contained in them and their temperature at center and at the boundary. For these cavities it is shown, in particular, that: i) there is no absolute limit to M as well to their central and boundary temperatures; ii) when radius R is fixed, however, limits exist both for mass and for boundary energy density rho_B: M <= K M_S(R) and rho_B <= Q/R^2, with K = 0.493 and Q = 0.02718, dimensionless, and M_S(R) the Schwarzschild mass for that radius. Some implications of the existence and the magnitude of these limits are considered. Finally the radial profiles for entropy for these systems are studied, in their dependence on the mass (or central temperature) of the ball of radiation.

gr-qc↗