Related papers: Masking a singularity with k-essence fields in an …
The motto of this work is to generate a general formalism of $f(\bar{R}, L(X))-$gravity in the context of dark energy under the framework of the {\bf K-}essence emergent geometry with the Dirac-Born-Infeld (DBI) variety of action, where…
The equations of motion for matter fields are invariant under the shift of the matter lagrangian by a constant. Such a shift changes the energy momentum tensor of matter by T^a_b --> T^a_b +\rho \delta^a_b. In the conventional approach,…
In this paper we show how a gravitational field generated by a given energy-momentum distribution (for all realistic cases) can be represented by distinct geometrical structures (Lorentzian, teleparallel and non null nonmetricity…
Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This…
We investigate the possibility for \textit{k}-essence dynamics to reproduce the primary features of inflation in the early universe, generate dark matter subsequently, and finally account for the presently observed acceleration. We first…
We present an elastic constitutive model of gravity where we identify physical space with the mid-hypersurface of an elastic hyperplate called the "cosmic fabric" and spacetime with the fabric's world volume. Using a Lagrangian formulation,…
We argue that space-time properties are not absolute with respect to the used frame of reference as is to be expected according to ideas of relativity of space and time properties by Berkley - Leibnitz - Mach- Poincar\'{e}. From this point…
We consider an extended theory of gravity with Lagrangian $\mathcal{L} = f(R,{\bf T}^{(n)})$, with ${\bf T}^{(n)}$ being a $2n$-th order invariant made of contractions of the energy-momentum tensor. When $n=1$ this theory reduces to…
After recalling the differential geometry of non-metric connections in the formalism of differential forms, we introduce the idea of a Non-Metricity (NM) connection, whose connection $1$--forms coincides with the non-metricity $1$--forms…
Utilizing various gauges of the radial coordinate, we give a General Relativistic (GR) description of static spherically symmetric spacetimes with a massive point source and vacuum outside this singularity. We show that in GR there exists a…
There were problems encountered in extending the K-slicing of the Schwarzschild and Reissner-Nordstrom (RN) spacetimes [1, 2] to the extreme case, when charge equals mass (in gravitational units). The earlier procedure is here modified so…
Modified General Relativity (MGR) is the natural extension of General Relativity (GR). MGR explicitly uses the smooth regular line element vector field $(\bm{X},-\bm{X}) $, which exists in all Lorentzian spacetimes, to construct a…
Chaplygin gas and other k-essence models exhibit emergent geometry, with perturbations propagating on an acoustic metric disformally related to the Einstein-frame metric. For superluminal sound speed, we identify the disformal metric as the…
We present a phenomenological analysis of current observational constraints on classes of FLRW cosmological models in which the matter side of Einstein's equations includes, in addition to the canonical term, a term proportional to some…
We study cosmological perturbations in a universe with only one matter component described by a triplet of fields. Configuration of these fields is the same as for body coordinates of a solid, and they enter the matter Lagrangian only…
Within the framework of metric-affine gravity (MAG, metric and an independent linear connection constitute spacetime), we find, for a specific gravitational Lagrangian and by using {\it prolongation} techniques, a stationary axially…
A dynamical model for varying light velocity in cosmology is developed, based on the idea that there are two metrics in spacetime. One metric $g_{\mu\nu}$ describes the standard gravitational vacuum, and the other ${\hat g}_{\mu\nu}…
It is shown that the dynamical evolution of perturbations on a static spacetime is governed by a standard pulsation equation for the extrinsic curvature tensor. The centerpiece of the pulsation equation is a wave operator whose spatial part…
The $ \gamma $-spacetime metric is a static and axially symmetric vacuum solution of the Einstein equation. This spacetime represents a naked singularity and it has an extra parameter $ \gamma $ which signifies deviations from spherical…
We develop a Lagrangian formulation for gravity with matter where the gravitational couplings are universally treated as being field-dependent. The solutions for FLRW geometries and the associated time evolution of the Newton and…