arXiv subjects

Marcelo Schiffer

Publications and source records attributed to Marcelo Schiffer.

At least 19 recordsLinked to original sources

arXiv2023

Charge Fluctuations of a Schwarzschild Black-Hole

In this paper, we consider charge fluctuations of a Schwarzschild black hole of mass $M$ in thermal equilibrium with a plasma consisting of photons, electrons, and positrons confined inside a cavity . The final result is astonishingly simple: charge fluctuations have two independent contributions: one that comes from the black hole itself, with no respect to the plasma, and another one that arises from the plasma; both are Universal, do not depend on the black hole mass and none of them depends on the charge of the charge carriers. They differ by a numerical factor of order one if we assume the cut-off parameter to be Planckian. Therefore, we regard them as physically identical. Interestingly enough, the black hole's charge (squared) fluctuations are of the order $\hbar$ which is not too far from the fine structure constant. The physical origin of charge fluctuations remains raises a puzzle. Since it does not depend upon the charge of the charge carriers, it cannot be regarded as resulting from the trade of charges between the black hole and the quantum fields and is truly of quantum gravity nature (albeit in a semi-classical approximation). There are at least two possible ways of interpreting our results: either charge is trapped inside the black hole and the average must be regarded over an ensemble of black-holes or eventuality charge fluctuations arise from particles crossing the Cauchy horizon $\overline{r_-} \sim \hbar/2M$ in both directions.

gr-qc↗

arXiv2023

Angular Momentum Fluctuations

In this paper, we consider angular momentum fluctuations of a Schwartzschild black hole in thermal equilibrium with radiation which, for the sake of simplicity is here modeled by a scalar field. Important, we do not set the black hole angular momentum $J$ identically to zero at the outset; we allow it to have a small value (in the sense that $J/M<<1$) and then study the conditions for thermodynamical equilibrium; only then take the $J\rightarrow 0$ limit. We calculate the black hole's angular momentum fluctuations which turn out to have two independent contributions: one that comes from the black hole itself, with no respect to the radiation, and another one that arises from the radiation. The result is astonishingly simple: the radiation contribution depends exclusively on the cut-off proper distance from the horizon (or equivalently, the width of the brick wall), while the black hole contribution is proportional to its event horizon area. Accordingly, there are no strictly static black holes in nature, they randomly rotate in all possible directions. Since a black hole is nothing but geometry, we are dealing with geometry fluctuations -- our results are of quantum-gravitational nature (albeit at a semi-classical level). Interestingly enough, if we apply to the black hole fluctuations component the (quantum) rules of angular momentum we obtain an event horizon area quantization rule, albeit with a different spectrum from an equally spaced area spectrum which is widely accepted in the literature.

gr-qc↗

arXiv2022

The Width Paradox and the Internal Structure of a Black-Hole

In the early days of Black Hole Thermodynamics, Bekenstein calculated the mass dispersion of a macroscopic black hole that results from the stochasticity of the thermal radiation it emits -- it turned out to be negative for black holes massive than $M \stackrel{>}{\sim} 10^{30}g$. He named it the {\it "mass width paradox"}. Here we revisit his early calculation, in an axiomatic approach with a set of more economical assumptions and reach similar conclusions. We argue that the mass paradox results from considering a black hole as a classical system, without an inner quantum structure. As a matter of fact, when we take into account the discreteness of the area levels and assume identical probability transition between contiguous quantum states \cite{bekenstein}, the paradox disappears. In the process we obtain the probability of finding a black-hole in some area eigenstate for a given averaged area. As a by-product, the quantum scenario also points towards a possible solution of the black hole information conundrum.

gr-qc↗

arXiv2021

Trapped Gravitational Waves in Jackiw-Teitelboim Gravity

We discuss the possibility that gravitational fluctuations ("gravitational-waves") are trapped in space by gravitational interactions in two dimensional Jackiw-Teitelboim gravity. In the standard geon (gravitational electromagnetic entity) approach, the effective energy is entirely deposited in a thin layer, the active region, that achieves spatial self-confinement and raises doubts about the geon's stability. In this paper we relinquish the "active region" approach and obtain self-confinement of "gravitational waves" that are trapped by the vacuum geometry and can be stable against the backreaction due to metric fluctuations.

gr-qc↗

arXiv2020

Black Hole Area Quantization rule from Black Hole Mass Fluctuations

We calculate the black hole mass distribution function that follows from the random emission of quanta by Hawking radiation and with this function we calculate the black hole mass fluctuation. From a complete different perspective we regard the black hole as quantum mechanical system with a quantized event horizon area and transition probabilities among the various energy levels and then calculate the mass dispersion. It turns out that there is a perfect agreement between the statistical and the microscopic calculations if and only if the area spectrum is linear. Accordingly, the quantum mechanical properties of the black hole which are supposedly relevant only at Planckian scales do leave an imprint in the black hole mass dispersion at much larger scales where gravity can be dealt classically, as one would expect from the correspondence principle.

gr-qc↗

arXiv2016

Charge Fluctuations of an Uncharged Black Hole

In this paper we calculate charge fluctuations of a Schwarzschild black-hole of mass $M$ confined within a perfectly reflecting cavity of radius R in thermal equilibrium with various species of radiation and fermions . Charge conservation is constrained by a Lagrange multiplier (the chemical potential). Black hole charge fluctuations are expected owing to continuous absorption and emission of particles by the black hole. For black holes much more massive than $10^{16} g$ , these fluctuations are exponentially suppressed. For black holes lighter than this, the Schwarzschild black hole is unstable under charge fluctuations for almost every possible size of the confining vessel. The stability regime and the fluctuations are calculated through the second derivative of the entropy with respect to the charge. The expression obtained contains many puzzling terms besides the expected thermodynamical fluctuations: terms corresponding to instabilities that do not depend on the specific value of charge of the charge carriers and one of them depends on Newton's constant instead. One of the contributions to the charge fluctuations $\hbar/4π$ does not depend neither on number of species, nor on the the specific charge or even the size of the confining vessel. As a matter of fact, this term emerges from the second derivative of the black hole entropy alone, which means that it corresponds to a genuine quantum mechanical property of the black hole itself. Such a contribution would cause the event horizon to recede from $2M$ to $2M-T_{BH}$ or equivalently, by $(4π)^{-1}$ of the black hole' s Compton wave length. Similarly, a Cauchy horizon emerges at the same distance the event horizon receded.

gr-qc↗

arXiv2011

Electrically Deformable Liquid Marbles

Liquid marbles, which are droplets coated with a hydrophobic powder, were exposed to a uniform electric field. It was established that a threshold value of the electric field, 15 cgse, should be surmounted for deformation of liquid marbles. The shape of the marbles was described as a prolate spheroid. The semi-quantitative theory describing deformation of liquid marbles in a uniform electric field is presented. The scaling law relating the radius of the contact area of the marble to the applied electric field shows a satisfactory agreement with the experimental data.

cond-mat.soft↗

arXiv2010

Hamiltonian Map to Conformal Modification of Spacetime Metric: Kaluza-Klein and TeVeS

It has been shown that the orbits of motion for a wide class of nonrelativistic Hamiltonian systems can be described as geodesic flows on a manifold and an associated dual. This method can be applied to a four dimensional manifold of orbits in spacetime associated with a relativistic system. We show that a relativistic Hamiltonian which generates Einstein geodesics, with the addition of a world scalar field, can be put into correspondence with another Hamiltonian with conformally modified metric. Such a construction could account for part of the requirements of Bekenstein for achieving the MOND theory of Milgrom in the post-Newtonian limit. The constraints on the MOND theory imposed by the galactic rotation curves, through this correspondence, would then imply constraints on the structure of the world scalar field. We then use the fact that a Hamiltonian with vector gauge fields results, through such a conformal map, in a Kaluza-Klein type theory, and indicate how the TeVeS structure of Bekenstein and Sanders can be put into this framework. We exhibit a class of infinitesimal gauge transformations on the gauge fields ${\cal U}_μ$ which preserve the Bekenstein-Sanders condition ${\cal U}_μ{\cal U}^μ= -1$. The underlying quantum structure giving rise to these gauge fields is a Hilbert bundle, and the gauge transformations induce a non-commutative behavior to the fields, i.e., they become of Yang-Mills type. Working in the infinitesimal gauge neighborhood of the initial Abelian theory, we show that in the Abelian limit the Yang-Mills field equations provide nonlinear terms which may avoid the caustic singularity found by Contaldi, et al.

math-ph↗

arXiv2009

Varying fine structure "constant" and charged black holes

Speculation that the fine-structure constant $α$ varies in spacetime has a long history. We derive, in 4-D general relativity and in isotropic coordinates, the solution for a charged spherical black hole according to the framework for dynamical $α$ (Bekenstein 1982). This solution coincides with a previously known one-parameter extension of the dilatonic black hole family. Among the notable properties of varying-$α$ charged black holes are adherence to a ``no hair'' principle, the absence of the inner (Cauchy) horizon of the Reissner-Nordstrom black holes, the nonexistence of precisely extremal black holes, and the appearance of naked singularities in an analytic extension of the relevant metric. The exteriors of almost extremal electrically (magnetically) charged black holes have simple structures which makes their influence on applied magnetic (electric) fields transparent. We re-derive the thermodynamic functions of the modified black holes; the otherwise difficult calculation of the electric potential is done by a shortcut. We confirm that variability of $α$ in the wake of expansion of the universe does not threaten the generalized second law

gr-qc↗

arXiv2008

Local enrichment and its nonlocal consequences for victim-exploiter metapopulations

The stabilizing effects of local enrichment are revisited. Diffusively coupled host-parasitoid and predator-prey metapopulations are shown to admit a stable fixed point, limit cycle or stable torus with a rich bifurcation structure. A linear toy model that yields many of the basic qualitative features of this system is presented. The further nonlinear complications are analyzed in the framework of the marginally stable Lotka-Volterra model, and the continuous time analog of the unstable, host-parasitoid Nicholson-Bailey model. The dependence of the results on the migration rate and level of spatial variations is examined, and the possibility of "nonlocal" effect of enrichment, where local enrichment induces stable oscillations at a distance, is studied. A simple method for basic estimation of the relative importance of this effect in experimental systems is presented and exemplified.

q-bio.PE↗

arXiv2007

On the geometry of Hamiltonian chaos

We show that Gutzwiller's characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian can be extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model when a transition is made to the dual manifold, and the geodesics in the dual space coincide with the orbits of the Hamiltonian potential model. We therefore find a direct geometrical description of the time development of a Hamiltonian potential model. The second covariant derivative of the geodesic deviation in this dual manifold generates a dynamical curvature, resulting in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We discuss some examples of unstable Hamiltonian systems in two dimensions giving, in particular, detailed results for a potential obtained from a fifth order expansion of a Toda lattice Hamiltonian.

physics.class-ph↗

arXiv2007

Desynchronization and sustainability of noisy metapopulation cycles

The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration, amplitude-dependent frequency, and noise: small differences between spatial patches, induced by the noise, are amplified by the frequency gradient. Migration among desynchronized regions then stabilizes the oscillations in the vicinity of the homogenous manifold. A simple model of diffusively coupled oscillators allows the derivation of quantitative results, like the dependence of the desynchronization upon diffusion strength and frequency differences. For an unstable system, a noise-induced transition is demonstrated, from extinction for small noise to stability if the noise exceeds some threshold. The coupled oscillator model is shown to reproduce all previously suggested stabilizing mechanisms. Accordingly, we suggest using this model as a standard tool for identification and classification of population oscillations on spatial domains.

q-bio.PE↗

arXiv2003

Quantum Limitations on the Storage and Transmission of Information

Information must take up space, must weigh, and its flux must be limited. Quantum limits on communication and information storage leading to these conclusions are here described. Quantum channel capacity theory is reviewed for both steady state and burst communication. An analytic approximation is given for the maximum signal information possible with occupation number signal states as a function of mean signal energy. A theorem guaranteeing that these states are optimal for communication is proved. A heuristic "proof" of the linear bound on communication is given, followed by rigorous proofs for signals with specified mean energy, and for signals with given energy budget. And systems of many parallel quantum channels are shown to obey the linear bound for a natural channel architecture. The time--energy uncertainty principle is reformulated in information language by means of the linear bound. The quantum bound on information storage capacity of quantum mechanical and quantum field devices is reviewed. A simplified version of the analytic proof for the bound is given for the latter case. Solitons as information caches are discussed, as is information storage in one dimensional systems. The influence of signal self--gravitation on communication is considerd. Finally, it is shown that acceleration of a receiver acts to block information transfer.

quant-ph↗

arXiv2001

The Inertial Polarization Principle: The Mechanism Underlying Sonoluminescence?

In this paper we put forward a mechanism in which imploding shock waves emit electromagnetic radiation in the spectral region $λ_{0}\cong 2πR_{0}.$, where R$_{0}$ is the radius of the shock by the time it is first formed. The mechanism relies on three different pieces of Physics: Maxwell's equations, the existence of corrugation instabilities of imploding shock waves and, last but not least, the{\em Inertial Polarization Principle}. The principle is extensively discussed: how it emerges from very elementary physics and finds experimental support in shock waves propagating in water. The spectrum of the emitted light is obtained and depends upon two free parameters, the amplitude of the instabilities and the cut-off $% R_{\max}$, the shocks' spatial extension. The spectral intensity is determined by the former, but its shape turns out to have only a mild dependence on the latter, in the region of physical interest. The matching with the observed spectrum $ $requires a fine tuning of the perturbation amplitude $ε\sim 10^{-14},${\em indicating a quantum mechanical origin. Indeed, we support this conjecture with an order of magnitude estimative. The Inertial Polarization Principle clues the resolution of the noble gas puzzle in SL.

physics.class-ph↗

arXiv1998

The gravitational Vavilov-Cherenkov effect

In this essay we show that an uncharged black-hole moving superluminally in a transparent dielectric medium violates Hawking's area theorem. The violation is overcome through the emission of radiation. Since modes cannot emerge from the black hole itself, this radiation must originate from a collective effect in the medium, in complete analogy with the Vavilov-Cherenkov effect. However, because the black-hole is uncharged, the emission mechanism must be different. We discuss the physical origin of the effect and obtain a Newtonian estimative. Then we obtain the appropriate equations in the relativistic case and show that the field which is radiated away is a combination of gravitational and electromagnetic degrees of freedom. Possible astrophysical relevance for the detection of primordial black-holes and binary systems is discussed.

gr-qc↗

arXiv1998

The many faces of superradiance

Inertial motion superradiance, the emission of radiation by an initially unexcited system moving inertially but superluminally through a medium, has long been known. Rotational superradiance, the amplification of radiation by a rotating rigid object, was recognized much later, principally in connection with black hole radiances. Here we review the principles of inertial motion superradiance and prove thermodynamically that the Ginzburg--Frank condition for superradiance coincides with the condition for superradiant amplification of already existing radiation. Examples we cite include a new type of black hole superradiance. We correct Zel'dovich's thermodynamic derivation of the Zel'dovich--Misner condition for rotational superradiance by including the radiant entropy in the bookkeeping . We work out in full detail the electrodynamics of a Zel'dovich rotating cylinder, including a general electrodynamic proof of the Zel'dovich--Misner condition, and explicit calculations of the superradiant gain for both types of polarization. Contrary to Zel'dovich's pessimistic conclusion we conclude that, if the cylinder is surrounded by a dielectric jacket and the whole assembly is placed inside a rotating cavity, the superradiance is measurable in the laboratory.

gr-qc↗

arXiv1997

The random walks of a Schwarzschild black hole

We show that spinless and neutral black holes in thermal equilibrium with radiation undergo fluctuations of charge and angular momentum. The corresponding spreads for a black hole in contact with charged scalar particles is calculated. The angular momentum spread turns out to grow with the size of the cavity. Charge spread does not depend either on the size of the cavity nor on the elementary charge of the field. Then, either the scale of the elementary chage is fixed by black hole physics $α\sim 1/4π$ or the underlying physics of these fluctuations is not the random absorption and emission of charged particles from the bath, it remains unknown and must be clarified.

gr-qc↗

arXiv1997

Bound states due to an accelerated mirror

We discuss an effect of accelerated mirrors which remained hitherto unnoticed, the formation of a field condensate near its surface for massive fields. From the view point of an observer attached to the mirror, this is effect is rather natural because a gravitational field is felt there. The novelty here is that since the effect is not observer dependent even inertial observers will detect the formation of this condensate. We further show that this localization is in agreement with Bekenstein's entropy bound.

gr-qc↗