Geometrization of the theory of electromagnetic and spinor fields on the background of the Schwarzschild spacetime

The geometrical Kosambi–Cartan–Chern approach has been applied to study the systems of differential equations which arise in quantum-mechanical problems of a particle on the background of non-Euclidean geometry. We calculate the geometrical invariants for the radial system of differential equations arising for electromagnetic and spinor fields on the background of the Schwarzschild spacetime. Because the second invariant is associated with the Jacobi field for geodesics deviation, we analyze its behavior in the vicinity of physically meaningful singular points r = M, ∞. We demonstrate that near the Schwarzschild horizon r = M the Jacobi instability exists and geodesics diverge for both considered problems.

On the Quantification of Relativistic Trajectories

The geodesics on a relativistic manifold are given by the well-known equation involving the Christoffel coefficients. This equation can be solved numerically step by step and transposed into a quantization. We study here the effect of this quantization on the Schwarzschild spacetime, more precisely in the Kruskal-Szekeres map.

Ringing of the Regular Black Hole with Asymptotically Minkowski Core

A Regge–Wheeler analysis is performed for a novel black hole mimicker ‘the regular black hole with asymptotically Minkowski core’, followed by an approximation of the permitted quasi-normal modes for propagating waveforms. A first-order WKB approximation is computed for spin zero and spin one perturbations of the candidate spacetime. Subsequently, numerical results analysing the respective fundamental modes are compiled for various values of the a parameter (which quantifies the distortion from Schwarzschild spacetime), and for various multipole numbers ℓ. Both electromagnetic spin one fluctuations and scalar spin zero fluctuations on the background spacetime are found to possess shorter-lived, higher-energy signals than their Schwarzschild counterparts for a specific range of interesting values of the a parameter. Comparison between these results and some analogous results for both the Bardeen and Hayward regular black holes is considered. Analysis as to what happens when one permits perturbations of the Regge–Wheeler potential itself is then conducted, first in full generality, before specialising to Schwarzschild spacetime. A general result is presented explicating the shift in quasi-normal modes under perturbation of the Regge–Wheeler potential.

Forces in Schwarzschild, Vaidya and generalized Vaidya spacetimes

In this paper we investigate how the leading term in the geodesic equation in Schwarzschild spacetime changes under the coordinate transformation to Eddington-Finkelstein coordinates. This term corresponds to the Newton force of attraction. Also we consider this term when we add the energy-momentum tensor of the form of the null dust and the null perfect fluid into right-hand side of the Einstein equation. We estimate the value of this force in Vaidya spacetime when the naked singularity formation occurs. Also we give conditions in generalized Vaidya spacetime when this force of attraction is replaced by the force of repulsion.

Rotating spacetime: black-bounces and quantum deformed black hole

Recently, two kinds of deformed schwarzschild spacetime have been proposed, which are the black-bounces metric (Simpson and Visser in J Cosmol Astropart Phys 2019:042, 2019, Lobo et al. in Phys Rev D 103:084052, 2021) and quantum deformed black hole (BH) (Berry et al. in arXiv:2102.02471, 2021). In present work, we investigate the rotating spacetime of these deformed Schwarzschild metric. They are exact solutions to the Einstein’s field equation. We analyzed the properties of these rotating spacetimes, such as event horizon (EH), stationary limit surface (SIS), structure of singularity ring, energy condition (EC), etc., and found that these rotating spacetime have some novel properties.

The evolutions of the innermost stable circular orbits in dynamical spacetimes

In this paper, we studied the evolutions of the innermost stable circular orbits (ISCOs) in dynamical spacetimes. At first, we reviewed the method to obtain the ISCO in Schwarzschild spacetime by varying its conserved orbital angular momentum. Then, we demonstrated this method is equivalent to the effective potential method in general static and stationary spacetimes. Unlike the effective potential method, which depends on the presence of the conserved orbital energy, this method requires the existence of conserved orbital angular momentum in spacetime. So it can be easily generalized to the dynamical spacetimes where there exists conserved orbital angular momentum. From this generalization, we studied the evolutions of the ISCOs in Vaidya spacetime, Vaidya-AdS spacetime and the slow rotation limit of Kerr–Vaidya spacetime. The results given by these examples are all reasonable and can be compared with the evolutions of the photon spheres in dynamical spacetimes.