Related papers: Geodesic congruences in quantum improved spacetime…
A possible model for quantum kinematics of a test particle in a curved space-time is proposed. Every reasonable neighbourhood V_e of a curved space-time can be equipped with a nonassociative binary operation called the geodesic…
We investigate the effects of the underlying quantum geometry in loop quantum cosmology on spacetime curvature invariants and the extendibility of geodesics in the Bianchi-I model for matter with a vanishing anisotropic stress. Using the…
We derive a set of equations describing the linear response of the convergence properties of a geodesic congruence to arbitrary geometry variations. It is a combination of equations describing the deviations from the standard…
The classical uncertainty principle inequalities were imposed over the general relativity geodesic equation as a mathematical constraint. In this way, the uncertainty principle was reformulated in terms of proper space-time length element,…
In the context of general relativity, the geodesic deviation equation (GDE) relates the Riemann curvature tensor to the relative acceleration of two neighboring geodesics. In this paper, we consider the GDE for the generalized hybrid…
We construct a generally-covariant formulation of non-equilibrium thermodynamics in General Relativity. We find covariant entropic forces arising from gradients of the entropy density, and a corresponding non-conservation of the energy…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
A Poisson coalgebra analogue of a (non-standard) quantum deformation of sl(2) is shown to generate an integrable geodesic dynamics on certain 2D spaces of non-constant curvature. Such a curvature depends on the quantum deformation parameter…
In this paper, we derive corrections to the geodesic equation due to the $k$-deformation of curved space-time, up to the first order in the deformation parameter a. This is done by generalizing the method from our previous paper [31], to…
The idea that spacetime geometry is built from quantum entanglement has been widely accepted in the last years. But how exactly the geometry is related with quantum states is still unclear. In this note, based on the idea of deep learning,…
In "extended phase space" approach to quantum geometrodynamics numerical solutions to Schrodinger equation corresponding to various choice of gauge conditions are obtained for the simplest isotropic model. The "extended phase space"…
Geodesics are studied in one of the Weyl metrics, referred to as the M--Q solution. First, arguments are provided, supporting our belief that this space--time is the more suitable (among the known solutions of the Weyl family) for…
This paper is a continuation of the papers [gr-qc/9409010, gr-qc/9505034]. A revision of the Einstein equation shows that its dynamic incompleteness, contrary to a popular opinion, cannot be circumvented by so-called coordinate conditions.…
Several physical problems such as the `twin paradox' in curved spacetimes have purely geometrical nature and may be reduced to studying properties of bundles of timelike geodesics. The paper is a general introduction to systematic…
We derive the geodesic equation for point particles propagating in Moyal-type noncommutative spacetimes using a field-theoretic approach based on the quasi-classical limit of the noncommutative Klein-Gordon equation. Starting from a…
The evolution of timelike geodesic congruences in a spherically symmetric, nonstatic, inhomogeneous spacetime representing gravitational collapse of a massless scalar field is studied. We delineate how initial values of the expansion,…
We study the kinematics of timelike geodesic congruences in two and four dimensions in spacetime geometries representing stringy black holes. The Raychaudhuri equations for the kinematical quantities (namely, expansion, shear and rotation)…
We show that tensoriality constraints in noncommutative Riemannian geometry in the 2-dimensional bicrossproduct model quantum spacetime algebra [x,t]=\lambda x drastically reduce the moduli of possible metrics g up to normalisation to a…
We study the passive influence of quantum matter fluctuations on the expansion parameter of a congruence of timelike geodesics in a semiclassical regime. In particular, we show that, the perturbations of this parameter can be considered to…
Despite being created through a fundamentally quantum-mechanical process, cosmological structures have not yet revealed any sign of genuine quantum correlations. Among the obstructions to the direct detection of quantum signatures in…