arXiv subjects
Publications and source records attributed to Abbas Sherif.
Let $M$ be a locally rotationally symmetric spacetime with at least one of the rotation or spatial twist being non-zero. It is proved that $M$ cannot admit a non-minimal marginally trapped tube of the form $χ=X(t)$.
We construct a Geroch-like boundary (when restricted to geodesic curves, this boundary contains as a subset the Geroch's $g$ boundary), which we denote by $\tilde{g}$, and establish an explicit embedding of the $\tilde{g}$ boundary into the $a$ boundary of Scott and Szekeres. This construction, and subsequently the explicit embedding, is done in a 'natural' way (the emphasis on the word natural here will be clarified in the text), thereby answering in the affirmative the outstanding question as to whether there exists a natural way to relate the $g$ and the $a$ boundary constructions.
Extending a previous work by the same authors, we investigate the existence of expansion-free dynamical stars with non-zero spatial twist and rotation and show that such stars cannot exist. Firstly, it is shown that a rotating expansion-free dynamical star with zero twist cannot exist. This is due to the fact that such stars cannot radiate and they are shear-free, in which case the energy density $ρ$ is time independent. Secondly, we prove that a non-rotating expansion-free dynamical star with non-zero spatial twist also cannot exist, as either the strong energy condition must be violated, i.e. $ρ+3p<0$, or the star must be shear-free in which case the star is static ($Θ=Ω=Σ=0$). Finally, if we insist that the rotation and spatial twist are simultaneously non-zero, then the star cannot be shear-free in which case we obtain a quadratic polynomial equation in $ϕ$ and $Σ$ with no real solutions. Therefore such stars cannot exist.
We study the evolution of horizons of black holes in the $1+1+2$ covariant setting and investigate various properties intrinsic to the geometry of the foliation surfaces of these horizons. This is done by interpreting formulations of various quantities in terms of the geometric and thermodynamic quantities. We establish a causal classification for horizons in different classes of spacetimes. We have also recovered results by Ben-Dov and Senovilla which put cut-offs on the equation of state parameter $σ$, determining the spacelike, timelike and non-expanding horizons in the the Robertson-Walker class of spacetimes. We show that stability of marginally trapped surfaces (MTS) in the Robertson-Walker spacetimes is only achievable under the conditions of negative pressure, and also classify the spacelike future outer trapping horizons (SFOTH) in the Robertson-Walker spacetimes via bounds on the equation of state parameter $σ$. For the Lemaitre-Tolman-Bondi (LTB) model, it is shown that a relationship between the energy density and the electric part of the Weyl curvature, $\mathcal{E}$, gives the causal classification of the MTTs. It is further shown that only spacelike MTTs are foliated by stable MTS, and that this stability guarantees no shell crossing. We also provide an explicit proof of the third law of black hole thermodynamics for the LRS II class of spacetimes, and by extension, any spacetime whose outgoing and ingoing null geodesics are normal to the MTS.
We study the geometrical and dynamical features of expansion-free dynamical stars in general relativity. Such stars can exist only if particular physical and geometric conditions are satisfied. Firstly, for trapping to exist in an expansion-free dynamical star, the star must accelerate and radiate simultaneously. If either are zero, then the shear \(Sigma\) must be zero through out the star, in which case the star is static (\(Θ=Σ=0\)). Secondly, we prove that with nonzero acceleration and radiation expansion-free dynamical stars must be conformally flat.
In this paper, we perform a detailed investigation on the various geometrical properties of trapped surfaces and the boundaries of trapped region in general relativity. This treatment extends earlier work on LRS II spacetimes to a general 4 dimensional spacetime manifold. Using a semi-tetrad covariant formalism, that provides a set of geometrical and matter variables, we transparently demonstrate the evolution of the trapped region and also extend Hawking's topology theorem to a wider class of spacetimes. In addition, we perform a stability analysis for the apparent horizons in this formalism, encompassing earlier works on this subject. As examples, we consider the stability of MOTS of the Schwarzschild geometry and Oppenheimer-Snyder collapse.