Related papers: A note on behaviour at an isotropic singularity
We consider the tidal forces between test particles falling along geodesics in the exterior spacetime generated by a static and axially symmetric compact matter source with non-vanishing mass quadrupole. Specifically, we analyze the radial…
An explicit expression for the Jacobi metric for a general Lagrangian system is obtained as a series expansion in the square root of the kinetic energy of the system and the corresponding geodesics are described in terms of an appropriate…
It is shown explicitly that when the characteristic vector field that defines a Godel-type metric is also a Killing vector, there always exist closed timelike or null curves in spacetimes described by such a metric. For these geometries,…
Naturally reductive spaces, in general, can be seen as an adequate generalization of Riemannian symmetric spaces. Nevertheless, there are some that are closer to symmetric spaces than others. On the one hand, there is the series of Hopf…
The Raychaudhuri equation for a geodesic congruence in the presence of a zero-point length has been investigated. This is directly related to the small-scale structure of spacetime and possibly captures some quantum gravity effects. The…
We present a complete study of the geodesics around naked singularities in AdS$_3$, the three-dimensional anti-de Sitter spacetime. These stationary spacetimes, characterized by two conserved charges --mass and angular momentum--, are…
The Kerr geometry is believed to represent the exterior spacetime of astrophysical black holes. We here re-analyze the geometry of Kerr-like metrics (Kerr, Kerr-Newman, Kerr-de Sitter, and Kerr-anti de Sitter), paying particular attention…
It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded…
The generalized Jacobi equation is a differential equation in local coordinates that describes the behavior of infinitesimally close geodesics with an arbitrary relative velocity. In this note we study some transformation properties for…
A unified treatment of all known types of singularities for flat, isotropic and homogeneous spacetimes in the framework of loop quantum cosmology (LQC) is presented. These include bangs, crunches and all future singularities. Using…
Studying the behaviour of a quantum field in a classical, curved, spacetime is an extraordinary task which nobody is able to take on at present time. Independently by the fact that such problem is not likely to be solved soon, still we…
We analyze the directional properties of general gravitational, electromagnetic, and spin-s fields near conformal infinity I. The fields are evaluated in normalized tetrads which are parallelly propagated along null geodesics which approach…
We study the possible singularities of isotropic cosmological models that have a varying speed of light as well as a varying gravitational constant. The field equations typically reduce to two dimensional systems which are then analyzed…
In this work, we have investigated the outcome of gravitational collapse in Husain space-time in the presence of electro-magnetic and a scalar field with potential. In order to study the nature of the singularity, global behavior of radial…
Killing vector fields of a closed homogeneous and isotropic universe are studied. It is shown that in general case there is no time-like Killing vector fields in such a universe. Two exceptional cases are revealed.
A recent work showing that homogeneous and isotropic cosmologies involving scalar fields are equivalent to the geodesics of certain effective manifolds is generalized to the non-minimally coupled and anisotropic cases. As the…
The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the image of a non-closed geodesic has 0 distance from the set of conical points.…
We review recent work on the existence and nature of cosmological singularities that can be formed during the evolution of generic as well as specific cosmological spacetimes in general relativity. We first discuss necessary and sufficient…
We study Jacobi matrices on trees with one end at inifinity. We show that the defect indices cannot be greater than 1 and give criteria for essential selfadjointness. We construct certain polynomials associated with matrices, which mimic…
We show that any Jacobi field along a harmonic map from the 2-sphere to the complex projective plane is integrable (i.e., is tangent to a smooth variation through harmonic maps). This provides one of the few known answers to this problem of…