Narrow Results

We take another look at the equations behind the description of light bending in a Universe with a cosmological constant. We show that even within the impact parameter entering into the photon's differential equation, and which is defined here with exclusive reference to the beam of light as it bends around the central mass, lies the contribution of the cosmological constant. The latter is shown to enter in a novel way into the equation. When the latter is solved our approach implies, beyond the first two orders in the mass-term and the lowest-order in the cosmological constant, a slightly different expression for the bending angle from what is previously found in the literature.

In this paper, we show that the causally connected four-dimensional line element of the $\kappa$-deformed Minkowski spacetime induces an upper cut-off on the proper acceleration and derive this maximal acceleration, valid up to first order in the deformation parameter. We find a contribution to maximal acceleration which is independent of $\hslash$ and thus signals effect of the non-commutativity alone. We also construct the $\kappa$-deformed geodesic equation and obtain its $\kappa$-deformed Newtonian limit, valid up to first order in deformation parameter. Using this, we constrain non-commutative parameters present in the expression for maximal acceleration. We analyze different limits of the maximal acceleration and also discuss its implication to maximal temperature. We also obtain a bound on the deformation parameter.

The semiclassical tunneling technique proposed by Parikh and Wilczek to study Hawking radiation of static and stationary black holes has been extensively used to investigate the Hawking radiation of different types of black holes. In this paper, the geodesic equation of charged massive particle and the massless particle are obtained by using the Lagrangian analysis. The geodesic equations of charged massive particle and massless particle are determined uniformly and consistently. Based on the geodesic equation, the Hawking radiation of the charged massive particle is investigated near the event horizon of Kerr–Newman–de Sitter black hole. By finding the imaginary part of the action of charged massive particle, the Hawking temperature and the tunneling probability of charged massive particle across the event horizon of KNdS black hole are obtained. The finding of this paper is a development for Parikh–Wilczek’s tunneling technique.

Relativistic mechanics on an arbitrary manifold is formulated in the terms of jets of its one-dimensional submanifolds. A generic relativistic Lagrangian is constructed. Relativistic mechanics on a pseudo-Riemannian manifold is particularly considered.

In this study, we obtain Noether gauge symmetries of geodesic motion for geodesic Lagrangian of stationary and nonstatic Gödel-type spacetimes, and find the first integrals of corresponding spacetimes to derive a complete characterization of the geodesic motion. Using the obtained expressions for of each spacetimes, we explicitly integrate the geodesic equations of motion for the corresponding stationary and nonstatic Gödel-type spacetimes.

There is much talk of a “mysterious form of energy”, called “dark energy” that forms the bulk of the energy content of the Universe. Perhaps the most mysterious aspect of it is why it should be regarded as mysterious in the first place. This question is discussed in the context of the development of relativity and relativistic cosmology. It will be argued that there is no good reason to treat it as other than Einstein’s cosmological constant.

We argue that the minimal length discretization generalizing the Heisenberg uncertainty principle, in which the gravitational impacts on the non–commutation relations are thoughtfully taken into account, radically modifies the spacetime geometry. The resulting metric tensor and geodesic equation combine the general relativity terms with additional terms depending on higher–order derivatives. Suggesting solutions for the modified geodesics, for instance, isn’t a trivial task. We discuss on the properties of the resulting metric tensor, line element, and geodesic equation.

With a new method based on the theory of hyperelliptic functions we solve geodesic equations in higher dimensional spherically symmetric space-times: Schwarzschild (9,11), Schwarzschild-de Sitter (9,11), Reissner-Nordström (7) and Reissner-Nordström-de Sitter (4,7). The equations of motion in the considered space-times contain the underlying polynomial of degree 5 or 6, corresponding to a genus 2 curve.

It has been shown that the Hamilton-Jacobi equation corresponding to the geodesic equation in a Petrov type D space-time is separable and, thus, integrable. All Petrov type D space-times are exhausted by the Plebański-Demiański electrovac solutions with vanishing acceleration of the gravitating source. Here we present the analytical integration of the geodesic equations in these space-times. Based on the general solution we discuss the special cases of geodesics in Taub-NUT and Kerr-de Sitter space-times. We define observables and also address the issue of geodesic incompleteness.

In this article we have considered and analyzed the new aspects of the rest mass concept of the 5D charged test particle which interacts with the scalar gravitational field and also it was shown that the 5D Ricci identities give us the way to clear the magnetic monopole problem.