Related papers: Equivalent Gravities and Equivalence Principle: Fo…
An outstanding open issue in our quest for physics beyond Einstein is the unification of general relativity (GR) and quantum physics. Loop quantum gravity (LQG) is a leading approach toward this goal. At its heart is the central lesson of…
Emergent gravity views spacetime as an entity emergent from a more complete theory of interacting fundamental constituents valid at much finer resolution or higher energies, usually assumed to be above the Planck energy. In this view…
General Relativity (GR) is not the only way gravity can be geometrised. Instead of curvature, the Teleparallel Theory attributes gravity to torsion $T$, which is related to the antysimmetric part of connection, and the Symmetric…
In this work, we present a review of Energy-Momentum Squared Gravity (EMSG) -- more specifically, $f(R,T_{\mu\nu}T^{\mu\nu})$ gravity, where $R$ represents the Ricci scalar and $T_{\mu\nu}$ denotes the energy-momentum tensor. The inclusion…
Starting from the origin of Einstein general relativity (GR) the request of Mach on the theory's structure has been the core of the foundational debate. That problem is strictly connected with the nature of the mass-energy equivalence. It…
We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime…
It was generally believed that, in general relativity, the fundamental laws of nature should be invariant or covariant under a general coordinate transformation. In general relativity, the equivalence principle tells us the existence of a…
We present a novel derivation of the spacetime metric generated by matter, without invoking Einstein's field equations. For static sources, the metric arises from a relativistic formulation of D'Alembert's principle, where the inertial…
Despite the fact that General Relativity (GR) has been very successful, many alternative theories of gravity have attracted the attention of a significant number of theoretical physicists. Among these theories, we have theories with…
The discovery of the accelerated expansion of the universe highlighted General Relativity's inability to naturally account for dark energy without invoking a finely tuned cosmological constant. In response, a wide range of alternative…
Teleparallel theories of gravity are described in terms of the tetrad of a metric and a flat connection with torsion. In this paper, we study spherical symmetry in a modified teleparallel theory of gravity which is based on an arbitrary…
General Relativity (GR) is a phenomenologically successful theory that rests on firm foundations, but has not been tested on cosmological scales. The advent of dark energy (and possibly even the requirement of cold dark matter), has…
This paper brings a methodological character where we present a comprehensive formalism for constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR) and Symmetric Teleparallel Equivalent of General…
According to the teleparallel equivalent of general relativity, curvature and torsion are two equivalent ways of describing the same gravitational field. Despite equivalent, however, they act differently: whereas curvature yields a…
There is a set of first-order differential equations for the curvature tensor in general relativity (the curvature equations or CEs for short) that are strikingly similar to the Maxwell equations of electrodynamics. This paper considers…
Teleparallel gravity can be seen as a gauge theory for the translation group. As such, its fundamental field is neither the tetrad nor the metric, but a gauge potential assuming values in the Lie algebra of the translation group. This gauge…
The Gauss-Bonnet topological scalar is presented in metric-teleparallel formalism as well as in the symmetric and general teleparallel formulations. In all of the aforementioned frameworks, the full expressions are provided explicitly in…
We first investigate the form the General Relativity Theory would have taken had the gravitational mass and the inertial mass of material objects been different. We then extend this analysis to electromagnetism and postulate an equivalence…
The teleparallel formulation of gravity theories reveals close structural analogies to electrodynamics, which are more hidden in their usual formulation in terms of the curvature of spacetime. We show how every locally Lorentz invariant…
f(T) gravity is a generalization of the teleparallel equivalent of general relativity (TEGR), where T is the torsion scalar made up of the Weitzenb\"{o}ck connection. This connection describes a spacetime with zero curvature but with…