Related papers: Schr\"odinger equation in a general curved space-t…
Quantum fluctuations on curved spacetimes cause the emission of pairs of particles from the quantum vacuum, as in the Hawking effect from black holes. We use an optical analogue to gravity to investigate the influence of the curvature on…
In this paper, using Hamilton-Jacobi method, we address the tunnelling of fermions in a 4-dimensional Schwarzschild spacetime. Base on the generalized uncertainty principle, we introduce the influence of quantum gravity. After solving the…
Recent work in the literature has studied the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat space-time and weak radiation at a very late time. The relevant quantum amplitudes…
The combined action of gravity and quantum mechanics gives rise to a minimum time uncertainty in the lowest order approximation of a perturbative scheme, in which quantum effects are regarded as corrections to the classical spacetime…
The quantum Schrodinger-Newton equation is solved for a self-gravitating Bose gas at zero temperature. It is derived that the density is non-uniform and a central hollow cavity exists. The radial distribution of the particle momentum is…
In contrast to the 3D case, different approaches for deriving the gravitational corrections to the Heisenberg uncertainty relation do not lead to the unique result whereas additional spatial dimensions are present in the theory. We suggest…
A derivation is presented of the quantummechanical wave equations based upon the Equity Principle of Einstein's General Relativity Theory. This is believed to be more generic than the common derivations based upon Einstein's energy…
We derive the wave equation obeyed by electromagnetic fields in curved spacetime. We find that there are Riemann and Ricci curvature coupling terms to the photon polarisation which result in a polarisation dependent deviation of the photon…
We study quantum gravity effects for Myers-Perry black holes assuming that the leading contributions arise from the renormalization group evolution of Newton's coupling. Provided that gravity weakens following the asymptotic safety…
A model is proposed for the classical electron as a point charge with finite electromagnetic self-energy. Modifications of the Reissner-Nordstr{\o}m (spin 0) and Kerr-Newman (spin 1/2) solutions of the Einstein-Maxwell equations are…
Using classical statistics, Schrodinger equation in quantum mechanics is derived from complex space model. Phase-space probability amplitude, that can be defined on classical point of view, has connections to probability amplitude in…
We show that the dynamics of Schwarzschild-(A)dS black holes admits a symmetry under the 2d Schr\"odinger group, whatever the sign or value of the cosmological constant. This is achieved by reformulating the spherically-symmetric reduction…
We present a discussion of the periodicity in imaginary time of maximally extended black hole spacetimes without reference to Euclidean manifolds. As motivation, we first demonstrate our approach for the Rindler geometry in flat space…
We analyze the solutions of the Schr\"odinger equation with the low frequency initial data and a time-dependent weakly random potential. We prove a homogenization result for the low frequency component of the wave field. We also show that…
From the curved spacetime Lagrangian the first approximation scalar particle quantum equation was obtained following the canonical formalism. The roots of this equation in Schwarzschild's pseudo flat space were found. As it was shown in a…
We study further a general relativistic mechanism for the acquisition of tidal energy by free test particles near a gravitationally collapsed configuration. Specifically, we investigate the solutions of timelike geodesic equation in a Fermi…
We introduce a procedure to determine the size and shape of normal neighborhoods in any spacetimes and their dependence on the precision of the measurements performed by arbitrary observers. As an example, we consider the Schwarzschild…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
In the context of an extended General Relativity theory with boundary terms included, we introduce a new nonlinear quantum algebra involving a quantum differential operator, with the aim to calculate quantum geometric alterations when a…
In relativistic quantum field theory with local interactions, charge is locally conserved. This implies local conservation of probability for the Dirac and Klein-Gordon wavefunctions, as special cases; and then in turn for non-relativistic…