Narrow Results

We study null bulk geodesic motion in the brane world cosmology in the RS2 scenario and in the static universe in the bulk of the charged topological AdS black hole. We obtain equations describing the null bulk geodesic motion as observed in one lower dimension. We find that the null geodesic motion in the bulk of the brane world cosmology in the RS2 scenario is observed to be under the additional influence of extra non-gravitational force by the observer on the three-brane, if the brane universe does not possess the Z₂ symmetry. As for the null geodesic motion in the static universe in the bulk of the charged AdS black hole, the extra force is realized even when the brane universe has the Z₂ symmetry.

A natural way to obtain quintessence, i.e. negative pressure contributions in cosmological dynamics and then accelerated behavior of the Hubble fluid, is to take into account a torsion fluid whose effects become relevant at large scale. We investigate a model where a totally antisymmetric torsion field is taken into account and discuss the conditions to obtain quintessence. We obtain exact solutions where dust dominated Friedmann behavior is recovered as soon as torsion effects are not relevant.

We show that any analytic f(R)-gravity model, in the metric approach, presents a weak field limit where the standard Newtonian potential is corrected by a Yukawa-like term. This general result has never been pointed out but often derived for some particular theories. This means that only f(R) = R allows to recover the standard Newton potential while this is not the case for other relativistic theories of gravity. Some considerations on the physical consequences of such a general solution are addressed.

Some quantum-cosmic scaling relations indicate that the MOND acceleration parameter a₀ could be a fundamental quantity ruling the self-gravitating structures, ranging from stars and globular clusters up to superclusters of galaxies and the whole observed universe. We discuss such coincidence relations starting from the Dirac quantization condition ruling the masses of primordial black holes.

We linearize the field equations for higher order theories of gravity that contain scalar invariants other than the Ricci scalar. We find that besides a massless spin-2 field (the standard graviton), the theory contains also spin-0 and spin-2 massive modes with the latter being, in general, ghost modes. The rate at which such particles would emit gravitational Cherenkov radiation is calculated for some interesting physical cases.

In this paper we suggest an approach to analyze the motion of a test particle in the spacetime of a global monopole within a f(R)-like modified gravity. The field equations are written in a simplified form in terms of . Since we are dealing with a spherically symmetric metric, we express F(R) as a function of the radial coordinate only, e.g., . So, the choice of a specific form for f(R) will be equivalent to adopt an Ansatz for . By choosing an explicit functional form for , we obtain the weak field solutions for the metric tensor also compute the time-like geodesics and analyze the motion of a massive test particle. An interesting feature is an emerging attractive force exerted by the monopole on the particle.

The semiclassical effects of anti-evaporating black holes can be discussed in the framework of f(R) gravity. In particular, the Bousso–Hawking–Nojiri–Odinstov anti-evaporation instability of degenerate Schwarzschild–de Sitter black holes (the so-called Nariai spacetime) leads to a dynamical increasing of black hole horizon in f(R) gravity. This phenomenon causes the following transition: emitting marginally trapped surfaces (TS) become space-like surfaces before the effective Bekenstein–Hawking emission time. As a consequence, Bousso–Hawking thermal radiation cannot be emitted in an anti-evaporating Nariai black hole. Possible implications in cosmology and black hole physics are also discussed.

The extended Einstein–Maxwell-aether-axion model describes internal interactions inside the system, which contains gravitational, electromagnetic fields, the dynamic unit vector field describing the velocity of an aether, and the pseudoscalar field associated with the axionic dark matter. The specific feature of this model is that the axion field controls the dynamics of the aether through the guiding functions incorporated into Jacobson’s constitutive tensor. Depending on the state of the axion field, these guiding functions can control and switch on or switch off the influence of acceleration, shear, vorticity and expansion of the aether flow on the state of physical system as a whole. We obtain new exact solutions, which possess the pp-wave symmetry, and indicate them by the term pp-wave aether modes in contrast to the pure pp-waves, which cannot propagate in this field conglomerate. These exact solutions describe a specific dynamic state of the pseudoscalar field, which corresponds to one of the minima of the axion potential and switches off the influence of shear and expansion of the aether flow; the model does not impose restrictions on Jacobson’s coupling constants and on the axion mass. Properties of these new exact solutions are discussed.

In this paper, we find the cosmological solutions of the massive conformal gravity field equations in the presence of matter fields. In particular, we show that the solution of negative curvature is in good agreement with the late universe.

The neutral time-like particle’s bound orbits around modified Hayward black holes have been investigated. We find that both in the marginally bound orbits (MBO) and the innermost stable circular orbits (ISCO), the test particle’s radius and its angular momentum are all more sensitive to one of the parameters $\beta$. Especially, modified Hayward black holes with $\beta =10$ could mimic the same ISCO radius around the Kerr black hole with the spin parameter up to $a/M\approx 0.99$. Small $\beta$ could mimic the ISCO of small-spinning test particles around Schwarzschild black holes. Meanwhile, rational (periodic) orbits around modified Hayward black holes have also been studied. The epicyclic frequencies of the quasi-circular motion around modified Hayward black holes are calculated and discussed with respect to the observed Quasi-periodic oscillations (QPOs) frequencies. Our results show that rational orbits around modified Hayward black holes have different values of the energy from the ones of Schwarzschild black holes. The epicyclic frequencies in modified Hayward black holes have different frequencies from Schwarzschild and Kerr ones. These might provide hints for distinguishing modified Hayward black holes from Schwarzschild and Kerr ones by using the dynamics of time-like particles around the strong gravitational field.

We find the linearized gravitational field of a static spherically symmetric mass distribution in massive conformal gravity and test it with some solar system experiments. The result is that the theory agrees with the general relativistic observations in the solar system for a determined lower bound on the graviton mass.

The generalized uncertainty principle provides a promising phenomenological approach to reconciling the fundamentals of general relativity with quantum mechanics. As a result, noncommutativity, measurement uncertainty, and the fundamental theory of quantum mechanics are subject to finite gravitational fields. The generalized uncertainty principle (RGUP) on curved spacetime allows for the imposition of quantum-induced elements on general relativity (GR) in four dimensions. In the relativistic regimes, the determination of a test particle’s spacetime coordinates, $〈x^{\mu }〉$, becomes uncertain. There exists a specific range of coordinates where the accessibility to $〈{(x^{\mu })}^2〉$ is notably limited. Consequently, the spacetime coordinates lack both smoothness and continuity. The quantum-mechanical calculations of the spacetime coordinates are directly linked to their measurement through the expectation value $〈x^{\mu }〉$. This expectation value is dependent on $〈{(x^{\mu })}^2〉$, which is itself limited by a minimum measurable length $\mathrm{\Delta }{x}_{min}^2$. A crucial finding presented in this script is the existence of a lower bound for the Hamiltonian, which implies the stability of the quantum nature of spacetime. The direct correlation between $\mathrm{\Delta }{x}_{min}$ and $\sqrt{-{〈g〉}^{\mu \nu }}$ is a significant discovery, suggesting a proportional relationship. The conjecture is made that the primary metric g carries all essential information regarding spacetime curvature and serves a role akin to the Jacobian determinant in general relativity. Moreover, the linear relationship between $\mathrm{\Delta }{x}_{min}$ and the Planck length ${\ell }_p$ is established with a proportionality factor of $\sqrt{-{〈g〉}^{\mu \nu }}\sqrt{{\beta }_2}$, where ${\beta }_2$ denotes the RGUP parameter. The discretization of spacetime coordinates results in the discontinuity of the test particle’s wavefunction $\psi (x,t)$, leading to an unrealistic $\mathrm{\Delta }p$. It is also noted that the lower limit of $〈{(p^{\mu })}^2〉$ is directly proportional to the fundamental tensor.

We discuss semiclassical Nariai black holes in the framework of f(T)-gravity. For a diagonal choice of tetrads, stable Nariai metrics can be found, emitting Bekenstein–Hawking radiation in semiclassical limit. However, for a nondiagonal choice of tetrads, evaporation and anti-evaporation instabilities are turned on. In turn, this causes a backreaction effect suppressing the Bekenstein–Hawking radiation. In particular, evaporation instabilities produce a new radiation — different by Bekenstein–Hawking emission — nonviolating unitarity in particle physics sector.

The Einstein–Cartan–Kibble–Sciama (ECKS) theory of gravity naturally extends Einstein’s general relativity (GR) to include intrinsic angular momentum (spin) of matter. The main feature of this theory consists of an algebraic relation between space–time torsion and spin of matter, which indeed deprives the torsion of its dynamical content. The Lagrangian of ECKS gravity is proportional to the Ricci curvature scalar constructed out of a general affine connection so that owing to the influence of matter energy–momentum and spin, curvature and torsion are produced and interact only through the space–time metric. In the absence of spin, the space–time torsion vanishes and the theory reduces to GR. It is however possible to have torsion propagation in vacuum by resorting to a model endowed with a nonminimal coupling between curvature and torsion. In the present work we try to investigate possible effects of the higher order terms that can be constructed from space–time curvature and torsion, as the two basic constituents of Riemann–Cartan geometry. We consider Lagrangians that include fourth-order scalar invariants from curvature and torsion and then investigate the resulting field equations. The solutions that we find show that there could exist, even in vacuum, nontrivial static space–times that admit both black holes and naked singularities.

In this work, we propose a model of noncommutative cosmology through the deformation of minisuperspace. We focus on an exponentially potential with a homogeneous scalar field minimally coupled to gravity in the spatially flat universe. To process, we use a particular case of noncommutativity by making a deformation of space coordinates only. Then, we compare results in both the commutative model and the noncommutative one.

Predictions of the CMB spectrum from a bimetric gravity theory (BGT)¹ are presented. The initial inflationary period in BGT is driven by a vanishingly small speed of gravitational waves v_g in the very early universe. This initial inflationary period is insensitive to the choice of scalar field potential and initial values of the scalar field. After this initial period of inflation, v_g will increase rapidly and the effects of a potential will become important. We show that a quadratic potential introduced into BGT yields an approximately flat spectrum with inflation parameters: n_s=0.98, n_t=-0.027, α_s=-3.2×10^-4 and α_t=-5.0×10^-4, with r ≥ 0.014.

Working in the Lagrangian framework, we develop a geometric theory in vacuum with propagating torsion; the antisymmetric and trace parts of the torsion tensor, considered as derived from local potential fields, are taken and, using the minimal action principle, their field equations are calculated. Actually these will show themselves to be just equations for propagating waves giving torsion a behavior similar to that of metric which, as known, propagates through gravitational waves. Then we establish a principle of minimal substitution to derive test particles equation of motion, obtaining, as result, that they move along autoparallels. We then calculate the analogous of the geodesic deviation for these trajectories and analyze their behavior in the nonrelativistic limit, showing that the torsion trace potential ϕ has a phenomenology which is indistinguishable from that of the gravitational newtonian field; in this way we also give a reason for why there have never been evidence for it.

We analyzed the Rotation Curves (RCs) of two crucial objects, the dwarf galaxy Orion and the low luminosity Spiral NGC 3198, in the framework of Rⁿ gravity. We surprisingly found that the no dark matter (DM) power-law F(R) case fits them well, performing much better than LCDM halo models. The level of this unexpected success can be a boost for Rⁿ gravity.

We study spherically symmetric perturbations determined by alternative theories of gravity to the gravitational field of a central mass in General Relativity (GR). In particular, we focus on perturbations in the form of power laws and calculate their effect on the secular variations of the orbital elements of a Keplerian orbit. We show that, to lowest approximation order, only the argument of pericenter and mean anomaly undergo secular variations; furthermore, we calculate the variation of the orbital period. We give analytic expressions for these variations which can be used to constrain the impact of alternative theories of gravity.

Inflation and dark energy are two of the most relevant aspects of modern cosmology. These different epochs provide the universe is passing through accelerated phases soon after the Big–Bang and at present stage of its evolution. In this review paper, we discuss that both eras can be, in principle, described by a geometric picture, under the standard of f(R) gravity. We give the fundamental physics motivations and outline the main ingredients of f(R) inflation, quintessence and cosmography. This wants to be a quick summary of f(R) paradigm without claiming of completeness.