arXiv subjects

Abbas M Sherif

Publications and source records attributed to Abbas M Sherif.

4 recordsLinked to original sources

arXiv2026

A complete correspondence between the Newman-Penrose and 1+1+2 formalisms

We establish a correspondence between the Newman-Penrose and 1+1+2 semitetrad covariant formalisms by expressing all Newman-Penrose spin coefficients, Ricci scalars, and Weyl scalars in terms of the scalar, vector, and tensor variables of the 1+1+2 decomposition. In addition, we provide some discussions on the correspondence between the gauge structures of the formalisms. This provides a direct dictionary between two widely used approaches to general relativity and gives a geometrical interpretation of Newman-Penrose quantities in terms of covariantly defined 1+1+2 variables. As a simple demonstration, we use this mapping to derive inequalities on the Newman-Penrose scalars and the cosmological constant, which constrains the existence of future outer trapping horizons in spacetimes exhibiting local rotational symmetry.

gr-qc↗

arXiv2024

Gradient conformal stationarity and the CMC condition in LRS spacetimes

We study the existence of gradient conformal Killing vectors (CKVs) in the class of locally rotationally symmetric (LRS) spacetimes which generalizes spherically symmetric spacetimes, and investigate some implications for the evolutionary character of marginally outer trapped surfaces. We first study existence of gradient CKVs via the obtention of a relationship between the Ricci curvature and the gradient of the divergence of the CKV. This provides an alternative set of equations, for which the integrability condition is obtained, to analyze the existence of gradient CKVs. A uniqueness result is obtained in the case of perfect fluids, where it is demonstrated that the Robertson-Walker solution is the unique perfect fluid solution with a nonvanishing pressure, admitting a timelike gradient CKV. The constant mean curvature condition for LRS spacetimes is also obtained, characterized by three distinct conditions which are specified by a set of three scalars. Linear combinations of these scalars, whose vanishing define the constant mean curvature condition, turn out to be related to the evolutions of null expansions of 2-spheres along their null normal directions. As such, some implications for the existence of black holes and the character of the associated horizons are obtained. It is further shown that dynamical black holes of increasing area, with a non-vanishing heat flux across the horizon, will be in equilibrium, with respect to the frame of the conformal observers.

gr-qc↗

arXiv2024

Existence of gradient CKV and gradient conformally stationary LRS spacetimes

In this work, we study the existence of gradient (proper) CKVs in locally rotationally symmetric spacetimes (LRS), those CKVs in the space spanned by the tangent to observers' congruence and the preferred spatial direction, allowing us to provide a (partial) characterization of gradient conformally static (GCSt) LRS solutions. Irrrotational solutions with non-zero spatial twist admit an irrotational timelike gradient conformal Killing vector field and hence are GCSt. In the case that both the vorticity and twist vanish, that is, restricting to the LRS II subclass, we obtain the necessary and sufficient condition for the spacetime to admit a gradient CKV. This is given by a single wave-like PDE, whose solutions are in bijection to the gradient CKVs on the spacetime. We then introduce a characterization of these spacetimes as GCSt using the character of the divergence of the CKV, provided that the metric functions of the spacetimes obey certain inequalities.

gr-qc↗

arXiv2021

On some locally symmetric embedded spaces with non-negative scalar curvature and their characterization

In this work we perform a general study of properties of a class of locally symmetric embedded hypersurfaces in spacetimes admitting a $1+1+2$ spacetime decomposition. The hypersurfaces are given by specifying the form of the Ricci tensor with respect to the induced metric. These are slices of constant time in the spacetime. Firstly, the form of the Ricci tensor for general hypersurfaces is obtained and the conditions under which the general case reduces to those of constant time slices are specified. We provide a characterization of these hypersurfaces, with key physical quantities in the spacetime playing a role in specifying the local geometry of these hypersurfaces. Furthermore, we investigate the case where these hypersurfaces admit a Ricci soliton structure. The particular cases where the vector fields associated to the solitons are Killing or conformal Killing vector fields are analyzed. Finally, in the context of spacetimes with local rotational symmetry it is shown that, only spacetimes in this class with vanishing rotation and spatial twist can admit the hypersurface types considered, and that the hypersurfaces are necessarily flat. And if such hypersurface do admit a Ricci soliton structure, the soliton is steady, with the components of the soliton field being constants.

gr-qc↗