Narrow Results

We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the presence of dark matter, is the result of the dynamical evolution of particles in higher dimensional spacetimes. Hence, dark matter may be a direct consequence of the presence of an extra force, generated by the presence of extra dimensions, which modifies the dynamic law of motion, but does not change the intrinsic properties of the particles, like, for example, the mass (inertia). We discuss in some detail several possible particular forms for the extra force, and the acceleration law of the particles is derived. Therefore, the constancy of the galactic rotation curves may be considered as an empirical evidence for the existence of the extra dimensions.

In this paper, we construct some new classes of topological black hole solutions in the context of mimetic gravity and investigate their properties. We study the uncharged and charged black holes, separately. We find the following novel results: (i) In the absence of a potential for the mimetic field, black hole solutions can address the flat rotation curves of spiral galaxies and alleviate the dark matter problem without invoking particle dark matter. Thus, mimetic gravity can provide a theoretical background for understanding flat galactic rotation curves through modifying Schwarzschild space–time. (ii) We also investigate the casual structure and physical properties of the solutions. We observe that in the absence of a potential, our solutions are not asymptotically flat, while in the presence of a negative constant potential for the mimetic field, the solutions are asymptotically anti-de Sitter (AdS). (iii) Finally, we explore the motion of massless and massive particles and give a list of the types of orbits. We study the differences of geodesic motion in the Einstein gravity and in mimetic gravity. In contrast to the Einstein gravity, massive particles always move on bound orbits and cannot escape the black hole in mimetic gravity. Furthermore, we find stable bound orbits for massless particles.

Depending on five parameters, rotating counterparts of Einstein–Maxwell–dilaton black holes are derived. We discuss their physical and geometric properties and investigate their null and timelike geodesics including circular orbits. The Lense–Thirring effect is considered.

The geodesic motion of a massive test particle in a $G_2$ massless scalar field universe is investigated. The time evolution of the peculiar velocity is connected to the values of the cosmological parameters, and it is quantified how the spacetime shearing effects affect the deviations from the asymptotic value of comoving matter flow at late epochs. On the other hand, it is shown that the energy scale of the cosmic fluid does not affect the evolution of the peculiar velocity. The existence of a turning point in the motion of the astronomical object is identified. The potential astrophysical relevance of this study in the modeling of cosmic filaments and Large Quasar Groups is briefly discussed.

We provide a detailed and rigorous proof of (a generalized version of) the Ehlers–Geroch theorem on geodesic motion in metric theories of gravity: we assume that (M, g) is a spacetime satisfying an averaged form of the dominant energy condition and some further technical assumptions indicated in the bulk of this paper. Then, a small body which is allowed to deform the original spacetime metric g moves, nonetheless, along a geodesic of (M, g).

The equivalence principle is considered in the framework of metric-affine gravity. We show that it naturally emerges as a Noether symmetry starting from a general non-metric theory. In particular, we discuss the Einstein equivalence principle and the strong equivalence principle showing their relations with the non-metricity tensor. Possible violations are also discussed pointing out the role of non-metricity in this debate.

The presence of matter in general relativity can cause spacetime to curve. This paper investigates the spacetime properties of the Einstein–Maxwell–Yang–Mills (EMYM) black hole by discussing the geodesic motion of neutral and charged particles. By studying the Lagrangian of these particles, equations of motion and effective potential are obtained in the asymptotic flat and (A)dS spacetimes. Moreover, for the motion of a neutral particle, it is found that there exist stable elliptic/hyperbolic orbits and unstable orbits with different energies by discussing the effective potential and the phase-plane analysis. However, for the motion of a charged particle, there exists an equilibrium point that separates these orbits. In addition, the effects of the system parameters on the potential are analyzed, including the masses of the black hole and charged particles, charges, the cosmological constant, and the strength of the external magnetic field.

The trajectory of any accelerated body in flat Minkowski background geometry η_μν can be represented as a geodesic motion in another metric which depends only on g_μν and on the motion of the body. As an example, we apply this method to the Gordon-type metrics.