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Topic Review

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.

66
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.

21
23 Jan 2026

Topic Review

New Theoretical Improvements in the Investigation of the Neutron-Star-Accretion-Objects Cusps

It is my aim to revise the relevant features of the cusp structures that arise on from the accretion objects of neutron stars. The theoretical characteristics of the known schemes and the pertinent observational techniques and evidences are described. The complete description of a neutron star is that of the celestial object surrounded of macroscopic matter (solution of the Einstein Field Equations), where the scheme of the dust can be takes as a simple instance, from which the cusps structures arise. The accretion object can be modellized as a thin disc, a thick disc, an advection-dominated flow (which is analysed as gaseous) , or an accretion ring. The presence of magnetic fields is included in the magneto-hydro-dynamics complete parametrization of the neutron star. The identification of the neutron-star accretion objects from those of other relativistic stars has been a relevant effort, i.e., the discrimination of the neutron star accretion objects from the blackhole accretion objects has been pursued both from a theoretical point of view, and experimentally, according also to the luminosity of the objects and from the ejecta. At the moment, the theoretical interpretation of the accretion objects of neutron stars is delineated, and the present limitations in the description of cusps are elucidated. The new consequences of the understandings of the further missing elements in the theoretical analysis of the analytical functional dependences among the description of the foundational components of the neutron stars (i.e., spin, mass, and radius) are exposed. The geometries of these spacetimes are described after the metric tensor; the use of cataclysmic variables is commented as a valid tool: nevertheless, new sets of variables are to be considered. The role of the gravitational pressure within the radiation-pressure-supported objects is revised to be applied; as a further development, the implementation of the new corresponding General-Relativistic-Magneto-Hydro-Dynamics is to be now looked for.

17
14 May 2026

Topic Review

Preparation of General-Relativistic Solitons from Calabi-Yau Varieties- from Conic-Singularity Manifolds to GR-Geodesics Paths: The Instance of the Calabi-Yau Crepant Cones Resolutions

It is my aim to investigate the conditions under which a manifold with conic singularity is made to correspond to the GR spacetimes, i.e., to one endowed with the complete fundamental group, after the base point of the conic singularity is removed. The crepant resolution of conical singularities is discussed within this context. For these purposes, the meterization conditions of Zariski topologies are recalled after the Troyanov theorems are scrutinized. The preparation of the General-Relativistic spacetimes originated after the exposed methodologies from the pertinent Calabi-Yau manifolds is described. In particular, the tangent ﬂows on meterized Ricci gradient solitons is proven to be unique after the Einstein Field Equations are imposed; the details of the preparation are discussed for shrinkers. The Einsteinian spacetimes with vanishing volume growth of the meterized solitons are then prepared.

10
25 Apr 2026

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