相关论文: Raychaudhuri and optical equations for null geodes…

It has been shown numerically that the performance of the Levenberg-Marquardt algorithm can be improved by including a second order correction known as the geodesic acceleration. In this paper we give the method a more sound theoretical…

We investigate motion of test particles in exact spacetimes with an expanding impulsive gravitational wave which propagates in Minkowski, de Sitter or anti-de Sitter universe. Using the continuous form of these metrics we derive explicit…

The Noether symmetry analysis is applied in a multi-scalar field cosmological model in teleparallel gravity. In particular, we consider two scalar fields with interaction in scalar-torsion theory. The field equations have a minisuperspace…

Recently we have introduced a nonrelativistic cosmological model (NRCM) exhibiting a dynamical spatial curvature. For this model the present day cosmic acceleration is not attributed to a negative pressure (dark energy) but it is driven by…

Extremely compact objects containing a region of trapped null geodesics could be of astrophysical relevance due to trapping of neutrinos with consequent impact on cooling processes or trapping of gravitational waves. These objects have…

When a small, uncharged, compact object is immersed in an external background spacetime, at zeroth order in its mass it moves as a test particle in the background. At linear order, its own gravitational field alters the geometry around it,…

Using a new geometrical approach introduced by Gibbons and Werner we study the deflection angle by Reissner-Nordstr\"{o}m black holes in the background spacetimes with a global monopole and a cosmic string. By calculating the corresponding…

In the present paper we have discussed the mechanics of incompressible test bodies moving in Riemannian spaces with non-trivial curvature tensors. For Hamilton's equations of motion the solutions have been obtained in the parametrical form…

We attempt to study three significant tests of general relativity in higher dimensions both in commutative and non-commutative spaces. In the context of non-commutative geometry, we will consider a solution of the Einstein equation in…

We consider General Relativity (GR) on a space-time whose spatial slices are compact manifolds $M$ with non-empty boundary $\partial M$. We argue that this theory has a non-trivial space of `vacua', consisting of spatial metrics obtained by…

The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order theories of gravity. We can define effective pressure and energy density directly connected to the Ricci scalar of curvature of a generic…

Geodesic convexity (g-convexity) is a natural generalization of convexity to Riemannian manifolds. However, g-convexity lacks many desirable properties satisfied by Euclidean convexity. For instance, the natural notions of half-spaces and…

Equations of motion of null cosmic strings near black holes, or other massive sources, are solved exactly in the weak field approximation. The stress-energy tensor of a null string in a curved spacetime is introduced and used to show how…

We analyze the null geodesic equations in five dimensional spherically symmetric spacetime with collapsing inhomogeneous dust cloud. By using a new method, we prove the existence and non-existence of solutions to null geodesic equation…

An earlier scheme [arXiv:2404.03360], where torsion plays an essential part in a flat spacetime account of fermion spin, is extended to spacetimes with non-zero Riemann curvature. It is found that further essential features of the fermion,…

Implications of the Raychaudhuri equation in focusing of geodesic congruences are studied in the framework of scalar--tensor theory of gravity. Specifically, we investigate the Brans--Dicke theory and Bekenstein's scalar field theory. In…

The minimal requirement for cosmography - a nondynamical description of the universe - is a prescription for calculating null geodesics, and timelike geodesics as a function of their proper time. In this paper, we consider the most general…

The null geodesic equations in the Alcubierre warp drive spacetime are numerically integrated to determine the angular deflection and redshift of photons which propagate through the distortion of the ``warp drive'' bubble to reach an…

The null energy or null convergence condition (NEC) is one of the fundamental assumptions necessary for many celebrated results from Lorentzian Geometry and Mathematical General Relativity. As such there have been several recent efforts to…

We study the apparition of event horizons in accelerated expanding cosmologies. We give a graphical and analytical representation of the horizons using proper distances to coordinate the events. Our analysis is mainly kinematical. We show…