$$\varLambda $$CDM suitably embedded in f(R) with a non-minimal coupling to matter

In this work, we further study a metric modified theory of gravity which contains a non-minimal coupling to matter, more precisely, we assume two functions of the scalar curvature, $$f_1$$ f 1 and $$f_2$$ f 2 , where the first one generalises the Hilbert–Einstein action, while the second couples to the matter Lagrangian. On the one hand, assuming a $$\varLambda $$ Λ CDM background, we calculate analytical solutions for the functions $$f_1$$ f 1 and $$f_2$$ f 2 . We consider two setups: on the first one, we fix $$f_2$$ f 2 and compute $$f_1$$ f 1 and on the second one, we fix $$f_1$$ f 1 and compute $$f_2$$ f 2 . Moreover, we do the analysis for two different energy density contents, a matter dominated universe and a general perfect fluid with a constant equation of state fuelling the universe expansion. On the other hand, we complete our study by performing a cosmographic analysis for $$f_1$$ f 1 and $$f_2$$ f 2 . We conclude that the gravitational coupling to matter can drive the accelerated expansion of the universe.

Cosmological models with squared trace in modified gravity

In this work, we present a few simple cosmological models under the modified theory of gravity in the particular form of [Formula: see text], where [Formula: see text] is the Ricci Scalar and [Formula: see text] is the trace of the energy–momentum tensor. Two special cosmological models are studied with (i) hyperbolic scale factor and (ii) specific form of the Hubble parameter. The models are observed to predict relevant cosmological parameters closer to the observational values. Both the models reduce to overlap with the [Formula: see text]CDM model at late times. We have discussed some interesting results related to wormhole solutions as evolved from our model. The possible occurrence of Big Trip in wormholes for the models are also discussed.

Quasi-periodic oscillations around Kerr-MOG black holes

The study of the quasi-periodic oscillations (QPOs) of X-ray flux observed in the stellar-mass black hole (BH) binaries can provide a powerful tool for testing the phenomena occurring in strong gravity regime. We thus present and apply to three known microquasars the model of epicyclic oscillations of Keplerian discs orbiting rotating BHs governed by the modified theory of gravity (MOG). We show that the standard geodesic models of QPOs can explain the observationally fixed data from the three microquasars, GRO 1655-40, XTE 1550-564, and GRS 1915+105. We perform a successful fitting of the high frequency (HF) QPOs observed in these microquasars, under assumption of MOG BHs, for epicyclic resonance and its variants, relativistic precession and its variants, tidal disruption, as well as warped disc models and discuss the corresponding constraints of parameters of the model, which are the mass and spin and parameter $$\alpha $$α of the BH.

Gravitomagnetism in modified theory of gravity

We study the gravitomagnetism in the Scalar-Vector-Tensor theory or Moffat’s Modified theory of Gravity (MOG). We compute the gravitomagnetic field that a slow-moving mass distribution produces in its Newtonian regime. We report that the consistency between the MOG gravitomagnetic field and that predicted by the Einstein’s gravitational theory and measured by Gravity Probe B, LAGEOS and LAGEOS 2, and with a number of GRACE and Laser Lunar ranging measurements requires [Formula: see text].

Nonsingular Model of Magnetized Black Hole Based on Nonlinear Electrodynamics

We find solutions of a magnetically charged non-singular black hole in some modified theory of gravity coupled with nonlinear electrodynamics. The metric of a magnetized black hole is obtained which has one (an extreme horizon), two horizons, or no horizons (naked singularity). Corrections to the Reissner-Nordstrom solution are found as the radius approaches to infinity. The asymptotic of the Ricci and Kretschmann scalars are calculated showing the absence of singularities. We study the thermodynamics of black holes by calculating the Hawking temperature and the heat capacity. It is demonstrated that phase transitions take place and we show that black holes are thermodynamically stable at some range of parameters.

Modified theory of gravity and clustering of multi-component system of galaxies

In this paper, we analyze the clustering of galaxies using a modified theory of gravity, in which the field content of general relativity has been be increased. This increasing in the field content of general relativity changes the large distance behavior of the theory, and in weak field approximation, it will also modify the large distance behavior of Newtonian potential. So, we will analyzing the clustering of multi-component system of galaxies interacting through this modified Newtonian potential. We will obtain the partition function for this multi-component system, and study the thermodynamics of this system. So, we will analyze the effects of the large distance modification to the Newtonian potential on Helmholtz free energy, internal energy, entropy, pressure and chemical potential of this system. We obtain also the modified distribution function and the modified clustering parameter for this system, and hence observe the effect of large distance modification of Newtonian potential on clustering of galaxies.

Kerr Black Holes within a Modified Theory of Gravity

The Kerr black hole is studied within a modified theory of gravity, which adds the effects of vacuum fluctuations near a black hole. These vacuum fluctuations are treated as a dark energy. A parameter is introduced to account for these fluctuations. It is zero for the standard theory and acquires a maximal value, just before there would be no event horizon. The existence of an event horizon not only depends on the value of this parameter, but also on the spin of the black hole. In addition, we study the existence of a light-ring. We also elaborate on the relation of the appearance and vanishing of the event horizon and light-ring to phase transitions.

Five-dimensional spherical symmetric perfect fluid collapse in f(R, T) gravity

This paper contains the study of spherically symmetric perfect fluid collapse in the framework of f(R, T) modified theory of gravity using five-dimensional background. We consider the five-dimensional spherical symmetric metric as the interior region and a five-dimensional Schwarzschild metric as an exterior region. The Darmois junction conditions between exterior and interior regions are discussed. By taking the particular f(R, T) model, the corresponding field equations are evaluated for both marginally bound L(r) = 1 and non-marginally bound L(r) ≠ 1 cases. We find the gravitational mass of the collapsing system and discuss the apparent horizons and their time formation for different possible cases. Also, the cosmological and black hole horizons have been discussed. It has been concluded that the term involving λ plays a double role: it accelerates the collapse in the region where ρ0 < 4p0 and it slows down the collapsing of matter when ρ0 > 4p0. Further, it is noted that our results reduce to the results found by Sharif and Ahmad (J. Korean Phys. Soc. 52, 980 (2008). doi: 10.3938/jkps.52.980) in general relativity for λ = 0.