Related papers: Geodesic congruences in quantum improved spacetime…
The Levi-Civita connection and geodesic equations for a stationary spacetime are studied in depth. General formulae which generalize those for warped products are obtained. These results are applicated to some regions of Kerr spacetime…
The problem of obtaining canonical Hamiltonian structures from the equations of motion, without any knowledge of the action, is studied in the context of the spatially flat Friedmann-Robertson-Walker models. Modifications to Raychaudhuri…
We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of…
Hawking's singularity theorem concerns matter obeying the strong energy condition (SEC), which means that all observers experience a non-negative effective energy density (EED). The SEC ensures the timelike convergence property. However,…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
In this work we address the issue of studying the conditions required to guarantee the Focusing Theorem for both null and timelike geodesic congruences by using the Raychaudhuri equation. In particular we study the case of…
A reconciliation of gravitation and electromagnetism has eluded physics for neearly a century. It is argued here that this is because both quantum physics and classical physics are set in differentiable space time manifolds with point…
There are two disjointed problems in cosmology within General Relativity (GR), which can be addressed simultaneously by studying the nature of geodesics around $t\rightarrow 0$, where $t$ is the physical time. One is related to the past…
Classical methods of differential geometry are used to construct equations of motion for particles in quantum, electrodynamic and gravitational fields. For a five dimensional geometrical system, the equivalence principle can be extended.…
This study examines the formulation of a singularity theorem for timelike curves including torsion, and establishes the foundational framework necessary for its derivation. We begin by deriving the relative acceleration for an arbitrary…
Displacement and velocity memory effects in the exact, vacuum, plane gravitational wave line element have been studied recently by looking at the behaviour of pairs of geodesics or via geodesic deviation. Instead, one may investigate the…
The geodesic deviation equation (`GDE') provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the…
We show that the standard Heisenberg algebra of quantum mechanics admits a noncommutative differential calculus $\Omega^1$ depending on the Hamiltonian $p^2/2m + V(x)$, and a flat quantum connection $\nabla$ with torsion such that a…
The kinematical characteristics of distinct infalling homothetic fields are discussed by specifying the transverse subspace of their generated congruences to the energy-momentum deposit of the chosen gravitational system. This is pursued…
We consider the geodesic deviation equation, describing the relative accelerations of nearby particles, and the Raychaudhuri equation, giving the evolution of the kinematical quantities associated with deformations (expansion, shear and…
Given a curve in quantum spin state space, we inquire what is the relation between its geometry and the geometric phase accumulated along it. Motivated by Mukunda and Simon's result that geodesics (in the standard Fubini-Study metric) do…
In this paper, we compare the quantum corrections to the Schwarzschild black hole temperature due to quadratic and linear-quadratic generalized uncertainty principle, with the corrections from the quantum Raychaudhuri equation. The reason…
In this paper, we study the geodesic deviation equation (GDE) within the context of the Brans-Dicke (BD) theory in $D$ dimensions. Then, we restrict our attention to the GDE for the fundamental observers and null vector field past directed.…
The implications of restricting the covariance principle within a Gaussian gauge are developed both on a classical and a quantum level. Hence, we investigate the cosmological issues of the obtained Schr\"odinger Quantum Gravity with respect…
Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit…