International Journal of Modern Physics D

The Kerr metric is considered in a synchronous frame of reference obtained by using proper time and initial conditions for particles that freely move along a certain set of trajectories as coordinates. Modifying these coordinates in a certain way (keeping their interpretation as initial values at large distances), we still have a synchronous frame and the direct analogue of the Lemaitre metric, the singularities of which are exhausted by the physical Kerr singularity (the singularity ring).

In the Ellis wormhole metrics, we study the characteristics of fluid dynamics and the properties of linear sound waves. By implying the energy–momentum equation and the continuity equation in the general relativistic manner, we examine the flow dynamics and solve the corresponding equations for a relatively simple case — radial flow. To study the linear sound waves, the equations governing the mentioned physical system are linearized and solved and interesting characteristic properties are found.

The expansion of both sides of Einstein’s field equations in the weak-field approximation, up to terms of order $1/c^4$ is derived. This new approach leads to an extended form of gravitomagnetism (GEM) properly named as Beyond Gravitomagnetism (BGEM). The metric of BGEM includes a quadratic term in the gravitoelectric potential n the time and also space metric functions in contrast with first post-Newtonian $1$PN approximation where the quadratic term appears only in the time metric function. This nonlinear term does not appear in conventional GEM, but is essential in achieving the exact value of Mercury’s perihelion advance as we explicitly show. The new BGEM metric is also applied to the classical problem of light deflection by the Sun, but the contribution of the new nonlinear terms produce higher-order terms in this problem and can be neglected, giving the correct result obtained already in the Lense–Thirring (GEM) approximation. The BGEM approximation also provides new terms that depend on the dynamics of the system, which may bring new insights into galactic and stellar physics.

The Fe-K$\alpha$ fluorescence lines are commonly observed in AGNs and X-ray binaries. The lines are believed to be originated from the reflection of the hard X-ray continuum near the inner-most region of the accretion disks of black holes. The geometry of the accretion disk is usually assumed to be infinitely thin, but this assumption is not appropriate when the accretion rate is moderately super-Eddington. With the increase of the accretion rate, the disk becomes thick, which will significantly affect the properties of the fluorescence lines. For instance, the polarized radiation is strongly depended on the geometry of the accretion disk. In this work, based on the lamp-post model, we study the polarization properties of the relativistic Fe-K$\alpha$ lines from thick disks in the framework of fully general relativity. We find that with the increase of the disk thickness, the polarization degree (PD) at the blue edge of the iron line increase significantly, and there appears a peak at the profile of the PD of the iron emission line, which at most is one order higher that of the line from the thin disk. Thus, the polarization properties of relativistic broad Fe-K$\alpha$ lines can be used to as a tool to diagnose the disk thickness.

In this paper, a semi-simple and Maxwell extension of the (anti) de Sitter algebra is constructed. Then, a gauge-invariant model has been presented by gauging the Maxwell semi-simple extension of the (anti) de Sitter algebra. We firstly construct a Stelle–West-like model action for five-dimensional spacetime in which the effects of spontaneous symmetry breaking have been taken into account. In doing so, we get an extended version of Einstein’s field equations. Next, we decompose the five-dimensional extended Lie algebra and establish a MacDowell–Mansouri-like action that contains the Einstein–Hilbert term, the cosmological term as well as new terms coming from Maxwell extension in four-dimensional spacetime where the torsion-free condition is assumed. Finally, we have shown that both models are equivalent for an appropriately chosen gauge condition.

In this paper, we carry a dynamical system analysis of a holographic dark energy model of a modified theory of gravity based on braneworld scenario. The infra-red cutoff of the holographic dark energy is considered to be the Hubble scale in a first approach and the Ricci scalar curvature scale in a second approach. We present a detailed analysis of the critical points, their stability and the late-time cosmological viability of the solutions in the phase space. For both holographic dark energy models, we investigate the case of a noninteracting braneworld and extend our analysis to the interacting case between dark energy and cold dark matter by considering some specific forms of interaction.

In this paper, we study a particular modified gravity Equation of State (EoS), the so-called Jaime–Jaber–Escamilla, that emerges from the first gravity modified action principle and can reproduce three cosmological viable $f(R)$ theories: the Starobinsky, Hu–Sawicki and Exponential models. This EoS is a suitable candidate to reproduce the dynamical dark energy behaviour already reconstructed by the current data sets. Based on the joint statistical analysis, we found that our results are still in good agreement (within $1\sigma$) with the $\mathrm{\Lambda }$CDM, while at perturbative level, we note that the matter power spectrum normalisation factor ${\sigma }_8$ shows an agreement with SDSS and SNeIa+IRAS at 1-$\sigma$ for the Starobinsky model and with SDSS-vec for the Hu–Sawicki and Exponential models. Furthermore, we found that for the $H_0$ values, Starobinsky and Hu–Sawicki show the least tension in comparison with PL18 TT. All these aspects cannot be observed directly from other alternatives theories, where an equation of state is difficult to compute analytically.

In this paper, we investigate the holographic inflation in the framework of two gravitational theories like $f(T)$ gravity, where $T$ corresponds to the torsion scalar and DGP braneworld model which is based on the idea that our four-dimensional FRW universe located on five-dimensional manifold. The modified infrared cutoff is used to explore all the inflationary parameters as slow-roll parameters $({𝜖}_1,{𝜖}_2,{𝜖}_3)$, number of $e$-folds $N$, scalar spectral index $n_s$, tensor-to-scalar ratio $r$ and running of the scalar spectral index ${\alpha }_s$. Also, we investigate the behavior of inflationary parameters $n_s-N,{\alpha }_s-N,r-N,{\alpha }_s-n_s$ and $r-n_s$ through graphical presentation. The behavior of these parameters shows the consistency with Planck data $2018$.