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Mohamed Sherif, Abbas
기하학 수리물리 연구단
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On some locally symmetric embedded spaces with non-negative scalar curvature and their characterization

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Title
On some locally symmetric embedded spaces with non-negative scalar curvature and their characterization
Author(s)
Abbas M. Sherif; Dunsby, Peter K. S.; Goswami, Rituparno
Publication Date
2022-03
Journal
International Journal of Geometric Methods in Modern Physics, v.19, no.04
Publisher
World Scientific
Abstract
© 2022 World Scientific Publishing Company.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. First, 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 with 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. If such hypersurface does admit a Ricci soliton structure, the soliton is steady, with the components of the soliton field being constants.
URI
https://pr.ibs.re.kr/handle/8788114/12155
DOI
10.1142/S0219887822500517
ISSN
0219-8878
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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