International Journal of Modern Physics D

We discuss some main aspects of theories of gravity containing nonlocal terms in view of cosmological applications. In particular, we consider various extensions of general relativity based on geometrical invariants as $f(R,{\square }^{-1}R)$, $f({𝒢},{\square }^{-1}{𝒢})$ and $f(T,{\square }^{-1}T)$ gravity where $R$ is the Ricci curvature scalar, ${𝒢}$ is the Gauss–Bonnet topological invariant, $T$ the torsion scalar and the operator ${\square }^{-1}$ gives rise to nonlocality. After selecting their functional form by using Noether symmetries, we find out exact solutions in a cosmological background. It is possible to reduce the dynamics of selected models and to find analytic solutions for the equations of motion. As a general feature of the approach, it is possible to address the accelerated expansion of the Hubble flow at various epochs, in particular the dark energy issues, by taking into account nonlocality corrections to the gravitational Lagrangian. On the other hand, it is possible to search for gravitational nonlocal effects also at astrophysical scales. In this perspective, we search for symmetries of $f(R,{\square }^{-1}R)$ gravity also in a spherically symmetric background and constrain the free parameters, Specifically, by taking into account the S2 star orbiting around the Galactic Center SgrA${}^{\ast }$, it is possible to study how nonlocality affects stellar orbits around such a massive self-gravitating object.

We experience a golden era in testing and exploring relativistic gravity. Whether it is results from gravitational-wave detectors, satellite or lab experiments, radio astronomy plays an important complementary role. Here, one can mention the cosmic microwave background, black hole imaging and, obviously, binary pulsars. This talk will concentrate on the latter and new results from studies of strongly self-gravitating bodies with unrivalled precision. This presentation compares the results to other methods, discusses implications for other areas of relativistic astrophysics and will give an outlook of what we can expect from new instruments in the near future.

We study the optical appearance of a thin accretion disk around a Schwarzschild black hole pierced by a cosmic string with a semi-analytic method of Luminet [Astron. Astrophys. 75 (1979) 228]. Direct and secondary images with different parameters observed by a distant observer are plotted. The cosmic string parameter $s$ can modify the shape and size of the thin disk image. We calculate and plot the distribution of both redshift and observed flux as seen by distant observers at different inclination angles. Those distributions are dependent on the inclination angle of the observer and cosmic string parameter $s$.

Jeans instability is analyzed in an expanding universe within the framework of BGK model of the Boltzmann equation and Poisson equations. The background is characterized by a comoving Maxwellian distribution function and a spacetime Newtonian gravitational potential which satisfy the BGK model of the Boltzmann–Poisson equations without the necessity to invoke “Jeans swindle.” The perturbations of the distribution function and Newtonian gravitational potentials from their background states are represented by plane waves of small amplitudes and a differential equation for the density contrast is determined. The density contrast differential equation was solved numerically and it is shown: (i) Jeans instability is characterized by perturbation wavelengths larger than Jeans wavelength where the density contrast grows with time. The growth of the density contrast is less accentuated for the case where the particle collisions are considered due to an energy dissipation; (ii) for perturbation wavelengths smaller than Jeans wavelength the density contrast has an oscillatory behavior in time and the oscillations for the case where the collisions are taken into account fade away in time due to the energy dissipation.

The main goal of this paper is to present the Lemaître–Tolman–Bondi (LTB) spacetime for the radiating case by extending the study of [L. Herrera, A. Di Prisco, J. Ospino and J. Carot, Phys. Rev. D 82 (2010) 024021] in $f(R,T)$ theory, where $R$ is the Ricci scalar and $T$ is the energy–momentum tensor trace. We will start with some fundamental equations, such as the kinematical variables, mass function introduced by Misner and Sharp, the Weyl tensor under the influence of the $f(R,T)$ modified Bianchi identities. We have also considered the evolution of the modified constraint equation. Later on, we have analyzed LTB in terms of modified structure scalars emerging from the orthogonal splitting of the Riemann tensor, and the transport equation in $f(R,T)$ gravity theory. We will also discuss a case in order to generalize LTB metric.

The motive of this paper is to investigate the evolution of dissipative axially symmetry collapsing fluid in the presence of dark sources. For this purpose, we use the modified Gauss–Bonnet gravity as an exotic energy candidate. We formulate the dynamical variables and investigate the impacts of dark sources upon the heat dissipation and pressure anisotropy. We find scalar functions through orthogonal decomposition of Riemann tensor. The physical behavior of these scalars has been examined for matter as well as dark source configurations. Moreover, we develop a set of EEs related to the evolution of dynamical variables, heat transport equation, Weyl tensor and super-Poynting vector. These equations discuss collapse features like thermodynamics, density inhomogeneity and gravitational radiations in presences of exotic terms. It has been shown that the dark source terms have an effect on the thermodynamics of the system, evolution of kinematical variables and density inhomogeneity. The exotic terms can generate repulsive radiations which can induce cosmic expansion. Finally, the physical significance of modified Gauss–Bonnet gravity is explored in association to the stellar 4U1820-30.

We present a flat emergent universe model in modified Gauss–Bonnet gravity in four dimensions. The emergent universe model is free from a big-bang singularity and also describes the observed universe fairly well. It is assumed that the present universe emerged from a static Einstein universe phase that exists in the infinite past. To obtain the flat emergent universe model, we reconstruct mimetic modified $f(G)$-gravity ($G$ representing Gauss–Bonnet terms). The functional form of $f(G)$-gravity is determined with or without matter, and can accommodate the early inflation and late accelerating phases satisfactorily. In contrast, in Einstein’s general theory of relativity, a flat emergent universe was obtained within the modified matter sector.

This paper deals with formulation of analytic solution for greybody factor taking a rotating black hole (BH) in the vicinity of perfect fluid dark matter. To this end, the Klein–Gordon equation is transformed into the standard Schrödinger equation in order to portray the behavior of effective potential. We compute the asymptotic solutions in two different regimes, namely, BH and far field horizons under the influence of perfect fluid dark matter. The derived solutions are smoothly matched in an intermediate region for the sake of their viability. It is observed that a large amount of radiations approach infinity by decreasing intensity of dark matter in the surrounding of BH and hence the greybody factor increases. We also analyze the impact of thermal fluctuations on the considered gravitational background. In this context, the corrected entropy near the equilibrium state is computed which further modifies other thermodynamic potentials. We conclude that the larger BHs become more stable taking positive ranges of specific heat in the vicinity of quantum corrections.

General relativistic effects around massive astrophysical objects can be captured using a test gyro orbiting the object in a circular geodesic. This paper discusses how the tidal field due to a companion object affects the spin precession frequency and orbital angular velocity of a spinning gyro orbiting around a compact astrophysical object. The precession frequency is studied in a region of space around the central object using a perturbative approach. The central object is either a neutron star or a white dwarf in this study. The test gyro is any planetary or asteroid-like object orbiting a neutron star or a white dwarf. Moreover, the companion object that causes the tidal field can be a neutron star, white dwarf or a stellar black hole. It is seen that the tidal effect significantly affects the spacetime around the central object, which affects the gyro precession frequency and the orbital angular velocity. Slow rotation approximation has been considered for the central object, which creates negligible deformation. The change in the gyro’s precession frequency and the orbital angular velocity due to the tidal field increases with an increase in the companion object’s mass and decreases as the separation between the central star and the companion star increases. The tidal effect also varies with the stiffness of the equation of state of matter describing the host star. The lower the compactness of the host star, the greater is the tidal response; thus the greater is the change in the gyro’s precession and angular velocity of the geodesic.

One of the most favorable extensions of General Relativity is the $f(R)$ gravity. $f(R)$ gravity in Palatini formalism can be a realistic alternative to the dark energy problem. In this work, we study a recently introduced dark energy $f(R)$ gravity model along with two other models in cosmological perspectives under the Palatini formalism. First, we study the cosmic expansion history of these models with the help of the important cosmographic parameters, such as the Hubble parameter, luminosity distance, effective equation of state, etc. This study shows that the new model behaves similarly with the other two models as well as with the $\mathrm{\Lambda }$CDM model in some respects in the early or very early phases of the universe. It could predict the present accelerated expansion of the universe somewhat differently from the other models with a peculiar future history of the universe. Within a constrained range of parameters all models show a good agreement with the Union2.1 luminosity distance data. However, the new model shows a quite satisfactory agreement in the whole range of its allowed parameters than that of the other two models. We also obtain cosmological constraints on these models from the observed Hubble data. Further, models have been tested by using $Om(z)$ test and statefinder diagnostics. These diagnostics especially the statefinder diagnostic shows that the evolutionary differences between these models are distinct. The evolutionary trajectories of the new model are completely different from the other two models we have considered.