Lorentzian geometrical structures with global time, Gravity and Electrodynamics

We investigate Lorentzian structures in the four-dimensionalspace-time, supplemented either by a covector field of thetime-direction or by a scalar field of the global time. Furthermore,we propose a new metrizable model of the gravity. In contrast to theusual Theory of General Relativity where all ten components of thesymmetric pseudo-metrics are independent variables, the presentedhere model of the gravity essentially depend only on singlefour-covector field, restricted to have only three-independentcomponents. However, we prove that the Gravitational field, ruled bythe proposed model and generated by some massive body, resting andspherically symmetric in some coordinate system, is given by apseudo-metrics, which coincides with thewell known Schwarzschild metric from the General Relativity. TheMaxwell equations and Electrodynamics are also investigated in theframes of the proposed model. In particular, we derive the covariantformulation of Electrodynamics of moving dielectrics andpara/diamagnetic mediums.

Charged Particle Motions near Non-Schwarzschild Black Holes with External Magnetic Fields in Modified Theories of Gravity

A small deformation to the Schwarzschild metric controlled by four free parameters could be referred to as a nonspinning black hole solution in alternative theories of gravity. Since such a non-Schwarzschild metric can be changed into a Kerr-like black hole metric via a complex coordinate transformation, the recently proposed time-transformed, explicit symplectic integrators for the Kerr-type spacetimes are suitable for a Hamiltonian system describing the motion of charged particles around the non-Schwarzschild black hole surrounded with an external magnetic field. The obtained explicit symplectic methods are based on a time-transformed Hamiltonian split into seven parts, whose analytical solutions are explicit functions of new coordinate time. Numerical tests show that such explicit symplectic integrators for intermediate time steps perform well long-term when stabilizing Hamiltonian errors, regardless of regular or chaotic orbits. One of the explicit symplectic integrators with the techniques of Poincaré sections and fast Lyapunov indicators is applied to investigate the effects of the parameters, including the four free deformation parameters, on the orbital dynamical behavior. From the global phase-space structure, chaotic properties are typically strengthened under some circumstances, as the magnitude of the magnetic parameter or any one of the negative deformation parameters increases. However, they are weakened when the angular momentum or any one of the positive deformation parameters increases.

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.

$$a_{1}$$ meson-nucleon coupling constant at finite temperature from the soft-wall AdS/QCD model

We study the temperature dependence of the $$a_1$$ a 1 meson-nucleon coupling constant in the framework of the soft-wall AdS/QCD model with thermal dilaton field. Profile functions for the axial-vector and fermion fields in the AdS-Schwarzschild metric are presented. It is constructed an interaction Lagrangian for the fermion-axial-vector-thermal dilaton fields system in the bulk of space-time. From this Lagrangian integral representation for the $$g_{a_1NN}$$ g a 1 N N coupling constant is derived. The temperature dependence of this coupling constant is numerically analyzed.

First-order perturbations of Gödel-type metrics in non-dynamical Chern-Simons modified gravity

G\"{o}del-type metrics that are homogeneous in both space and time remain, like the Schwarzschild metric, consistent within Chern-Simons modified gravity; this is true in both the non-dynamical and dynamical frameworks, each of which involves an additional pseudoscalar field coupled to the Pontryagin density. In this paper, we consider stationary first-order perturbations to these metrics in the non-dynamical framework. Under certain assumptions we find analytical solutions to the perturbed field equations. The solutions of the first-order field equations break the translational and cylindrical symmetries of the unperturbed metrics. The effective potential controlling planar geodesic orbits is also affected by the perturbation parameter, which changes the equilibrium radii for the orbits of both massive particles and massless photons.

Rotating spacetime: black-bounces and quantum deformed black hole

Recently, two kinds of deformed schwarzschild spacetime have been proposed, which are the black-bounces metric (Simpson and Visser in J Cosmol Astropart Phys 2019:042, 2019, Lobo et al. in Phys Rev D 103:084052, 2021) and quantum deformed black hole (BH) (Berry et al. in arXiv:2102.02471, 2021). In present work, we investigate the rotating spacetime of these deformed Schwarzschild metric. They are exact solutions to the Einstein’s field equation. We analyzed the properties of these rotating spacetimes, such as event horizon (EH), stationary limit surface (SIS), structure of singularity ring, energy condition (EC), etc., and found that these rotating spacetime have some novel properties.

Quantum probing of singularities at event horizons of black holes

It is proved that coordinate transformations of the Schwarzschild metric to new static and stationary metrics do not eliminate the mode of a particle “fall” to the event horizon of a black hole. This mode is unacceptable for the quantum mechanics of stationary states.

Charged black hole and radiating solutions in entangled relativity

In this manuscript, we show that the external Schwarzschild metric can be a good approximation of exact black hole solutions of entangled relativity. Since entangled relativity cannot be defined from vacuum, the demonstrations need to rely on the definition of matter fields. The electromagnetic field being the easiest (and perhaps the only) existing matter field with infinite range to consider, we study the case of a charged black hole – for which the solution of entangled relativity and a dilaton theory agree – as well as the case of a pure radiation – for which the solution of entangled relativity and general relativity seem to agree, despite an apparent ambiguity in the field equations. Based on these results, we argue that the external Schwarzschild metric is an appropriate mathematical idealization of a spherical black hole in entangled relativity. The extension to rotating cases is briefly discussed.