arXiv subjects

Sheref Nasereldin

Publications and source records attributed to Sheref Nasereldin.

4 recordsLinked to original sources

arXiv2026

Static axisymmetric Einstein spaces with a cosmological constant and the limitation of canonical Weyl coordinates

The canonical Weyl form for four-dimensional static axisymmetric vacuum metrics is obtained by identifying the area function of the two Killing orbits with a harmonic coordinate on the twodimensional orbit space. This construction is valid in Ricci-flat vacuum, but it is no longer available in Einstein spaces with nonzero cosmological constant. In this paper, we consider the generalized orthogonally transitive static axisymmetric line element and derive the reduced Einstein- $\Lambda$ field equations. We show that the canonical Weyl choice $W=\rho$ is locally admissible if and only if $\Lambda=0$. The Kottler metric gives the simplest explicit example of the resulting equation for the area function. Thus, the statement that "Weyl metrics do not allow $\Lambda \neq 0$ " is precise only when the metric is assumed to be in canonical Weyl coordinates. The issue is not staticity or axisymmetry, but rather the fact that the area function is no longer harmonic.

gr-qc↗

arXiv2023

Constructing maximal extensions of the Vaidya metric in Israel coordinates: II. The completeness of Israel coordinates

We present the results of an analysis of three maximal extensions of the Vaidya metric in Israel coordinates, a spherically symmetric solution to the Einstein field equations for the energy momentum tensor of pure radiation in the high-frequency approximation. This metric is necessary for various applications, such as describing the exterior geometry of a radiating star in astrophysics and studying possible formation of naked singularities in the geometry of spacetime. Contrary to the common Eddington-Finkelstein-like (EFL) coordinates, these maximal extensions, in Israel coordinates, are complete and cover the entirety of the Vaidya manifold. We develop three mass functions, one for each extension, and consider the qualitative characteristics of the three mass models and the surfaces of constant (dynamical) radius. We demonstrate that each maximal extension is null geodesically complete, which we assess by solving the radial null geodesics equation and forming the Penrose conformal diagram for each extension.

gr-qc↗

arXiv2023

Constructing Maximal Extensions of the Vaidya Metric in Israel Coordinates: I. Integration of the Field Equations

This paper explores a complete representation of the Vaidya model, a radial flux of radiation in the eikonal approximation, used for modeling various phenomena in both classical and semi-classical General Relativity and Astrophysics. The majority of the applications of the Vaidya model have been formulated in an incomplete representation. A complete representation is obtained here by direct integration of the Einstein field equations. We present the methodology to obtain this complete representation, and its utility in the modeling of general relativistic phenomena.

gr-qc↗

arXiv2019

Boundary Orbits: 1 Static Spacetimes

The study of circular orbits in spacetime is of astrophysical importance. The identification and classification of circular orbits in both static and stationary spacetimes remains an active area of interest. Even in the simplest static spherically symmetric case, it is well known that the introduction of a cosmological constant in vacuum leads to the study of quartic polynomials in order to locate \textit{boundary orbits}, those that straddle between stable and unstable orbits. These orbits are often referred to as `marginally stable orbits' or `indifferently stable orbits'. A comprehensive study of texts offers little clarification as to the stability or instability of these boundary orbits. Here we argue that the direct use of second order perturbation theory immediately shows that these boundary orbits are unstable in the perturbative sense. Our study here includes the two-particle Curzon-Chazy solution.

gr-qc↗