arXiv subjects

Sebastiano Sonego

Publications and source records attributed to Sebastiano Sonego.

30 records · Page 2Linked to original sources

arXiv2004

Deriving relativistic momentum and energy

We present a new derivation of the expressions for momentum and energy of a relativistic particle. In contrast to the procedures commonly adopted in textbooks, the one suggested here requires only the knowledge of the composition law for velocities along one spatial dimension, and does not make use of the concept of relativistic mass, or of the formalism of four-vectors. The basic ideas are very general and can be applied also to kinematics different from the Newtonian and Einstein ones, in order to construct the corresponding dynamics.

physics.class-ph↗

arXiv2004

Causal structure of acoustic spacetimes

The so-called ``analogue models of general relativity'' provide a number of specific physical systems, well outside the traditional realm of general relativity, that nevertheless are well-described by the differential geometry of curved spacetime. Specifically, the propagation of acoustic disturbances in moving fluids are described by ``effective metrics'' that carry with them notions of ``causal structure'' as determined by an exchange of sound signals. These acoustic causal structures serve as specific examples of what can be done in the presence of a Lorentzian metric without having recourse to the Einstein equations of general relativity. (After all, the underlying fluid mechanics is governed by the equations of traditional hydrodynamics, not by the Einstein equations.) In this article we take a careful look at what can be said about the causal structure of acoustic spacetimes, focusing on those containing sonic points or horizons, both with a view to seeing what is different from standard general relativity, and to seeing what the similarities might be.

gr-qc↗

arXiv2003

Particle detectors, geodesic motion, and the equivalence principle

It is shown that quantum particle detectors are not reliable probes of spacetime structure. In particular, they fail to distinguish between inertial and non-inertial motion in a general spacetime. To prove this, we consider detectors undergoing circular motion in an arbitrary static spherically symmetric spacetime, and give a necessary and sufficient condition for the response function to vanish when the field is in the static vacuum state. By examining two particular cases, we show that there is no relation, in general, between the vanishing of the response function and the fact that the detector motion is, or is not, geodesic. In static asymptotically flat spacetimes, however, all rotating detectors are excited in the static vacuum. Thus, in this particular case the static vacuum appears to be associated with a non-rotating frame. The implications of these results for the equivalence principle are considered. In particular, we discuss how to properly formulate the principle for particle detectors, and show that it is satisfied.

gr-qc↗

arXiv2002

Faster-than-c signals, special relativity, and causality

Motivated by the recent attention on superluminal phenomena, we investigate the compatibility between faster-than-c propagation and the fundamental principles of relativity and causality. We first argue that special relativity can easily accommodate -- indeed, does not exclude -- faster-than-c signalling at the kinematical level. As far as causality is concerned, it is impossible to make statements of general validity, without specifying at least some features of the tachyonic propagation. We thus focus on the Scharnhorst effect (faster-than-c photon propagation in the Casimir vacuum), which is perhaps the most plausible candidate for a physically sound realization of these phenomena. We demonstrate that in this case the faster-than-c aspects are ``benign'' and constrained in such a manner as to not automatically lead to causality violations.

gr-qc↗

arXiv2001

Scharnhorst effect at oblique incidence

We consider the Scharnhorst effect (anomalous photon propagation in the Casimir vacuum) at oblique incidence, calculating both photon speed and polarization states as functions of angle. The analysis is performed in the framework of nonlinear electrodynamics and we show that many features of the situation can be extracted solely on the basis of symmetry considerations. Although birefringence is common in nonlinear electrodynamics it is not universal; in particular we verify that the Casimir vacuum is not birefringent at any incidence angle. On the other hand, group velocity is typically not equal to phase velocity, though the distinction vanishes for special directions or if one is only working to second order in the fine structure constant. We obtain an ``effective metric'' that is subtly different from previous results. The disagreement is due to the way that ``polarization sums'' are implemented in the extant literature, and we demonstrate that a fully consistent polarization sum must be implemented via a bootstrap procedure using the effective metric one is attempting to define. Furthermore, in the case of birefringence, we show that the polarization sum technique is intrinsically an approximation.

quant-ph↗

arXiv2000

Extremal Black holes and the limits of the third law

Recent results of quantum field theory on a curved spacetime suggest that extremal black holes are not thermal objects and that the notion of zero temperature is ill-defined for them. If this is correct, one may have to go to a full semiclassical theory of gravity, including backreaction, in order to make sense of the third law of black hole thermodynamics. Alternatively, it is possible that we shall have to drastically revise the status of extremality in black hole thermodynamics.

gr-qc↗

arXiv2000

Unexpectedly large surface gravities for acoustic horizons?

Acoustic black holes are fluid dynamic analogs of general relativistic black holes, wherein the behaviour of sound waves in a moving fluid acts as an analog for scalar fields propagating in a gravitational background. Acoustic horizons possess many of the properties more normally associated with the event horizons of general relativity, up to and including Hawking radiation. They have received much attention because it would seem to be much easier to experimentally create an acoustic horizon than to create an event horizon. We wish to point out some potential difficulties (and opportunities) in actually setting up an experiment that possesses an acoustic horizon. We show that in zero-viscosity, stationary fluid flow with generic boundary conditions, the creation of an acoustic horizon is accompanied by a formally infinite ``surface gravity'', and a formally infinite Hawking flux. Only by applying a suitable non-constant external body force, and for very specific boundary conditions on the flow, can these quantities be kept finite. This problem is ameliorated in more realistic models of the fluid. For instance, adding viscosity always makes the Hawking flux finite, but greatly complicates the behaviour of the acoustic radiation --- viscosity is tantamount to explicitly breaking ``acoustic Lorentz invariance''. Thus, this issue represents both a difficulty and an opportunity --- acoustic horizons may be somewhat more difficult to form than naively envisaged, but if formed, they may be much easier to detect than one would at first suppose.

gr-qc↗

arXiv2000

Relationships between various characterisations of wave tails

One can define several properties of wave equations that correspond to the absence of tails in their solutions, the most common one by far being Huygens' principle. Not all of these definitions are equivalent, although they are sometimes assumed to be. We analyse this issue in detail for linear scalar waves, establishing some relationships between the various properties. Huygens' principle is almost always equivalent to the characteristic propagation property, and in two spacetime dimensions the latter is equivalent to the zeroth order progressing wave propagation property. Higher order progressing waves in general do have tails, and do not seem to admit a simple physical characterisation, but they are nevertheless useful because of their close association with exactly solvable two-dimensional equations.

math-ph↗

arXiv1999

Observables and gauge invariance in the theory of non-linear spacetime perturbations

We discuss the issue of observables in general-relativistic perturbation theory, adopting the view that any observable in general relativity is represented by a scalar field on spacetime. In the context of perturbation theory, an observable is therefore a scalar field on the perturbed spacetime, and as such is gauge invariant in an exact sense (to all orders), as one would expect. However, perturbations are usually represented by fields on the background spacetime, and expanded at different orders into contributions that may or may not be gauge independent. We show that perturbations of scalar quantities are observable if they are first order gauge-invariant, even if they are gauge dependent at higher order. Gauge invariance to first order plays therefore an important conceptual role in the theory, for it selects the perturbations with direct physical meaning from those having only a mathematical status. The so-called ``gauge problem'', and the relationship between measured fluctuations and gauge dependent perturbations that are computed in the theory are also clarified.

gr-qc↗

arXiv1997

Gauge dependence in the theory of non-linear spacetime perturbations

Diffeomorphism freedom induces a gauge dependence in the theory of spacetime perturbations. We derive a compact formula for gauge transformations of perturbations of arbitrary order. To this end, we develop the theory of Taylor expansions for one-parameter families (not necessarily groups) of diffeomorphisms. First, we introduce the notion of knight diffeomorphism, that generalises the usual concept of flow, and prove a Taylor's formula for the action of a knight on a general tensor field. Then, we show that any one-parameter family of diffeomorphisms can be approximated by a family of suitable knights. Since in perturbation theory the gauge freedom is given by a one-parameter family of diffeomorphisms, the expansion of knights is used to derive our transformation formula. The problem of gauge dependence is a purely kinematical one, therefore our treatment is valid not only in general relativity, but in any spacetime theory.

gr-qc↗

arXiv1997

Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond

We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results concerning the Taylor expansion of tensor fields under the action of one-parameter families (not necessarily groups) of diffeomorphisms. Second, we define gauge invariance to an arbitrary order $n$. Finally, we give a generating formula for the gauge transformation to an arbitrary order and explicit rules to second and third order. This formalism can be used in any field of applied general relativity, such as cosmological and black hole perturbations, as well as in other spacetime theories. As a specific example, we consider here second order perturbations in cosmology, assuming a flat Robertson-Walker background, giving explicit second order transformations between the synchronous and the Poisson (generalized longitudinal) gauges.

gr-qc↗

arXiv1992

On the Tail Problem in Cosmology

The tail problem for the propagation of a scalar field is considered in a cosmological background, taking a Robertson-Walker spacetime as a specific example. The explicit radial dependence of the general solution of the Klein-Gordon equation with nonminimal coupling is derived, and the inapplicability of the standard calculation of the reflection and transmission coefficients to the study of scattering of waves by the cosmological curvature is discussed.

astro-ph↗