Modern Physics Letters A

Singularities are commonplace in general relativistic spacetimes. It is natural to hope that they might be “healed” (or resolved) by the inclusion of quantum mechanics, either in the theory itself (quantum gravity) or, more modestly, in the description of the spacetime geodesic paths used to define them. We focus here on the latter, mainly using a procedure proposed by Horowitz and Marolf to test whether singularities in broad classes of spacetimes can be resolved by replacing geodesic paths with quantum wave packets. We list the spacetime singularities that various authors have studied in this context, and distinguish those which are healed quantum mechanically (QM) from those which remain singular. Finally, we mention some alternative approaches to healing singularities.

Tilted Kantowski–Sachs cosmological model in Brans–Dicke theory for perfect fluid has been investigated. The general solution of field equations in Brans–Dicke theory for the combined scalar and tensor field are obtained by using power law relation. Also, some physical and geometrical parameters are obtained and discussed.

One of the spectacular results in mathematical physics is the expression of Racah matrices for symmetric representations of the quantum group ${\mathrm{\text{SU}}}_q(2)$ through the Askey–Wilson polynomials, associated with the $q$-hypergeometric functions ${}_4{\varphi }_3$. Recently it was shown that this is in fact the general property of symmetric representations, valid for arbitrary ${\mathrm{\text{SU}}}_q(N)$ — at least for exclusive Racah matrices $\bar{S}$. The natural question then is what substitutes the conventional $q$-hypergeometric polynomials when representations are more general? New advances in the theory of matrices $\bar{S}$, provided by the study of differential expansions of knot polynomials, suggest that these are multiple sums over Young sub-diagrams of the one which describes the original representation of ${\mathrm{\text{SU}}}_q(N)$. A less trivial fact is that the entries of the sum are not just the factorized combinations of quantum dimensions, as in the ordinary hypergeometric series, but involve non-factorized quantities, like the skew characters and their further generalizations — as well as associated additional summations with the Littlewood–Richardson weights.

Using an analytical solution for the relativistic equation of single $\mathrm{\Lambda }$-hypernuclei in the presence of Woods–Saxon (WS) potential we present, for the first time, an analytical form for the excited state binding energies of 1p, 1d, 1f and 1g shells of a number of hypernuclei.

Based on phenomenological analysis of the $\mathrm{\Lambda }$ binding energies in a set of $\mathrm{\Lambda }$-hypernuclei, the WS potential parameters are obtained phenomenologically for the set of $\mathrm{\Lambda }$-hypernuclei. Systematic study of the energy levels of single $\mathrm{\Lambda }$-hypernuclei enables us to extract more detailed information about the $\mathrm{\Lambda }$-nucleon interaction. We also study the root mean square (RMS) radii of the $\mathrm{\Lambda }$ orbits in the hypernuclear ground states. Our results are presented for several hypernuclei and it is shown that our results for the binding energies are in good agreement with experimental data.

A spinless particle coupled covariantly to a uniform magnetic field parallel to the string in the background of the rotating cosmic string is studied. The energy levels of the electrically charged particle subject to the Klein–Gordon oscillator are analyzed. Afterwards, we consider the case of the position-dependent mass and show how these energy levels depend on the parameters in the problem. Remarkably, it shows that for the special case, the Klein–Gordon oscillator coupled covariantly to a homogeneous magnetic field with the position-dependent mass in the rotating cosmic string background has the similar behaviors to the Klein–Gordon equation with a Coulomb-type configuration in a rotating cosmic string background in the presence of an external magnetic field.

The covariant free fields of any spin on anti-de Sitter (AdS) spacetimes are studied, pointing out that these transform under isometries according to covariant representations (CRs) of the AdS isometry group, induced by those of the Lorentz group. Applying the method of ladder operators, it is shown that the CRs with unique spin are equivalent with discrete unitary irreducible representations (UIRs) of positive energy of the universal covering group of the isometry one. The action of the Casimir operators is studied finding how the weights of these representations (reps.) may depend on the mass and spin of the covariant field. The conclusion is that on AdS spacetime, one cannot formulate a universal mass condition as in special relativity.

Radiative extensions of BTZ metric in 2 + 1 dimensions are found which are sourced by nonlinear Maxwell fields and a null current. This may be considered as generalization of the problem formulated long go by Vaidya and Bonnor. The mass and charge are functions of retarded/advanced null coordinate apt for decay/inflation. The new solutions are constructed through a Theorem that works remarkably well for any nonlinear electrodynamic model. Hawking temperature is analyzed for the case of the Born–Infeld electrodynamics.