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How to Apply the (Total)-Umbilicity Conditions Ofstatic-Fridman-Robertson-Walker Spacetimesin Vacuum

Generalized-Fridman-Robertson-Walker spacetimes are newly analyzed. The locally-conformal flatness of generalized Fridman-Robertson-Walker spacetimes is discussed within the framework of the study of the constant-ness of the sectional curvature. The cases of vanishing mean curvature are taken into account. The methodology to apply the results and the new prospective studies to weighted manifolds is introduced. The total-umbilicity condition(s) are examined. The application of the strong energy condition is followed after the definition of maximal spacelike hypersurfaces, which are spelled out to constitute a solution of the Ricci flow which obeys the Einstein-Field Equations.

44
19 Jan 2026

Topic Review

The Blackhole-Disc Cuspsin General Relativity

The presence of cusps in Astrophysical accretion objects of compact objects has long been theoretically predicted. The qualities of blackhole accretion objects are here reviewed. The properties of cusps are delineated. The description of Astrophysical sources allowing for a classification of the location of the radius of the inner cusp is presented. The qualifications of cusps in accretion objects from generalized Theories of gravity are scrutinized.

7
23 Jan 2026

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