Related papers: Kinematics of geodesic flows in stringy black hole…
In this paper we calculate the kinematical quantities of the Raychaudhuri equations, to characterize a congruence of time-like integral curves, according to the vacuum radial solution of Weyl theory of gravity. Also the corresponding flows…
We show that in a rapidly mixing flow with an invariant measure, the time which is needed to hit a given section is related to a sort of conditional dimension of the measure at the section. The result is applied to the geodesic flow of…
In this work we have obtained a charged black hole solution in the presence of perfect fluid dark matter (PFDM) and discuss its energy conditions. The metric corresponding to the rotating avatar of this black hole solution is obtained by…
Chaotic motion in time of a number of macroscopic systems has been analyzed, in the framework of scale relativity, as motion in a fractal space with topological dimension 3 and geodesics with fractal dimension 2. The motion equation is then…
We study the dynamical behavior of compressible fluids evolving on the outer domain of communication of a Schwarzschild background. To this end, we design several numerical methods which take the Schwarzschild geometry into account and we…
It is well-known that the thermal Hawking-like radiation can be emitted from the acoustic horizon, but the thermodynamic-like understanding for acoustic black holes was rarely made. In this paper, we will show that the kinematic connection…
We investigate the existence of supersymmetric static dyonic black holes with spherical horizon in the context of N= 2 U(1) gauged supergravity in four dimensions. We analyze the conditions for their existence and provide the general…
Based on some ideas emerged from the classical Kaluza-Klein theory, we present a $5D$ universe as a product bundle over the $4D$ spacetime. This enables us to introduce and study two categories of kinematic quantities (expansions, shear,…
Intrinsic time quantum geometrodynamics resolved `the problem of time' and bridged the deep divide between quantum mechanics and canonical quantum gravity with a Schrodinger equation which describes evolution in intrinsic time variable. In…
We discuss a recently proposed limiting curvature theory of gravity and its application to the problem of singularities inside black holes. In this theory the growth of the curvature is suppressed by specially chosen inequality constraints…
Recent work on an approach to the geometrodynamics of cylindrical gravity waves in the presence of interacting scalar matter fields, based on the Kucha\v{r} hypertime formalism, is extended to the analogous spherically symmetric system.…
We study the mean curvature flow of smooth $m$-dimensional compact submanifolds with quadratic pinching in the Riemannian manifold $\mathbb{C}P^n$. Our main focus is on the case of high codimension, $k\geq 2$. We establish a codimension…
Black hole solutions are studied here within the symmetric teleparallel formulation of gravity, employing the $f(Q)$ model in which the gravitational dynamics are governed by the non-metricity scalar $Q$. We focus on static, circularly…
We investigate local and global properties of timelike geodesics in three static spherically symmetric spacetimes. These properties are of its own mathematical relevance and provide a solution of the physical `twin paradox' problem. The…
With the recent progress in observations of astrophysical black holes, it has become more important to understand in detail the physics of strongly gravitating horizonless objects. If the objects identified in the observations are indeed…
Geodesic equations of the vacuum C-metric are derived and solved for various cases. The solutions describe the motion of timelike or null particles with conserved energy and angular momentum. Polar, nearly-circular orbits around weakly…
The null geodesics of a Schwarzschild black hole are studied from a dynamical systems perspective. Written in terms of Kerr-Schild coordinates, the null geodesic equation takes on the simple form of a particle moving under the influence of…
We show that the absence of unbounded algebraic curvature invariants constructed from polynomials of the Riemann tensor cannot guarantee the absence of strong singularities. As a consequence, it is not sufficient to rely solely on the…
The kinematic space could play a key role in constructing the bulk geometry from dual CFT. In this paper, we study the kinematic space from geometric points of view, without resorting to differential entropy. We find that the kinematic…
The curved geometry of a spacetime manifold arises as a solution of Einstein's gravitational field equation. We show that the metric of a spherically symmetric gravitational field configuration can be viewed as an optical metric created by…