We consider a timelike geodesic congruence in the presence of perturbative quantum fluctuations spacetime metric. calculate change volume bundle geodesics due to such and thereby obtain quantum-gravitationally modified Raychaudhuri equation. Quantum gravity generically increases convergence congruences production caustics.

Using general features of recent quantizations of the Hamiltonian constraint in loop quantum gravity and loop quantum cosmology, a dynamical interpretation of the constraint equation as evolution equation is presented. This involves a transformation from the connection to a dreibein representation and the selection of an internal time variable. Due to the discrete nature of geometrical quantiti...

OIC members have much potential in their economic development. Therefore, their economic integration leads to more increment for partners and deal with global system as a unique organization. Consequently, studying the convergence of OIC members and their encountered challenges has especial importance which can assist the policy makers to develop their commercial relationship and consequent...

A unified first law of black-hole dynamics and relativistic thermodynamics is derived in spherically symmetric general relativity. This equation expresses the gradient of the active gravitational energy E according to the Einstein equation. Projecting the equation along the flow of thermodynamic matter and along the trapping horizon of a black hole yield, respectively, first laws of relativisti...

In this article, we study the string equation of type (2, 2n + 1), which is derived from 2D gravity theory or the string theory. We consider the equation as a 2n-th order analogue of the first Painlev éequation, take the autonomous limit, and solve it concretely by use of the Weierstrass’ elliptic function.