Related papers: Generally covariant quantum mechanics
Canonical quantization of spherically symmetric initial data which is appropriate to classical interior black hole solutions in four dimensions is carried out and solved exactly without gauge fixing the remaining kinematic Gauss Law…
We describe a procedure naturally associating relativistic Klein-Gordon equations in static curved spacetimes to non-relativistic quantum motion on curved spaces in the presence of a potential. Our procedure is particularly attractive in…
We consider the motion of test particles in the spacetime of a black hole in f(R) gravity. The complete set of analytic solutions of the geodesic equation in the spacetime of this black hole are presented. The geodesic equations are solved…
We use the covariant formulation proposed in Tattersall et al (2017) to analyse the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasi-normal modes…
We consider relativistic quantum field theory in the presence of an external electric potential in a general curved space-time geometry. We utilise Fermi coordinates adapted to the time-like geodesic to describe the low-energy physics in…
We quantize a real massive Klein-Gordon field in curved spacetimes within the general boundary formulation. The vacuum wave function is given by a Gaussian in the Schr\"odinger representation and we study the general structure of the…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…
This study investigates the application of wave functions to explore various solutions of the Klein-Gordon and Schr\"{o}dinger equations within the framework of Lovelock gravity. We also present the derived Smarr formula from the…
The Bardeen solution corresponding to Einstein field equations with a cosmological constant is a regular black hole. The main goal of this manuscript is to investigate the geometric structures in terms of curvature conditions admitted by…
Solitary-particle quantum mechanics' inherent compatibility with special relativity is implicit in Schroedinger's postulated wave-function rule for the operator quantization of the particle's canonical three-momentum, taken together with…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
We perform a detailed study of the geodesic equations in the spacetime of the static and rotating charged black hole corresponding to the Kerr-Newman-(A)dS spacetime. We derive the equations of motion for test particles and light rays and…
We find a coordinate-independent wave-packet solution of the massive Klein-Gordon equation with the conformal coupling to gravity in the de-Sitter universe. This solution can locally be represented through the superposition of…
Black holes, as classical solutions of General Relativity, are expected to exhibit quantum properties near their horizons. In this paper, we examine the behavior of quantum particles near the Schwarzschild horizon by solving the…
Recently it was demonstrated that by adding to the Einstein-Hilbert action a series in powers of the curvature invariants with specially chosen coefficients one can obtain a theory of gravity which has spherically symmetric solutions…
The Schwarzschild geometry is investigated within the context of effective-field-theory models of gravity. Starting from its harmonic-coordinate expression, we derive the metric in standard coordinates by keeping the leading one-loop…
Classical methods of differential geometry are used to construct equations of motion for particles in quantum, electrodynamic and gravitational fields. For a five dimensional geometrical system, the equivalence principle can be extended.…
The classical Einstein-Hilbert (EH) action for general relativity (GR) is shown to be formally analogous to the classical system with position-dependent mass (PDM) models. The analogy is developed and used to build the covariant classical…
The issue of non-locality in quantum mechanics can potentially be resolved by considering relativistically covariant diffusion in four-dimensional spacetime. Stochastic particles described by the Klein-Gordon equation are shown to undergo a…
We first derive the relation between the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold using a method which identifies the…