Related papers: Gluing different gravitational models: $f(R)$ case
This thesis aims at improving our understanding of the strong-field regime of gravity, where deviations from General Relativity (GR) are expected to be found on theoretical grounds. In particular, we have been concerned with the formulation…
We establish a general gluing theorem for constant mean curvature solutions of the vacuum Einstein constraint equations. This allows one to take connected sums of solutions or to glue a handle (wormhole) onto any given solution. Away from…
Metric $f(R)$ gravity theories are conformally equivalent to models of quintessence in which matter is coupled to dark energy. We derive a condition for stable tracker solution for metric $f(R)$ gravity in the Einstein frame. We find that…
Classical equivalence between Jordan's and Einstein's frame counterparts of F(R) theory of gravity has recently been questioned, since the two produce different Noether symmetries, which couldn't be translated back and forth using…
We establish a well-posedness theory for the f(R) theory of modified gravity, which is a generalization of Einstein's theory of gravitation. The scalar curvature R of the spacetime, which arises in the integrand of the Einstein-Hilbert…
Gravitational collapse is still poorly understood in the context of $f(R)$ theories of gravity, since the Oppenheimer-Snyder model is incompatible with their junction conditions. In this work, we will present a systematic approach to the…
We show, considering a specific f(R)-gravity model, that the Jordan frame and the Einstein frame are physically non-equivalent, although they are connected by a conformal transformation which yields a mathematical equivalence. Since all the…
In this work we derive the junction conditions for the matching between two spacetimes at a separation hypersurface in the perfect-fluid version of $f\left(R,T\right)$ gravity, not only in the usual geometrical representation but also in a…
This thesis investigates a toy model for inflation in a class of modified theories of gravity in the metric formalism. Instead of the standard procedure -- assuming a non-linear Lagrangian $f(R)$ in the Jordan frame -- we start from a…
The generalized $f(R)$ gravity with curvature-matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal spacelike Killing vector field of 5D spacetime, and it can be reduced to the 4D…
Einstein's General Relativity (GR) is possibly one of the greatest intellectual achievements ever conceived by the human mind. In fact, over the last century, GR has proven to be an extremely successful theory, with a well established…
The $f(R)$ gravity and scalar-tensor theory are known to be equivalent at the classical level. We study if this equivalence is valid at the quantum level. There are two descriptions of the scalar-tensor theory in the Jordan and Einstein…
Modified $f(R)$ theories of gravity have been investigated for quite a long time in the literature as a possible explanation for the inflationary period of the universe. The correspondence to General Relativity with an extra scalar field…
The accelerated expansion of the universe demands presence of an exotic matter, namely the dark energy. Though the cosmological constant fits this role very well, a scalar field minimally coupled to gravity, or quintessence, can also be…
We study imbedded hypersurfaces in spacetime whose causal character is allowed to change from point to point. Inherited geometrical structures on these hypersurfaces are defined by two methods: first, the standard rigged connection induced…
The junction conditions for the most general gravitational theory with a Lagrangian containing terms quadratic in the curvature are derived. We include the cases with a possible concentration of matter on the joining hypersurface -termed as…
In this paper we present the techniques for computing cosmological bounces in polynomial $f(R)$ theories, whose order is more than two, for spatially flat FLRW spacetime. In these cases the conformally connected Einstein frame shows up…
We examine the conformal equivalence between the $f(R)$ gravity and the interacting dark sector model. We review the well-known result that the conformal transformation physically corresponds to the mass dilation which marks the strength of…
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is…
Global properties of vacuum static, spherically symmetric configurations are studied in a general class of scalar-tensor theories (STT) of gravity in various dimensions. The conformal mapping between the Jordan and Einstein frames is used…