Wave-wave interactions and gravitational instability

The instability of gravitational waves withk>k _Jeans in a weakly turbulent gas is discussed. Basic features of the processes leading to amplification or damping of gravitational waves are described. Growth rates of the amplitudes are calculated.     

Dissipation of modified entropic gravitational energy through gravitational waves

The phenomenological nature of a new gravitational type interaction between two different bodies derived from Verlinde’s entropic approach to gravitation in combination with Sorkin’s definition of Universe’s quantum information content, is investigated. Assuming that the energy stored in this entropic gravitational field is dissipated under the form of gravitational waves and that the Heisenberg principle holds for this system, one calculates a possible value for an absolute minimum time scale in nature t = \frac1516 \fracL^1/2(^h/_2p) Gc⁴ ~ 9.27×10^-105\tau=\frac{15}{16} \frac{\Lambda^{1/2}\hbar G}{c^{4}}\sim9.27\times10^{-105} seconds, which is much smaller than the Planck time t _P =(ħG/c ⁵)^1/2∼5.38×10⁻⁴⁴ seconds. This appears together with an absolute possible maximum value for Newtonian gravitational forces generated by matter F_g=\frac3230\fracc⁷L (^h/_2p) G² ~ 3.84×10¹⁶⁵F_{g}=\frac{32}{30}\frac{c^{7}}{\Lambda \hbar G^{2}}\sim 3.84\times 10^{165} Newtons, which is much higher than the gravitational field between two Planck masses separated by the Planck length F _gP =c ⁴/G∼1.21×10⁴⁴ Newtons.     

A reply to Richard Greenberg's review of interplanetary encounters: Close range gravitational interactions

The large-scale dynamics of the Martian winter atmosphere are analyzed and discussed. Results obtained from a baroclinic instability analysis, including a Newtonian radiational damping term, are compared with the Mariner 9 data. The beta plane baroclinic poleward heat fluxes are contrasted with those produced using spherical geometry, from the stationary orographically forced long waves.     

Kinetic equations for ultrarelativistic particles in a Robertson-Walker universe and isotropization of relict radiation by gravitational interactions

Kinetic equations for ultrarelativistic particles with due account of gravitational interactions with massive particles in the Robertson-Walker universe are obtained. On the basis of an exact solution of the kinetic equations thus obtained, a conclusion is made as to the high degree of the uniformity of the relict radiation on scales whih are less than 10.     

Weak gravitational flexion

Flexion is the significant third-order weak gravitational lensing effect responsible for the weakly skewed and arc-like appearance of lensed galaxies. Here we demonstrate how flexion measurements can be used to measure galaxy halo density profiles and large-scale structure on non-linear scales, via galaxy–galaxy lensing, dark matter mapping and cosmic flexion correlation functions. We describe the origin of gravitational flexion, and discuss its four components, two of which are first described here. We also introduce an efficient complex formalism for all orders of lensing distortion. We proceed to examine the flexion predictions for galaxy–galaxy lensing, examining isothermal sphere and Navarro–Frenk–White (NFW) profiles and both circularly symmetric and elliptical cases. We show that in combination with shear we can precisely measure galaxy masses and NFW halo concentrations. We also show how flexion measurements can be used to reconstruct mass maps in two-dimensional projection on the sky, and in three dimensions in combination with redshift data. Finally, we examine the predictions for cosmic flexion, including convergence–flexion cross-correlations, and we find that the signal is an effective probe of structure on non-linear scales.     

Solar gravitational redshift

Wavelengths of solar spectrum lines should be shifted toward the red by the Sun's gravitational field as predicted by metric theories of gravity according to the principle of equivalence. Photographic wavelengths of 738 solar Fe i lines and their corresponding laboratory wavelengths have been studied. The measured solar wavelength minus the laboratory wavelength (_observed) averaged for the strong lines agrees well with the theoretically predicted shift (_theoretical). Studies show that the departures depend on line strength. No dependence of the departures on wavelength was found within the existing data.By studying strong lines over a wide spectral range, velocity shifts caused by the complex motions in the solar atmosphere seem to affect the results in a minimal fashion.     

Random gravitational lensing

A simple three-dimensional approach to calculate the probability of observing gravitational lensing, caused by a chance superposition of lens and source, is presented. The formalism is then used to estimate the lensing probabilities in a number of astrophysical situations. As indicated in earlier works, we find that the chance of random gravitational lensing being detected locally is small, and the chance at extra-galactic distances is large.     

Self-consistent gravitational lens reconstruction

We present a new method for directly determining accurate, self-consistent cluster lens mass and shear maps in the strong lensing regime from the magnification bias of background galaxies. The method relies upon pixellization of the surface mass density distribution which allows us to write down a simple, solvable set of equations. We also show how pixellization can be applied to methods of mass determination from measurements of shear and present a simplified method of application. The method is demonstrated with cluster models and applied to magnification data from the lensing cluster Abell 1689.     

Towards gravitational wave asteroseismology

We present new results for pulsating neutron stars. We have calculated the eigenfrequencies of the modes that one would expect to be the most important gravitational wave sources: the fundamental fluid f mode, the first pressure p mode and the first gravitational wave w mode, for twelve realistic equations of state. From these numerical data we have inferred a set of 'empirical relations' between the mode frequencies and the parameters of the star (the radius R and the mass M ). Some of these relations prove to be surprisingly robust, and we show how they can be used to extract the details of the star from observed modes. The results indicate that, should the various pulsation modes be detected by the new generation of gravitational wave detectors that come online in a few years, the mass and the radius of neutron stars can be deduced with errors no larger than a few per cent.     

Rotation in gravitational lenses

Gravitational lensing deflects light. A single lens deflector can only shear images, but cannot induce rotations. Multiple lens planes can induce rotations. Such rotations can be observed in quadruply imaged sources, and can be used to distinguish between two proposed solutions of the flux anomaly problem: substructures in lensing galaxies versus large-scale structure. We predict the expected amount of rotation due to large-scale structure in strong lensing systems, and show how this effect can be measured using ∼mas very long baseline interferometry astrometry of quadruple lenses with extended source structures. The magnitude of rotation is around 1°. The biggest theoretical uncertainty is the power spectrum of dark matter on very small scales. This procedure can potentially be turned around to measure the dark matter power spectrum on very small scales. We list the predicted rms rotation angles for several quadruple lenses with known lens and source redshifts.     

A limit for gravitational collapse

Earlier, under certain simplifying assumptions, on the basis of the General Theory of Relativity, it has been concluded by many authors that when the radius of a gravitationally collapsing spherical object of massM reaches the critical value of the Scharzschild radiusR _s=2GM/c ², then, in a co-moving frame, the object collapses catastrophically to a point. However, in drawing this conclusion due consideration has not been given to the nuclear forces between the nucleons. In particular, the very strong ‘hard-core’ repulsive interaction between the nucleons which has the range ～0.4×10^?13 cm has been totally ignored. On taking into account this ‘hard-core’ repulsive interaction, it is found that no spherical object of massM g can collapse to a volume of radius smaller thanR _min=(1.68×10^?6)M ^1/3 cm or to a density larger than ρ_max=5.0 × 10¹⁶ g cm^?3. It has also been pointed out that objects of mass smaller thanM _c～1.21×10³³ g can not cross the Schwarzschild barrier and gravitationally collapse. The only course left to the objects of mass less thanM _cis to reach the equilibrium as either a white dwarf or a neutron star.     

Strong gravitational lensing with SKA

The advent of new observational facilities in the last two decades has allowed the rapid discovery and high-resolution optical imaging of many strong lens systems from galaxy to cluster scales, as well as their spectroscopic follow-up. Radio telescopes have played the dominant role in the systematic detection of dozens of new arcsec-scale lens systems. For the future, we expect nothing less! The next major ground- and space-based facilities, especially the Square Kilometer Array can discover tens of thousands of new lens systems in large sky surveys. For optical imaging and spectroscopic follow-up a strong synergy with planned optical facilities is needed. Here, we discuss the field where strong gravitational lensing is expected to play the dominant role and where SKA can have a major impact: The study of the internal mass structure and evolution of galaxies and clusters to z 1. In addition, studies of more exotic phenomena are contemplated. For example, milli- and micro-lensing can provide a way to measure the mass-functions of stars and CDM substructure at cosmological distances. All-sky radio monitoring will also rapidly develop the field of time-domain lensing.     

Phenomenological theory of gravitational vacuum

An idea is developed that the vacuum in the gravitational field acquires properties of an elastic medium described by a definite tension _ik . The vacuum is stated to also participate in the formation of the space-time metric, together with the usual matter. So, the matter, vacuum and metric form a complex unity determined by the solution of the field equations. The vacuum may prove to play an essential role in the extremely strong fields existing in superdense celestial bodies. The tensor _ik is not to be identified with the pseudo-tensor of the energy-momentum of the gravitational field the idea of which is preserved.The problem of vacuum is investigated in the case of the central symmetry static field. A number of properties of the tensor _ik is found using the symmetry of the field and comparison with the post-Newton limit. The external and internal problems, as well as the procedure of joining the solutions on the surface of a celestial body, have been formulated. The stellar surface is determined in the usual way:P(r) = 0 whereP is the matter pressure. The theory includes three dimensionless parametersa=p/,b=p / (,p, p are the density of the vacuum energy and of its pressures in the radial and transverse directions) and determining the vacuum elastic properties. Generally speaking, they depend on the valueP/c² in the stellar centre where is the mass density. From general physical considerations it is shown that 0 1 + lim _P (l/q). The field equations are solved for the simple version of the theoryb=–a. There are solutions corresponding to superdense celestial bodies with masses considerably exceeding that of the Sun.     

Submillimetre-wave gravitational lenses and cosmology

One of the most direct routes for investigating the geometry of the Universe is provided by the numbers of strongly magnified gravitationally lensed galaxies as compared with those that are either weakly magnified or de-magnified. In the submillimetre waveband the relative abundance of strongly lensed galaxies is expected to be larger as compared with the optical or radio wavebands, both in the field and in clusters of galaxies. The predicted numbers depend on the properties of the population of faint galaxies in the submillimetre waveband, which was formerly very uncertain; however, recent observations of lensing clusters have reduced this uncertainty significantly and confirm that a large sample of galaxy–galaxy lenses could be detected and investigated using forthcoming facilities, including the FIRST and Planck Surveyor space missions and a large ground-based millimetre/submillimetre-wave interferometer array (MIA). We discuss how this sample could be used to impose limits on the values of cosmological parameters and the total density and form of evolution of the mass distribution of bound structures, even in the absence of detailed lens modelling for individual members of the sample. The effects of different world models on the form of the magnification bias expected in sensitive submillimetre-wave observations of clusters are also discussed, because an MIA could resolve and investigate images in clusters in detail.     

Weak gravitational lensing by voids

We consider the prospects for detecting weak gravitational lensing by underdensities (voids) in the large-scale matter distribution. We derive the basic expressions for magnification and distortion by spherical voids. Clustering of the background sources and cosmic variance are the main factors that limit in principle the detection of lensing by voids. We conclude that only voids with radii larger than ∼100  h ⁻¹ Mpc have lensing signal-to-noise ratio larger than unity.     

Quantisation in stable gravitational systems

The similarities between gravitational and electric forces are used as a basis for explaining the stability of the various parts of the Solar System in terms of gravitational guiding waves, or quanta. This leads to commensurability and quantisation of all orbital and spin parameters. Ultimately, the theory proves that gravity is an electromagnetic quantum phenomenon.     

Optical approach to gravitational redshift

An optical approach begins by interpreting the gravitational redshift resulting to a change in the relative velocity of light due to the medium of propagation in the gravitational field. The discussion continues by pointing out an agreement in structure between the equation for rays in geometrical optics and the geodesic equation of general relativity. From their comparison we learn that the path of rays should be written in the form ds ²=n ²(r)dr ²+r ² dθ ², not ds ²=dr ²+r ² dθ ², in a medium with spherical symmetry of refractive index n(r). The development of an optical analogy suggests introducing n ²(r) in place of g _rr as an optical version of the Schwarzschild metric. In form and content, n ²(r) is different from g _rr . The optical point of view replaces the general-relativity explanations in terms of time and gravitation.