Narrow Results

Singularities in Newton’s gravitation, in general relativity (GR), in Coulomb’s law, and elsewhere in classical physics, stem from two ill conceived assumptions: (a) there are point-like entities with finite masses, charges, etc., packed in zero volumes, and (b) the non-quantum assumption that these point-likes can be assigned precise coordinates and momenta. In the case of GR, we argue that the classical energy–momentum tensor in Einstein’s field equation is that of a collection of point particles and is prone to singularity. In compliance with Heisenberg’s uncertainty principle, we suggest to replace each constituent of the gravitating matter with a suitable quantum mechanical equivalent, here a Klien–Gordon (KG) or a Yukawa-ameliorated version of it, YKG field. KG and YKG fields are spatially distributed entities. They do not end up in singular spacetime points nor predict singular blackholes. On the other hand, YKG waves reach infinity as $\frac{1}{r}{e}^{-(\kappa \pm ik)r}$. They create the Newtonian $r^{-2}$ term as well as a non-Newtonian $r^{-1}$ force. The latter is capable of explaining the observed flat rotation curves of spiral galaxies, and is interpretable as an alternative gravity, a dark matter scenario, etc. There are ample observational data on flat rotation curves of spiral galaxies, coded in the Tully–Fisher relation, to support our propositions.

By introducing a static and spherically symmetric geometry, we have solved the coupled electromagnetic and gravitational field equations in the presence of both, massive gravitons and nonlinear electrodynamics. The exact solutions show that massive gravity theory admits two novel classes of nonlinearly charged asymptotically AdS black holes. The black holes’ electric charge, mass, and other thermodynamic quantities have been calculated. Then, by use of a Smarr-type mass formula, it has been proved that the thermodynamical first law is valid for both the new massive black hole solutions. The black hole local stability has been investigated by use of the canonical ensemble and geometrical methods, separately. Through comparison of the results, we found that they are compatible provided that the HEPM or QII thermodynamic metrics are used. Global stability and Hawking–Page phase transition points have been studied by use of the grand canonical ensemble method and regarding the Gibbs free energy of the black holes.

Making use of a model of nonlinear electrodynamics (NED), whose action remains invariant under conformal transformations, a new class of charged higher-dimensional black holes (BHs) has been introduced in the massive gravity theory. Our exact solutions, with A(dS) asymptotic behavior, in addition to the BHs with one, two and three horizons, show the extreme and horizon-less ones. The conserved and thermodynamic quantities have been calculated in the presence of massive gravitons and NED. By use of a Smarr mass formula, it has been found that the standard form of the first law of BH thermodynamics (FLT) remains valid for our new massive BHs. Thermal stability of the BHs has been studied comparatively, by use of the geometrical and thermodynamical methods. The size of those BHs which undergo first- or second-order phase transition, as well as those of which are locally stable has been determined. The results of geometrical and thermodynamical approaches have been compared, for bout of dS and AdS cases, by use of the plots. It has been shown that both of the aforementioned methods produce the same results provided that HPEM or Quevedo type-two (QII) metrics are used. Critical behavior of the BHs has been studied by taking thermodynamic pressure proportional to the cosmological constant. It has been found that in addition to the Van der Waals (VdW) like phase transition, the so-called reentrant phase transition (RPT) can occur as well.

In this study, we have examined the evolving wormhole solution within Einstein-massive gravity, considering traceless, barotropic and anisotropic pressure fluids. We have conducted a comprehensive analysis of the constraints imposed by the constants derived from the wormhole solution. It is found that the wormhole throat, situated between two asymptotic universes, undergoes simultaneous expansion with acceleration. A detailed investigation of the energy conditions for traceless, barotropic, and anisotropic fluids suggests a wide range of possibilities for evolving wormhole configurations with nonexotic matter at the throat. The dependency of this feature on the various parameters arising from the study has also been examined.

Massive gravitational modes in effective field theories can be recovered by extending General Relativity and taking into account generic functions of the curvature invariants, not necessarily linear in the Ricci scalar R. In particular, adopting the minimal extension of f(R) gravity, an effective field theory with massive modes is straightforwardly recovered. This approach allows to evade shortcomings like ghosts and discontinuities if a suitable choice of expansion parameters is performed.

We examine a dark-energy equation of state. From there, we link early-universe graviton production by varying the DE equation from –1 to 1 with a Kaluza–Klein treatment of reacceleration and comment on how modification of gravitational $\frac{1}{r}$ potentials and the reacceleration of the universe also bridge between the first and second parts of this document, in terms DE physics and gravitons, as well as changing Q(z) reacceleration behavior. We close with a suggestion on redoing initial contributions to DE.