International Journal of Modern Physics D

From a hydrodynamicist’s point of view the inclusion of viscosity concepts in the macroscopic theory of the cosmic fluid would appear most natural, as an ideal fluid is after all an abstraction (exluding special cases such as superconductivity). Making use of modern observational results for the Hubble parameter plus standard Friedmann formalism, we may extrapolate the description of the universe back in time up to the inflationary era, or we may go to the opposite extreme and analyze the probable ultimate fate of the universe. In this review, we discuss a variety of topics in cosmology when it is enlarged in order to contain a bulk viscosity. Various forms of this viscosity, when expressed in terms of the fluid density or the Hubble parameter, are discussed. Furthermore, we consider homogeneous as well as inhomogeneous equations of state. We investigate viscous cosmology in the early universe, examining the viscosity effects on the various inflationary observables. Additionally, we study viscous cosmology in the late universe, containing current acceleration and the possible future singularities, and we investigate how one may even unify inflationary and late-time acceleration. Finally, we analyze the viscosity-induced crossing through the quintessence-phantom divide, we examine the realization of viscosity-driven cosmological bounces, and we briefly discuss how the Cardy–Verlinde formula is affected by viscosity.

We review a recently proposed effective Tolman temperature and present its applications to various gravitational systems. In the Unruh state for the evaporating black holes, the free-fall energy density is found to be negative divergent at the horizon, which is in contrast to the conventional calculations performed in the Kruskal coordinates. We resolve this conflict by invoking that the Kruskal coordinates could be no longer proper coordinates at the horizon. In the Hartle–Hawking–Israel state, despite the negative finite proper energy density at the horizon, the Tolman temperature is divergent there due to the infinite blueshift of the Hawking temperature. However, a consistent Stefan–Boltzmann law with the Hawking radiation shows that the effective Tolman temperature is eventually finite everywhere and the equivalence principle is surprisingly restored at the horizon. Then, we also show that the firewall necessarily emerges out of the Unruh vacuum, so that the Tolman temperature in the evaporating black hole is naturally divergent due to the infinitely blueshifted negative ingoing flux crossing the horizon, whereas the outgoing Hawking radiation characterized by the effective Tolman temperature indeed originates from the quantum atmosphere, not just at the horizon. So, the firewall and the atmosphere for the Hawking radiation turn out to be compatible, once we discard the fact that the Hawking radiation in the Unruh state originates from the infinitely blueshifted outgoing excitations at the horizon. Finally, as a cosmological application, the initial radiation energy density in warm inflation scenarios has been assumed to be finite when inflation starts. We successfully find the origin of the nonvanishing initial radiation energy density in the warm inflation by using the effective Tolman temperature.

In teleparallel gravity, we apply Lorenz type gauge fixing to cope with redundant degrees of freedom in the vierbein field. This condition is mainly to restore the Lorentz symmetry of the teleparallel torsion scalar. In cosmological application, this technique provides standard cosmology, turnaround, bounce or $\mathrm{\Lambda }$CDM as separate scenarios. We reconstruct the $f(T)$ gravity which generates these models. We study the stability of the solutions by analyzing the corresponding phase portraits. Also, we investigate Lorenz gauge in the unimodular coordinates, it leads to unify a nonsingular bounce and Standard Model cosmology in a single model, where crossing the phantom divide line is achievable through a finite-time singularity of Type IV associated with a de Sitter fixed point. We reconstruct the unimodular $f(T)$ gravity which generates the unified cosmic evolution showing the role of the torsion gravity to establish a healthy bounce scenario.

In this paper, we analyze some dynamical features of spherical celestial objects through structure scalars in $f(R,T)$ gravitational theory, where $R$ and $T$ are the Ricci scalar and the trace of energy–momentum tensor, respectively. In this framework, we consider our relativistic geometry to be spherical in shape filled with radiating viscous and shearing fluid content. We formulate extended version of structure scalars by orthogonal decomposition of the Riemann tensor with and without constant $R$ and $T$ backgrounds. We discuss the effects of dark source corrections on the construction of expansion and shear evolution equations via scalar variables. It is inferred that like general relativity, one can investigate the evolutionary stages of stellar compact objects with the help of extended scalar parameters.

A study of the shadow cast by rotating black holes in different models of modified gravity is presented. It is shown that the size of the shadow cast depends on the modified gravity model used. The distortions of the shadow cast by modified gravity black holes are investigated and the effects are compared with the distortions cast by Kerr black hole. The shadow of a rotating black hole in modified gravity is found to be similar to the shadow cast by Kerr black hole but with different sizes and distortion effects. The naked singularity by rotating modified gravity black hole is discussed. Finally, it is shown that some modified gravity models can present a considerable contribution to the size of black hole shadow.

The propagation of weak gravitational waves on the background of dark energy is studied. The consideration is carried out within the framework of an approximate approach where the cosmological scale factor is expanded as a power series for relatively small values of the redshift corresponding to the epoch of the present accelerated expansion of the universe. For several different dark energy models, we obtain dispersion relations for gravitational waves which can be used to estimate the viability of every specific model by comparing with observational data.

We study spherically symmetric timelike thin-shells in $3+1$-dimensional bulk spacetime with a variable equation-of-state for the fluid presented on the shell. In such a fluid, the angular pressure $p$ is a function of both surface energy density $\sigma$ and the radius $R$ of the thin-shell. Explicit cases of the thin shells connecting two nonidentical cloud of strings spacetimes and a flat Minkowski spacetime to the Schwarzschild metric are investigated.

In earlier work we showed that a frame dependent effective action motivated by the postulates of three-space general coordinate invariance and Weyl scaling invariance exactly mimics a cosmological constant in Robertson–Walker (RW) spacetimes. Here we study the implications of this effective action for small fluctuations around a spatially flat RW background geometry. The equations for the conserving extension of the modified stress-energy tensor can be integrated in closed form, and involve only the metric perturbation $h_{00}$. Hence the equations for tensor and vector perturbations are unmodified, but there are Hubble scale additions to the scalar perturbation equations, which nonetheless admit no propagating wave solutions. Consequently, there are no modifications to standard gravitational wave propagation theory, but there may be observable implications for cosmology. We give a self-contained discussion, including an analysis of the restricted class of gauge transformations that act when a frame dependent effective action is present.

So far the study of black hole perturbations has been mostly focused upon the classical black holes with singularities at the origin and hidden by event horizon. Compared to that, the regular black holes are a completely new class of solutions arising out of modification of general theory of relativity by coupling gravity to an external form of matter. Therefore it is extremely important to study the behavior of such regular black holes under different types of perturbations. Recently a new regular Bardeen black hole solution with a de Sitter branch has been proposed by Fernando [arXiv:1611.05337 [gr-qc]]. We compute the quasi-normal (QN) frequencies for the regular Bardeen de Sitter (BdS) black hole due to massless and massive scalar field perturbations as well as the massless Dirac perturbations. We analyze the behavior of both real and imaginary parts of QN frequencies by varying different parameters of the theory.

Lateral distribution function of extensive air showers of energetic cosmic rays, indicate how secondary particles spread over a surface detectors. There are many different universal formulas between lateral distribution parameters and shower age parameter which can be used to infer about maximum development of extensive air shower (which is a key parameter to estimate the mass composition of primary cosmic rays). At present work, an estimated percent of mass composition of ultra-high energy cosmic rays is investigated by comparison between Ivanov et al. modeling of simulated data, which has been done by CoRSiKa, and Yakutsk experimental data.

Whether Jordan’s and Einstein’s frame descriptions of $F(R)$ theory of gravity are physically equivalent, is a long standing debate. However, practically none questioned on true mathematical equivalence, since classical field equations may be translated from one frame to the other following a transformation relation. Here, we show that, neither Noether symmetries, Noether equations, nor may quantum equations be translated from one to the other. The reason being, — conformal transformation results in a completely different system, with a different Lagrangian. Field equations match only due to the presence of diffeomorphic invariance. Unless a symmetry generator is found which involves Hamiltonian constraint equation, mathematical equivalence between the two frames appears to be vulnerable. In any case, in quantum domain, mathematical and therefore physical equivalence cannot be established.

After a short critique of the Minkowski formulae for the electromagnetic constitutive laws in moving media, we argue that in actual fact the problem of Lorentz-covariant electromagnetic response theory is automatically solved within the framework of modern microscopic electrodynamics of materials. As an illustration, we first rederive the well-known relativistic transformation behavior of the microscopic conductivity tensor. Thereafter, we deduce from first principles the transformation law of the wavevector- and frequency-dependent dielectric tensor under Lorentz boost transformations.

In this paper, we discuss the dynamics of two- scalar-field cosmological models. Unlike in the situation of exponential potential, we find that there are late-time attractors in which one scalar field dominates the energy density of universe and the other one decay. We also discuss the possibility of multiple attractors model which is useful to realize the evolution of the universe from a scaling era to recent acceleration era. We also give the conditions of the existence of multiple attractors.

Classical singular black holes are known to obey the cosmic censorship conjecture, and therefore are indestructible until they get completely evaporated by the Hawking radiation phenomenon. However, a nonsingular quantum black hole may not be necessarily indestructible. To proceed in this test, we deduce the first law of thermodynamics for the renormalization technique based, quantum improved, nonsingular Kerr class black hole, and then the test is done by Wald’s method. It emerges that while the quantum improvement leads to an escape for black hole from complete evaporation, it also makes a spinning black hole well destructible against overspinning. Even though, in general, spinning quantum black holes appear quite destructible, in the regime of exceedingly low rate of allowed spin, slower the spin becomes, weaker happens to be the probability of black hole getting destroyed. In particular, the minimally energized black hole relic, which is of a Schwarzschild class, emerges absolutely indestructible. It has further been argued that the practical stable existence of “G-lumps” is improbable. In context of our formal work, we find a great scope for figuring out the quantum corrected differential version of “entropy-area law” for Kerr class black hole.

We study the Friedmann inflation in general covariant Horava–Lifshitz gravity (HLG) without the projectability conditions and with detailed and nondetailed balance conditions. Accordingly, we derive modifications in the Friedmann equations due to a single-scalar field potential describing minimal-supersymmetrically extended inflation. By implementing two time-independent equations of state (EoS) characterizing the cosmic background geometry filled up with dark energy, the dependence of the tensorial and scalar density fluctuations and their ratios on the inflation field are determined. The latter refers to the time evolution of the inflationary field relative to the Hubble parameter. Furthermore, the ratios of tensorial-to-spectral density fluctuations are calculated in dependence on the spectral index. For cold dark energy EoS $\omega =-1/3$, we find that the tensorial-to-spectral density fluctuations are not depending on the different theories of gravity and the results are very small relative to the recent BICEP2/Keck Array-Planck observations, $10^{-9}⪅r⪅10^{-3}$. We have also calculated the tensorial and scalar perturbations of the primordial spectra.

The Newman–Janis trick is a procedure, (not even really an ansatz), for obtaining the Kerr spacetime from the Schwarzschild spacetime. This 50 years old trick continues to generate heated discussion and debate even to this day. Most of the debate focusses on whether the Newman–Janis procedure can be upgraded to the status of an algorithm, or even an inspired ansatz, or is it just a random trick of no deep physical significance. (That the Newman–Janis procedure very quickly led to the discovery of the Kerr–Newman spacetime is a point very much in its favor.) In the current paper, we will not answer these deeper questions, we shall instead present a much simpler alternative variation on the theme of the Newman–Janis trick that might be easier to work with. We shall present a 2-step version of the Newman–Janis trick that works directly with the Kerr–Schild “Cartesian” metric presentation of the Kerr spacetime. That is, we show how the original 4-step Newman–Janis procedure can, (using the interplay between oblate spheroidal and Cartesian coordinates), be reduced to a considerably cleaner 2-step process.

In this paper, we continue the investigation concerning the propagation of gravitational waves in a cosmological background using Laplace transform. We analyze the possible physical consequences of the result present in Ref. 19 where it is argued that a nonvanishing positive abscissa of convergence caused by the de Sitter expansion factor $a(t)=e^{Ht}$ implies a shift in the frequencies domain of a traveling gravitational wave as measured by a comoving observer. In particular, we show that in a generic asymptotically de Sitter cosmological universe, this redshift effect does also arise. Conversely, in a universe expanding with, for example, a power law expansion, this phenomenon does not happen. This physically possible new redshift effect, although negligible for the actual very low value of $\mathrm{\Lambda }$, can have interesting physical consequences concerning for example its relation with Bose–Einstein condensation or more speculatively with the nature of the cosmological constant in terms of gravitons, as recently suggested in Ref. 21 near a Bose–Einstein condensation phase.

The geodesic equations are considered in a spacetime that represents a Schwarzschild metric coupled to a uniform external electromagnetic (em) field. Due to the em field horizon shrinks and geodesics are modified. By analyzing the behavior of the effective potentials for the massless and massive particle we study the radial and circular trajectories. Radial geodesics for both photons and particles are solved exactly. It is shown that a particle that falls toward the horizon in a finite proper time slows down so that the particle reaches the singularity slower than Schwarzschild case. Timelike and null circular geodesics are investigated. We have shown that, there are no stable circular orbits for photons, however stable and unstable second-kind orbits exist for the massive particle. An exact analytical solution for the innermost stable circular orbits (ISCO) has been obtained. It has been shown that the radius of the ISCO shrinks due to the presence of the em field.