Traversable wormhole solutions with non-exotic fluid in framework of f(Q) gravity

The presence of exotic matter for the existence of the wormhole geometry has been an unavoidable problem in GR. In recent studies, researchers have tried to deal with this issue using modified gravity theories where the WH geometry is explained by the extra curvature terms and NEC’s are not violated signifying the standard matter in the WH geometry. In this paper, we investigate the solutions of traversable wormholes with normal matter in the throat within the framework of symmetric teleparallel gravity [Formula: see text], where [Formula: see text] is the non-metricity scalar that defines the gravitational interaction. We analyze the wormhole geometries for three forms of function [Formula: see text]. First is the linear form [Formula: see text], second a nonlinear form [Formula: see text] and third one a more general quadratic form [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text] being the constants. For all the three cases, the shape function is taken as [Formula: see text] where [Formula: see text] is the throat radius. A special variable redshift function is considered for the discussion. All the energy conditions are then examined for the existence and stability of the wormhole geometry.

The Relation between General Relativity’s Metrics and Special Relativity’s Gravitational Scalar Generalized Potentials and Case Studies on the Schwarzschild Metric, Teleparallel Gravity, and Newtonian Potential

This paper shows that gravitational results of general relativity (GR) can be reached by using special relativity (SR) via a SR Lagrangian that derives from the corresponding GR time dilation and vice versa. It also presents a new SR gravitational central scalar generalized potential V=V(r,r.,ϕ.), where r is the distance from the center of gravity and r.,ϕ. are the radial and angular velocity, respectively. This is associated with the Schwarzschild GR time dilation from where a SR scalar generalized potential is obtained, which is exactly equivalent to the Schwarzschild metric. Thus, the Precession of Mercury’s Perihelion, the Gravitational Deflection of Light, the Shapiro time delay, the Gravitational Red Shift, etc., are explained with the use of SR only. The techniques used in this paper can be applied to any GR spacetime metric, Teleparallel Gravity, etc., in order to obtain the corresponding SR gravitational scalar generalized potential and vice versa. Thus, the case study of Newtonian Gravitational Potential according to SR leads to the corresponding non-Riemannian metric of GR. Finally, it is shown that the mainstream consideration of the Gravitational Red Shift contains two approximations, which are valid in weak gravitational fields only.

The 3+1 formalism in teleparallel and symmetric teleparallel gravity

Teleparallel and symmetric teleparallel gravity offer platforms in which gravity can be formulated in interesting geometric approaches, respectively given by torsion and nonmetricity. In this vein, general relativity can be expressed in three dynamically equivalent ways which may offer insights into the different properties of these decompositions such as their Hamiltonian structure, the efficiency of numerical analyses, as well as the classification of gravitational field degrees of freedom. In this work, we take a $$3+1$$ 3 + 1 decomposition of the teleparallel equivalent of general relativity and the symmetric teleparallel equivalent of general relativity which are both dynamically equivalent to curvature based general relativity. By splitting the spacetime metric and corresponding tetrad into their spatial and temporal parts as well as through finding the Gauss-like equations, it is possible to set up a general foundation for the different formulations of gravity. Based on these results, general 3-tetrad and 3-metric evolution equations are derived. Finally through the choice of the two respective connections, the metric $$3+1$$ 3 + 1 formulation for general relativity is recovered as well as the tetrad $$3+1$$ 3 + 1 formulation of the teleparallel equivalent of general relativity and the metric $$3+1$$ 3 + 1 formulation of symmetric teleparallel equivalent of general relativity. The approach is capable, in principle, of resolving common features of the various formulations of general relativity at a fundamental level and pointing out characteristics that extensions and alternatives to the various formulations can present.