arXiv subjects

Christian Corda

Publications and source records attributed to Christian Corda.

At least 55 records · Page 3Linked to original sources

arXiv2015

A Machian Request for the Equivalence Principle in Extended Gravity and non-geodesic motion

Starting from the origin of Einstein general relativity (GR) the request of Mach on the theory's structure has been the core of the foundational debate. That problem is strictly connected with the nature of the mass-energy equivalence. It is well known that this is exactly the key point that Einstein used to realize a metric theory of gravitation having an unequalled beauty and elegance. On the other hand, the current requirements of particle physics and the open questions within extended gravity theories request a better understanding of Equivalence Principle (EP). The MOND theory by Milgrom proposes a modification of Newtonian dynamics and we consider a direct coupling between the Ricci curvature scalar and the matter Lagrangian showing that a non geodesic ratio m_{i}/m_{g} can be fixed and that Milgrom acceleration is retrieved at low energies.

gr-qc↗

arXiv2015

Precise model of Hawking radiation from the tunnelling mechanism

We recently improved the famous result of Parikh and Wilczek, who found a probability of emission of Hawking radiation which is compatible with a non-strictly thermal spectrum, showing that such a probability of emission is really associated to two non-strictly thermal distributions for boson and fermions. Here we finalize the model by finding the correct value of the pre-factor of the Parikh and Wilczek probability of emission. In fact, that expression has the "of order" sign instead of the equality. In general, in this kind of leading order tunnelling calculations, the exponent arises indeed from the classical action and the pre-factor is an order Planck constant correction. But in the case of emissions of Hawking quanta, the variation of the Bekenstein-Hawking entropy is order 1 for an emitted particle having energy of order the Hawking temperature. As a consequence, the exponent in the Parikh and Wilczek probability of emission is order unity and one asks what is the real significance of that scaling if the pre-factor is unknown. Here we solve the problem assuming the unitarity of the black hole (BH) quantum evaporation and considering the natural correspondence between Hawking radiation and quasi-normal modes (QNMs) of excited BHs, in a "Bohr-like model" that we recently discussed in a series of papers. In that papers, QNMs are interpreted as natural BH quantum levels (the "electron states" in the "Bohr-like model"). Here we find the intriguing result that, although in general it is well approximated by 1, the pre-factor of the Parikh and Wilczek probability of emission depends on the BH quantum level n. We also write down an elegant expression of the probability of emission in terms of the BH quantum levels.

physics.gen-ph↗

arXiv2015

Quantum corrected non-thermal radiation spectrum from the tunnelling mechanism

Tunnelling mechanism is today considered a popular and widely used method in describing Hawking radiation. However, in relation to black hole (BH) emission, this mechanism is mostly used to obtain the Hawking temperature by comparing the probability of emission of an outgoing particle with the Boltzmann factor. On the other hand, Banerjee and Majhi reformulated the tunnelling framework deriving a black body spectrum through the density matrix for the outgoing modes for both the Bose-Einstein distribution and the Fermi-Dirac distribution. In contrast, Parikh and Wilczek introduced a correction term performing an exact calculation of the action for a tunnelling spherically symmetric particle and, as a result, the probability of emission of an outgoing particle corresponds to a non-strictly thermal radiation spectrum. Recently, one of us (C. Corda) introduced a BH effective state and was able to obtain a non-strictly black body spectrum from the tunnelling mechanism corresponding to the probability of emission of an outgoing particle found by Parikh and Wilczek. The present work introduces the quantum corrected effective temperature and the corresponding quantum corrected effective metric is written using Hawking's periodicity arguments. Thus, we obtain further corrections to the non-strictly thermal BH radiation spectrum as the final distributions take into account both the BH dynamical geometry during the emission of the particle and the quantum corrections to the semiclassical Hawking temperature.

gr-qc↗

arXiv2015

Quasi-normal modes: the "electrons" of black holes as "gravitational atoms"? Implications for the black hole information puzzle

Some recent important results on black hole (BH) quantum physics concerning the BH effective state and the natural correspondence between Hawking radiation and BH quasi-normal modes (QNMs) are reviewed, clarified and refined. Such a correspondence permits to naturally interpret QNMs as quantum levels in a semi-classical model. This is a model of BH somewhat similar to the historical semi-classical model of the structure of a hydrogen atom introduced by Bohr in 1913. In a certain sense, QNMs represent the "electron" which jumps from a level to another one and the absolute values of the QNMs frequencies "triggered" by emissions (Hawking radiation) and absorption of particles represent the energy "shells" of the "gravitational hydrogen atom". Important consequences on the BH information puzzle are discussed. In fact, it is shown that the time evolution of this "Bohr-like BH model" obeys to a time dependent Schrödinger equation which permits the final BH state to be a pure quantum state instead of a mixed one. Thus, information comes out in BH evaporation, in agreement with the assumption by 't Hooft that Schröedinger equations can be used universally for all dynamics in the universe. We also show that, in addition, our approach solves the entanglement problem connected with the information paradox. We emphasize that Bohr model is an approximated model of the hydrogen atom with respect to the valence shell atom model of full quantum mechanics. In the same way, we expect the Bohr-like BH model to be an approximated model with respect to the definitive, but at the present time unknown, BH model arising from a full quantum gravity theory.

gr-qc↗

arXiv2015

On quasi-normal modes, area quantization and Bohr correspondence principle

In Int. Journ. Mod. Phys. D 14, 181 (2005), the author Khriplovich verbatim claims that "the correspondence principle does not dictate any relation between the asymptotics of quasinormal modes and the spectrum of quantized black holes" and that "this belief is in conflict with simple physical arguments". In this paper we analyze Khriplovich's criticisms and realize that they work only for the original proposal by Hod, while they do not work for the improvements suggested by Maggiore and recently finalized by the author and collaborators through a connection between Hawking radiation and black hole (BH) quasi-normal modes (QNMs). This is a model of quantum BH somewhat similar to the historical semi-classical model of the structure of a hydrogen atom introduced by Bohr in 1913. Thus, QNMs can be really interpreted as BH quantum levels (the "electrons" of the "Bohr-like BH model"). Our results have also important implications on the BH information puzzle.

gr-qc↗

arXiv2015

Bohr-like black holes

The idea that black holes (BHs) result in highly excited states representing both the "hydrogen atom" and the "quasi-thermal emission" in quantum gravity is today an intuitive but general conviction. In this paper it will be shown that such an intuitive picture is more than a picture. In fact, we will discuss a model of quantum BH somewhat similar to the historical semi-classical model of the structure of a hydrogen atom introduced by Bohr in 1913. The model is completely consistent with existing results in the literature, starting from the celebrated result of Bekenstein on the area quantization.

gr-qc↗

arXiv2015

Interpretation of Mössbauer experiment in a rotating system: a new proof for general relativity

A historical experiment by Kündig on the transverse Doppler shift in a rotating system measured with the Mössbauer effect has been recently first re-analyzed and then replied [1,2]. The results have shown that a correct re-processing of Kündig's experimental data gives a deviation of a relative redshift between emission and absorption resonant lines from the prediction due to relativistic dilatation of time, which, at first-order in \frac{v^{2}}{c^{2}}, gives a redshift \frac{\nabla E}{E}\simeq-\frac{1}{2}\frac{v^{2}}{c^{2}} where v is the tangential velocity of the absorber of resonant radiationa and c is the velocity of light in vacuum. Data re-processing gave \frac{\nabla E}{E}\simeq-k\frac{v^{2}}{c^{2}} with k=0.596\pm0.006. Subsequent new experimental results [2] have shown a redshift with k=0.68\pm0.03 instead. Using Einstein Equivalence Principle on the equivalence between the gravitational "force" and the pseudo-force experienced by an observer in a rotating frame of reference, here we re-analyze the theoretical framework of Mössbauer rotor experiments directly in the rotating frame through a general relativistic treatment. We show that previous analyses missed an important effect of clock synchronization and that the correct general relativistic prevision in the rotating frame gives k\simeq\frac{2}{3} in perfect agreement with the new experimental results. Such an effect of clock synchronization has been missed in various papers in the literature with some subsequent claim of invalidity of relativity theory and/or some attempts to explain the experimental results through "exotic" effects. Our general relativistic interpretation shows, instead, that the new experimental results of the Mössbauer rotor experiment are a new, strong and independent, proof of general relativity. Finally, we discuss an analogy with the use of general relativity in Global Positioning Systems.

gr-qc↗

arXiv2014

Time-Dependent Schrodinger Equation for Black Hole Evaporation: no Information Loss

In 1976 S. Hawking claimed that "Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state" (Verbatim from ref. 2). This was the starting point of the popular "black hole (BH) information paradox". In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model, a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of an unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking's claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect 't Hooft's assumption that Schröedinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in an unitary time dependent evolution. In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.

gr-qc↗

arXiv2014

Non-strictly black body spectrum from the tunnelling mechanism

A modern and largely used approach to obtain Hawking radiation is the tunnelling mechanism. However, in various papers in the literature, the analysis concerned almost only to obtain the Hawking temperature through a comparison of the probability of emission of an outgoing particle with the Boltzmann factor. In a interesting and well written paper, Banerjee and Majhi improved the approach, by explicitly finding a black body spectrum associated with black holes. On the other hand, this result, which has been obtained by using a reformulation of the tunnelling mechanism, is in contrast which the remarkable result by Parikh and Wilczek, that, indeed, found a probability of emission which is compatible with a non-strictly thermal spectrum. By using our recent introduction of an effective state for a black hole, here we solve such a contradiction, through a slight modification of the analysis by Banerjee and Majhi. The final result will be a non-strictly black body spectrum from the tunnelling mechanism. We also show that, for an effective temperature, we can write the corresponding effective metric by Hawking's periodicity arguments. Potential important implications for the black hole information puzzle are also discussed

gr-qc↗

arXiv2014

f(R) Gravity, relic coherent gravitons and optical chaos

We discuss the production of massive relic coherent gravitons in a particular class of f(R) gravity which arises from string theory and their possible imprint in Cosmic Microwave Background. In fact, in the very early universe these relic gravitons could have acted as slow gravity waves. They may have then acted to focus the geodesics of radiation and matter. Therefore, their imprint on the later evolution of the universe could appear as filaments and domain wall in the Universe today. In that case, the effect on Cosmic Microwave Background should be analogous to the effect of water waves, which, in focusing light, create optical caustics which are commonly seen on the bottom of swimming pools. We analyze this important issue by showing how relic massive GWs perturb the trajectories of Cosmic Microwave Background photons (gravitational lensing by relic GWs). The consequence of the type of physics discussed is outlined by illustrating an amplification of what might be called optical chaos.

gr-qc↗

arXiv2014

Hawking radiation - quasi-normal modes correspondence and effective states for nonextremal Reissner-Nordström black holes

It is known that the nonstrictly thermal character of the Hawking radiation spectrum harmonizes Hawking radiation with black hole (BH) quasi-normal modes (QNM). This paramount issue has been recently analyzed in the framework of both Schwarzschild BHs (SBH) and Kerr BHs (KBH). In this assignment, we generalize the analysis to the framework of nonextremal Reissner-Nordström BHs (RNBH). Such a generalization is important because in both SBHs and KBHs an absorbed (or emitted) particle has only mass. Instead, in RNBHs the particle has charge as well as mass. In doing so, we expose that for the RNBH, QNMs can be naturally interpreted in terms of quantum levels for both particle emission and absorption. Conjointly, we generalize some concepts concerning the RNBH's "effective states".

physics.gen-ph↗

arXiv2013

Quantum transitions of minimum energy for Hawking quanta in highly excited black holes: problems for loop quantum gravity?

By analysing some recent results by Yoon, which arise from loop quantum gravity and from the assumption of the locality of photon emission in a black hole, we argue that they are not consistent with our recent semi-classical results for highly excited black holes. Maybe that the results by Yoon can be correct for non-highly excited black holes, but, in any case, our analysis renders further problematical the match between loop quantum gravity and semi-classical theory.

gr-qc↗

arXiv2013

Black hole quantum spectrum

Introducing a black hole (BH) effective temperature, which takes into account both the non-strictly thermal character of Hawking radiation and the countable behavior of emissions of subsequent Hawking quanta, we recently re-analysed BH quasi-normal modes (QNMs) and interpreted them naturally in terms of quantum levels. In this work we improve such an analysis removing some approximations that have been implicitly used in our previous works and obtaining the corrected expressions for the formulas of the horizon's area quantization and the number of quanta of area and hence also for Bekenstein-Hawking entropy, its sub-leading corrections and the number of micro-states, i.e. quantities which are fundamental to realize the underlying quantum gravity theory, like functions of the QNMs quantum "overtone" number n and, in turn, of the BH quantum excited level. An approximation concerning the maximum value of n is also corrected. On the other hand, our previous results were strictly corrected only for scalar and gravitational perturbations. Here we show that the discussion holds also for vector perturbations. The analysis is totally consistent with the general conviction that BHs result in highly excited states representing both the "hydrogen atom" and the "quasi-thermal emission" in quantum gravity. Our BH model is somewhat similar to the semi-classical Bohr's model of the structure of a hydrogen atom. The thermal approximation of previous results in the literature is consistent with the results in this paper. In principle, such results could also have important implications for the BH information paradox.

gr-qc↗

arXiv2013

Differential geometry and scalar gravitational waves

Following some strong argumentations of differential geometry in the Landau's book, some corrections about errors in the old literature on scalar gravitational waves (SGWs) are given and discussed. In the analysis of the response ofi nterferometers the computation is first performed in the low frequencies approximation, then the analysis is applied to all SGWs in the full frequency and angular dependences. The presented results are in agreement with the more recent literature on SGWs.

physics.gen-ph↗

arXiv2013

Novel considerations about the error budget of the LAGEOS-based tests of frame-dragging with GRACE geopotential models

A realistic assessment of the uncertainties in the even zonals of a given geopotential model must be made by directly comparing its coefficients with those of a wholly independent solution of superior formal accuracy. Otherwise, a favorable selective bias is introduced in the evaluation of the total error budget of the LAGEOS-based Lense-Thirring tests yielding likely too optimistic figures for it. By applying a novel approach which recently appeared in the literature, the second (L = 4) and the third (L = 6) even zonals turn out to be uncertain at a 2-3 10^-11 (L = 4) and 3-4 10^-11 (L = 6) level, respectively, yielding a total gravitational error of about 27-28%, with an upper bound of 37-39%. The results by Ries et al. themselves yield an upper bound for it of about 33%. The low-degree even zonals are not exclusively determined from the GRACE Satellite-to-Satellite Tracking (SST) range since they affect it with long-period, secular-like signatures over orbital arcs longer than one orbital period: GRACE SST is not accurately sensitive to such signals. Conversely, general relativity affects it with short-period effects as well. Thus, the issue of the a priori "imprinting" of general relativity itself in the GRACE-based models used so far remains open.

gr-qc↗

arXiv2013

Cosmology and gravitational waves in the Nordstrom-Vlasov system, a laboratory for Dark Energy

We discuss a cosmological solution of the system which was originally introduced by Calogero and is today popularly known as "Nordstrom-Vlasov system". Although the model is un-physical, its cosmological solution results interesting for the same reasons for which the Nordstrom-Vlasov system was originally introduced in the framework of galactic dynamics. In fact, it represents a theoretical laboratory where one can rigorously study some problems, like the importance of the gravitational waves in the dynamics, which at the present time are not well understood within the physical model of the Einstein-Vlasov system. As the cosmology of the Nordstrom-Vlasov system is founded on a scalar field, a better understanding of the system is important also in the framework of the Dark Energy problem. In fact, various attempts to achieve Dark Energy by using scalar fields are present in the literature. In the solution an analytical expression for the time dependence of the cosmological evolution of the Nordstrom's scalar field is also released.This analytical expression is unknown in the literature of the Nordstrom-Vlasov system. Based on their importance, the propagation of gravitational waves in the Nordstrom-Vlasov system and their effects on test masses are also discussed.

gr-qc↗

arXiv2012

General relativity and OPERA Experiment

In his paper "A very simple solution to the OPERA neutrino velocity problem" the author J. Manuel Garcia-Islas claims to have very easily solved and explained within the general theory of relativity that OPERA's neutrinos are not traveling faster than the speed of light and the early time arrival is due to the presence of the Earth's gravitational field. In this letter we easily show that the argument by Garcia-Islas does not work. Although it looks that data suggesting that neutrinos can travel faster than light probably resulted from a faulty connection in a GPS timing system, it is important to clarify that, in any case, the general relativistic effect discussed by Garcia-Islas cannot explain the original OPERA's data.

physics.gen-ph↗

arXiv2012

Dark Energy and Dark Matter like intrinsic curvature in extended gravity. Viability through gravitational waves

Towards the goal to quantize gravity, in this short review we discuss an intermediate step which consists in extending the picture of standard General Relativity by considering Extended Theories of Gravity. In this tapestry, the equations to quantize are not the standard Einstein field equations of General Relativity, but the extended Einstein field equations of such Extended Theories. The traditional relation between mass-energy and space-time curvature, which founds standard General Relativity, results modified in this new picture and, at least at the linearized approximation, variations of the space-time curvature generate the mass-energy. Various problems of the Dark Universe, Dark Energy, Dark Matter and Pioneer anomaly, can be, in principle, solved through this approach, while a definitive endorsement for Extended Theories of Gravity could arrive from the realization of a consistent gravitational wave astronomy. We also discuss the quantization of both mass-energy and space-time curvature in the early Universe by using the process of amplification of vacuum fluctuations which is connected with the primordial production of relic gravitational waves. A future detection of such relic gravitational waves will be an ultimate endorsement for the quantum rather than classical feature of the gravitational interaction.

gr-qc↗