International Journal of Modern Physics D

This paper reviews the inviscid shear-stability theory that led to the first calibrated measurement of Saturn's rotation period. The roots trace back to 1880, when Kelvin argued that there are two distinct branches, which Arnol'd established in the 1960s as two nonlinear stability theorems. Vortical eddies must lean into the shear to be unstable, and vorticity (Rossby) waves, which are uni-directional, control the physics. The analog of the Mach number for vorticity waves, here denoted "Mach" or "Ma," is treated as a signed quantity that takes on negative values when the intrinsic wave propagation is in the downstream direction. The Kelvin–Arnol'd first branch, which includes the Rayleigh, Kuo, Charney–Stern and Fjørtoft theorems — a century of results — establishes shear stability by restricting to negative "Ma" numbers. Violation of the most well-known of these, Charney–Stern, which implies the existence of at least one potential vorticity (PV; also known as vortensity) extremum, is equivalent to allowing some positive "Ma" numbers in the domain. The Kelvin–Arnol'd second branch is the "supersonic" condition. Taken together, the two branches prove that "subsonic" flow is necessary for instability. Consequently, the shock of vorticity waves in shear may be identified as the onset of shear instability itself. Observationally, positive "Ma" numbers prove to be the norm, not the exception, on Earth, Jupiter and Saturn, and nearly "choked PV" conditions are found to hold for the jets of Jupiter and Saturn, not "mixed PV," yielding a clear, connected and calibrated determination of Saturn's rotation period.

Radio observations prove the existence of relativistic particles and magnetic field associated with the intra-cluster-medium (ICM) through the presence of extended synchrotron emission in the form of radio halos and peripheral relics. This observational evidence has fundamental implications on the physics of the ICM. Nonthermal components in galaxy clusters are indeed unique probes of very energetic processes operating within clusters that drain gravitational and electromagnetic energy into cosmic rays (CRs) and magnetic fields. These components strongly affect the (micro-)physical properties of the ICM, including viscosity and electrical conductivities, and have also potential consequences on the evolution of clusters themselves. The nature and properties of CRs in galaxy clusters, including the origin of the observed radio emission on cluster-scales, have triggered an active theoretical debate in the last decade. Only recently we can start addressing some of the most important questions in this field, thanks to recent observational advances, both in the radio and at high energies. The properties of CRs and of cluster nonthermal emissions depend on the dynamical state of the ICM, the efficiency of particle acceleration mechanisms in the ICM and on the dynamics of these CRs. In this paper, we discuss in some detail the acceleration and transport of CRs in galaxy clusters and the most relevant observational milestones that have provided important steps on our understanding of this physics. Finally, looking forward to the possibilities from new generations of observational tools, we focus on what appear to be the most important prospects for the near future from radio and high-energy observations.

It has recently been proposed to combine the node drifts of the future constellation of 27 Galileo spacecraft together with those of the existing Laser Geodynamics Satellites (LAGEOS)-type satellites to improve the accuracy of the past and ongoing tests of the Lense–Thirring (LT) effect by removing the bias of a larger number of even zonal harmonics J_ℓ than either done or planned so far. Actually, it seems a difficult goal to be achieved realistically for a number of reasons. First, the LT range signature of a Galileo-type satellite is as small as 0.5 mm over three-days arcs, corresponding to a node rate of just milliarcseconds per year (mas yr^-1). Some tesseral and sectorial ocean tides such as K₁ and K₂ induce long-period harmonic node perturbations with frequencies which are integer multiples of the extremely slow Galileo's node rate completing a full cycle in about 40 yr. Thus, over time spans, T, of some years, they would act as superimposed semisecular aliasing trends. Since the coefficients of the J_ℓ-free multisatellite linear combinations are determined only by the semimajor axis a, the eccentricity e and the inclination I, which are nominally equal for all the Galileo satellites, it is not possible to include all of them. Even using only one Galileo spacecraft together with the LAGEOS family would be unfeasible because of the fact that the resulting Galileo coefficient would be ≳ 1, thus enhancing the aliasing impact of the uncancelled nonconservative and tidal perturbations.

We generalize the scalar-curvature coupling model ξΦ²R of Higgs inflation to ξΦ^aR^b to study inflation. We compute the amplitude and spectral index of curvature perturbations generated during inflation and fix the parameters of the model by comparing these with the Planck + WP data. We find that if the scalar self-coupling λ is in the range 10^-5–0.1, parameter a in the range 2.3–3.6 and b in the range 0.77–0.22 at the Planck scale, one can have a viable inflation model even for ξ ≃ 1. The tensor to scalar ratio r in this model is small and our model with scalar-curvature couplings is not ruled out by observational limits on r unlike the pure theory. By requiring the curvature coupling parameter to be of order unity, we have evaded the problem of unitarity violation in scalar-graviton scatterings which plague the ξΦ²R Higgs inflation models. We conclude that the Higgs field may still be a good candidate for being the inflaton in the early universe if one considers higher-dimensional curvature coupling.

By utilizing the improved Damour–Ruffini method with a new tortoise transformation, we study the Hawking radiation of Dirac particles from a general dynamical spherically symmetric black hole. In the improved Damour–Ruffini method, the position of the event horizon of the black hole is an undetermined function, and the temperature parameter κ is an undetermined constant. By requiring the Dirac equation to be the standard wave equation near the event horizon of the black hole, κ can be determined automatically. Therefore, the Hawking temperature can be obtained. The result is consistent with that of the Hawking radiation of scalar particles.

Velocity effects in first-order Schwarzschild deflection of light and particles have been explored in the previous literature. In this paper, we investigate the roto-translational-motion induced deflection by one moving Kerr black hole with an arbitrary, but constant speed. It is shown that the coupling between the effects of the rotation and the translational motion always exists for both light and particles. The contribution of the roto-translational deflection to the total bending angle is discussed in detail. This ratio takes upper limit for light and it decreases monotonically with increasing translational velocity for a massive particle. For a given translational velocity of black hole, this ratio increases with the particle's velocity. In addition, the post-Newtonian dynamics of the photon and particle is also presented.

Employing higher-order perturbation theory, we find a new class of perturbative extremal rotating black hole solutions with Born–Infeld electric charge in odd D dimensional spacetime. The seed solution is an odd-dimensional extremal Myers–Perry black hole with equal angular momenta to which a perturbative, nonlinear, electric Born–Infeld field charge q is added maintaining the extremality condition. The perturbations are performed up to third-order. We also study some physical properties of these black holes. In particular, it is shown that the values of the gyromagnetic ratio of the black holes are modified by the perturbative parameter q and the Born–Infeld parameter β.

To explain the accelerated expansion of the universe, models with interacting dark components has been considered in the literature. Generally, the dark energy component is physically interpreted as the vacuum energy. However, at the other side of the same coin, the influence of the vacuum energy in the gravitational collapse is a topic of scientific interest. Based in a simple assumption on the collapsed rate of the matter fluid density that is altered by the inclusion of a vacuum energy component that interacts with the matter fluid, we study the final fate of the collapse process.

The Bianchi I cosmological models containing radiation, stiff fluid and a nonminimally coupled material scalar field with polynomial potentials of the fourth degree are considered in the framework of the Einstein–Cartan theory (ECT). Exact partial solutions are obtained for arbitrary positive values of the coupling constant ξ. The restrictions on ξ are found from the integrability conditions. It is demonstrated that singular models with the asymptotical isotropization by the de Sitter type and by the power-law (t^4/3) type at late-times are possible. It is shown that the bouncing models with the isotropization by the de Sitter law of expansion at late-times are admissible. The role of sources in the evolution of models is elucidated.

Minkowski spacetime is transitive under ordinary translations, a transformation that do not have matrix representations. The de Sitter spacetime, on the other hand, is transitive under a combination of translations and proper conformal transformations, which do have a matrix representation. Such matrix, however, is not by itself a de Sitter generator: it gives rise to a conformal re-scaling of the metric, a transformation not belonging to the de Sitter group, and in general not associated with diffeomorphisms in spacetime. When dealing with variational principles and Noether's theorem in de Sitter spacetime, it is necessary to regularize the transformations in order to eliminate the conformal re-scaling of the metric.

In this paper, we revisit the solar system tests of f(R) gravity. When the sun sits in a vacuum, the field f′ is light, which leads to a metric different from the observations. We reobtain this result in a simpler way by directly focusing on the equations of motion for f(R) gravity in the Jordan frame (JF). The discrepancy between the metric in the f(R) gravity and the observations can be alleviated by the chameleon mechanism. The implications from the chameleon mechanism on the functional form f(R) are discussed. Considering the analogy of the solar system tests to the false vacuum decay problem, the effective potentials in different cases are also explored. The combination of analytic and numerical approaches enables us to ascertain whether an f(R) model can pass the solar system tests or not.

We introduce the Triangular Ring (TR) resonator. We show that the difference between the clockwise and anti-clockwise resonant frequencies of a vacuum TR resonator is sensitive to the birefringence parity-odd parameters of the photon's sector of the minimal Standard Model Extension (mSME): the Standard Model plus all the perturbative parameters encoding the break of the Lorentz symmetry. We report that utilizing the current technology allows for direct measurement of these parameters with a sensitivity of the parity-even ones and improves the best current resonator bounds by couple of orders of magnitudes.

We note that, designing an optical table that rotates perpendicular to the gravitational equipotential surface (geoid) allows for direct measurement of the constancy of the light speed at the vicinity of the earth in all directions, in particular, perpendicular to the geoid. If this table could achieve the precision of the ordinary tables, then it would improve the GPS bounds on the constancy of the light speed perpendicular to geoid by about eight orders of magnitude.

We consider λϕ⁴ kink and sine-Gordon soliton in the presence of a minimal length uncertainty proportional to the Planck length. The modified Hamiltonian contains an extra term proportional to p⁴ and the generalized Schrödinger equation is expressed as a fourth-order differential equation in quasiposition space. We obtain the modified energy spectrum for the discrete states and compare our results with one-loop resummed and Hartree approximations for the quantum fluctuations. We finally find some lower bounds for the deformations parameter, so that the effects of the minimal length have the dominant role.

In this paper, we investigate the phase transition of Bardeen black hole for the first time. First, we calculate thermodynamic quantities and correct the misuse of formula in former literature. Second, we investigate in detail the behavior of specific heat. We not only discuss the influence of parameter on phase transition, but also show the three-dimensional behavior of the specific heat. It is shown that phase transition takes place from a locally unstable large black hole to a locally stable small black hole. It is also shown that the location of phase transition point is proportional to the charge. Meanwhile, we study the behavior of the inverse of the isothermal compressibility and find that it diverges at the phase transition point. Thirdly, we build up geometrothermodynamics to examine the phase transition structure. It is shown that Legendre invariant thermodynamic scalar curvature diverges exactly where the specific heat diverges, which leads to the conclusion that the Legendre invariant metrics can correctly produce the behavior of the phase transition structure. Furthermore, to gain a thorough understanding of critical behavior, we calculate the relevant critical exponents and examine the scaling laws. It is shown that they are in agreement with the scaling laws.