Regular model of magnetized black hole with rational nonlinear electrodynamics

A modified Hayward metric of magnetically charged black hole space–time based on rational nonlinear electrodynamics with the Lagrangian [Formula: see text] is considered. We introduce the fundamental length, characterizing quantum gravity effects. If the fundamental length vanishes the general relativity coupling to rational nonlinear electrodynamics is recovered. We obtain corrections to the Reissner–Nordström solution as the radius approaches infinity. The metric possesses a de Sitter core without singularities as [Formula: see text]. The Hawking temperature and the heat capacity are calculated. It was shown that phase transitions occur and black holes are thermodynamically stable at some event horizon radii. We demonstrate that curvature invariants are bounded and the limiting curvature conjecture takes place.

Non-Singular Model of Magnetized Black Hole Based on Nonlinear Electrodynamics

A new modified Hayward metric of magnetically charged non-singular black hole spacetime in the framework of nonlinear electrodynamics is constructed. When the fundamental length introduced, characterising quantum gravity effects, vanishes, one comes to the general relativity coupled with the Bronnikov model of nonlinear electrodynamics. The metric can have one (an extreme) horizon, two horizons of black holes, or no horizons corresponding to the particle-like solution. Corrections to the Reissner–Nordström solution are found as the radius approaches infinity. As r → 0 the metric has a de Sitter core showing the absence of singularities, the asymptotic of the Ricci and Kretschmann scalars are obtained and they are finite everywhere. The thermodynamics of black holes, by calculating the Hawking temperature and the heat capacity, is studied. It is demonstrated that phase transitions take place when the Hawking temperature possesses the maximum. Black holes are thermodynamically stable at some range of parameters.

Applications of Polymeric Quantisation

Polymer quantisation is a background independent quantisation scheme inspired by loop quantum gravity. Under this quantisation scheme, it predicts that space is discretised and changes in multiples of a fundamental length scale λ. As a result, the momentum operator is not well-defined. However, a new operator can be defined such that a Schrödinger-like equation can be retrieved. The solutions give rise to eigenspectra which are similar to the standard counterparts, with an additional correction term due to λ. We present the basic principles of the polymer representation and apply it to the harmonic oscillator to study the phenomenological implications of such solutions. In addition, we consider an ensemble of such oscillators and calculated the thermodynamical properties for systems that safisty the bosonic and fermionic statistics. The results presented may have physical significance at high energy scales or in exotic matter.

Snyder-like modified gravity in Newton's spacetime

This work is focused on searching a geodesic interpretation of the dynamics of a particle under the effects of a Snyder-like deformation in the background of the Kepler problem. In order to accomplish that task, a Newtonian spacetime is used. Newtonian spacetime is not a metric manifold, but allows to introduce a torsion-free connection in order to interpret the dynamic equations of the deformed Kepler problem as geodesics in a curved spacetime. These geodesics and the curvature terms of the Riemann and Ricci tensors show a mass and a fundamental length dependence as expected, but are velocity-independent that is a feature present in other classical approaches to the problem. In this sense, the effect of introducing a deformed algebra is examined and the corresponding curvature terms calculated, as well as the modifications of the integrals of motion.