Modern Physics Letters A

We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant whose physical dimension is of (length)² in natural unit introduces a symplectic structure of spacetime which causes a noncommutative spacetime at the Planck scale L_P. The symplectic structure of spacetime M leads to an isomorphism between symplectic geometry (M, ω) and Riemannian geometry (M, g) where the deformations of symplectic structure ω in terms of electromagnetic fields F = dA are transformed into those of Riemannian metric g. This approach for quantum gravity allows a background independent formulation where spacetime as well as matter fields is equally emergent from a universal vacuum of quantum gravity which is thus dubbed as the quantum equivalence principle.

A recent work by Dey and Sen derived the approximate light deflection angle α by an Ellis wormhole in terms of proper radial distance ℓ that covers the entire spacetime. On the other hand, Bodenner and Will calculated the expressions for light bending in Schwarzschild geometry using various coordinates and showed that they all reduce to a single formula when re-expressed in the coordinate independent language of "circumferential radius" r_C identified with the standard radial coordinate r_S. We shall argue that the coordinate invariant language for two-way wormholes should be ℓ rather than r_S. Hence here we find the exact deflection α in Ellis wormhole geometry first in terms of ℓ and then in terms of r_S. We confirm the latter expression using three different methods. We argue that the practical measurement scheme does not necessarily single out either ℓ or r_S. Some errors in the literature are corrected.

Just like the vector gauge bosons in the gauge theories, it is now known that gravitons acquire mass in the process of spontaneous symmetry breaking of diffeomorphisms through the condensation of scalar fields. The point is that we should find the gravitational Higgs mechanism such that it results in massive gravity in a flat Minkowski spacetime without non-unitary propagating modes. This is usually achieved by including higher-derivative terms in scalars and tuning the cosmological constant to be a negative value in a proper way. Recently, a similar but different gravitational Higgs mechanism has been advocated by Chamseddine and Mukhanov where one can relax the negative cosmological constant to zero or positive one. In this work, we investigate why the non-unitary ghost mode decouples from physical Hilbert space in a general spacetime dimension. Moreover, we generalize the model to possess an arbitrary potential and clarify under what conditions the general model exhibits the gravitational Higgs mechanism. By searching for solutions to the conditions, we arrive at two classes of potentials exhibiting gravitational Higgs mechanism. One class includes the model by Chamseddine and Mukhanov in a specific case while the other is a completely new model.

We propose a way to remove black hole singularities by using a particular nonlinear electrodynamics Lagrangian that has been recently used in various astrophysics and cosmological frameworks. In particular, we adapt the cosmological analysis discussed in a previous work to the black hole physics. Such analysis will be improved by applying the Oppenheimer–Volkoff equation to the black hole case. At the end, fixed the radius of the star, the final density depends only on the introduced quintessential density term ρ_γ and on the mass.

We study the absorption and scattering of massless scalar waves propagating in spherically symmetric spacetimes with dynamical cosmological constant both in low-energy and high-energy zones. In the former low-energy regime, we solve analytically the Regge–Wheeler wave equation and obtain an analytic absorption probability expression which varies with , where M is the central mass and Λ is cosmological constant. The low-energy absorption probability, which is in the range of [0, 0.986701], increases monotonically with increase in Λ. In the latter high-energy regime, the scalar particles adopt their geometric optics limit value. The trajectory equation with effective potential emerges and the analytic high-energy greybody factor, which is relevant with the area of classically accessible regime, also increases monotonically with increase in Λ, as long Λ is less than or of the order of 10⁴. In this high-energy case, the null cosmological constant result reduces to the Schwarzschild value .

Dirac equation is solved for Mie-type potential. The energy spectra and the corresponding wave functions are investigated with pseudospin and spin symmetry. The Nikiforov–Uvarov method is used to obtain an analytical solution of the Dirac equation and closed forms of energy eigenvalues are obtained for any spin-orbit coupling term κ. We also present some numerical results of Dirac particles for the well-known Kratzer–Fues and modified Kratzer potentials which are Mie-type potential.

We show that the previously known off-shell nilpotent and absolutely anticommuting (s_b s_ab + s_ab s_b = 0) Becchi–Rouet–Stora–Tyutin (BRST) transformations (s_b) and anti-BRST transformations (s_ab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3+1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific constrained field condition through a Lagrange multiplier 4D vector field. The above condition, which is the analogue of the Curci–Ferrari restriction of the non-Abelian 1-form gauge theory, emerges from the Euler–Lagrange equations of motion of our present theory and ensures the absolute anticommutativity of the transformations s_(a)b. Thus, the coupled Lagrangian densities, proposed in our present investigation, are aesthetically more appealing and more economical.