Related papers: The Inverse Variational Problem for Autoparallels
The inverse problem for electromagnetic field produced by arbitrary altered charge distribution in dipole approximation is solved. The charge distribution is represented by its dipole moment. It is assumed that the spectral properties of…
Teleparallel gravity theories employ a tetrad and a Lorentz spin connection as independent variables in their covariant formulation. In order to solve their field equations, it is helpful to search for solutions which exhibit certain…
We continue our study in 4-dimension to derive non-charged and charged (Anti)-de Sitter black hole solutions in conformal teleparallel equivalent of general relativity. The non-charged and charged equations of motion are applied to a…
We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results…
Although equivalent to general relativity, teleparallel gravity is conceptually speaking a completely different theory. In this theory, the gravitational field is described by torsion, not by curvature. By working in this context, a new…
A relativistic theory constructed on Riemann-Cartan manifold with a derived totally antisymmetric torsion is proposed. It follows the coincidence of the autoparallel curve and metric geodesic. The totally antisymmetric torsion naturally…
We study global scale invariance along with the unimodular gravity in the vacuum. The global scale invariant gravitational action which follows the unimodular general coordinate transformations is considered without invoking any scalar…
Although the cosmological perturbations with inverse-volume corrections from loop quantum cosmology have been studied using the anomaly-free algebra approach in much of the literature, there still remains an important issue that some…
We study linear perturbations around a static and spherically symmetric black hole solution in spatially covariant gravity with just two tensorial degrees of freedom. In this theory, gravity modification is characterized by a single…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
Teleparallel gravity and its popular generalization $f(T)$ gravity can be formulated as fully invariant (under both coordinate transformations and local Lorentz transformations) theories of gravity. Several misconceptions about teleparallel…
This manuscript is devoted to introduce a gauge theory of the Lorentz Group based on the ambiguity emerging in dealing with isometric diffeo-morphism-induced Lorentz transformations. The behaviors under local transformations of fermion…
Axially symmetric spacetimes play an important role in the relativistic description of rotating astrophysical objects like black holes, stars, etc. In gravitational theories that venture beyond the usual Riemannian geometry by allowing…
This study examines the formulation of a singularity theorem for timelike curves including torsion, and establishes the foundational framework necessary for its derivation. We begin by deriving the relative acceleration for an arbitrary…
We highlight the fact that the lack of scale invariance in the gravitational field equations of General Relativity results from the underlying assumption that the appropriate scale for the gravitational force should be linked to the atomic…
Time reversal symmetry is studied in a space with noncommutativity of coordinates and noncommutativity of momenta of canonical type. The circular motion is examined as an apparent example of time reversal symmetry breaking in the space. On…
We study the nonminimally coupled complex scalar field within the framework of teleparallel gravity. Coupling of the field nonminimally to the torsion scalar destroys the Lorentz invariance of the theory in the sense that the resulting…
We investigate static, spherically symmetric solutions in gravitational theories which have limited curvature invariants, aiming to remove the singularity in the Schwarzschild space-time. We find that if we only limit the Gauss-Bonnet term…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
We show that scale invariance provides a solution to the fine tuning problem of the cosmological constant. We construct a generalization of the standard model of particle physics which displays exact quantum scale invariance. The matter…