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This work focuses on the emergence of dark phases (dark energy-induced phases) in the radial wave function of scalar particles. We achieve this by presenting novel solutions to the Klein-Gordon equation in a spherically symmetric spacetime,…

We study the interaction between massive scalar fields and the gravitational field produced by a higher dimensional Schwarzschild solution in a string cloud model. Exact analytical solutions of both angular and radial parts of the…

We obtain generally covariant operator-valued geodesic equations on a pseudo-Riemannian manifold $M$ as part of the construction of quantum geodesics on the algebra $D(M)$ of differential operators. Geodesic motion arises here as an…

This short paper should serve as basis for further analysis of a previously found new symmetry of the solutions of the wave equation in the gravitational field of a Kerr black hole. Its main new result is the proof of essential…

This paper studies a class of $D=n+2(\ge 6)$ dimensional solutions to Lovelock gravity that is described by the warped product of a two-dimensional Lorentzian metric and an $n$-dimensional Einstein space. Assuming that the angular part of…

In this paper, we consider the propagation of waves in the space-time of a single black hole with a static Schwarzschild radius in the expanding universe, namely, the solutions of the linear and semilinear Klein-Gordon equations.

We look for Schroedinger solutions in Lovelock gravity in $D > 4$. We span the entire parameter space and determine parametric relations under which the Schroedinger solution exists. We find that in arbitrary dimensions pure Lovelock…

Recently, it was discovered that lower-dimensional versions of Lovelock gravity exist as scalar-tensor theories that are examples of Horndeski gravity. We study the thermodynamics of the static black hole solutions in these theories up to…

The Klein-Gordon equation describes the wave-like behavior of spinless particles since it is Lorentz invariant. While it seemed initially ripe for explaining the electronic structure of the hydrogen atom, the lack of a unconditional…

We revisit the Schwarzschild singularity in a semiclassical setting where the background geometry is classical and quantum effects enter through Bohmian (quantal) trajectories associated with a Klein Gordon wave packet. Using the…

We follow and modify the Feshbach-Villars formalism by separating the Klein-Gordon equation into two coupled time-dependent Schroedinger equations for particle and antiparticle wave function components with positive probability densities.…

We source the Lovelock gravity theories indexed by an integer k and fixed by requiring a unique anti-de Sitter vacuum with a self-interacting nonminimal scalar field in arbitrary dimension d. For each inequivalent Lovelock gravity theory…

Starting from relativistic mass-less Madelung fluid, we shall develop a class of typical wave functions by imposing it to maximize Shannon entropy given its finite average quantum potential. We show that there is a class of solutions in…

We seek to introduce a mathematical method to derive the Klein-Gordon equation and a set of relevant laws strictly, which combines the relativistic wave functions in two inertial frames of reference. If we define the stationary state wave…

This work deals with the influence of the gravitational field produced by a charged and rotating black hole (Kerr-Newman spacetime) on massive scalar fields. We obtain an exact solution of the Klein-Gordon equation in this spacetime, which…

We generalize the quasilocal definition of the stress energy tensor of Einstein gravity to the case of third order Lovelock gravity, by introducing the surface terms that make the action well-defined. We also introduce the boundary…

In this study, we analyze solutions of the wave equation for scalar particles in a space-time with nontrivial topology. Solutions for the Klein--Gordon oscillator are found considering two configurations of this space-time. In the first…

The quantum hydrodynamic-like equations for two real variables (i.e., the phase and the amplitude of the wave function) of the relativistic Klein-Gordon equation are derived in the present paper. The paper also shows that in classical limit…

We obtain a slowly rotating black hole solution in the scalar-tensor theory of gravity with nonminimal derivative coupling to the Einstein tensor. Properties of the obtained solution have been examined carefully. We also investigate the…

Using conformal coordinates associated with conformal relativity -- associated with de Sitter spacetime homeomorphic projection into Minkowski spacetime -- we obtain a conformal Klein-Gordon partial differential equation, which is…