Abstract
Ultra-Compact Objects (ucos) have been found tobe interesting astrophysical entities. The existence ofsuch a possible stable object has been discussed byconsidering the stability of Tolman's type VII solution which is one of the few physicallyrelevant exact solutions of Einstein's field equationsfor a static and spherically symmetric massdistribution. A distinctive feature of this solutionamong the others is that the surface density alsodrops to zero (i.e., the continuity of density, and therespective derivative of the metric parameter(λ′) is also assured at the surface of theconfiguration). The stability analysis of this solution,according to the variational method [20], as well as thebinding-energy criteria of fluid spheres shows that theconfiguration remains stable at least up to a central redshift, z0 ≤ 5.09, and surfaceredshift, za ≤ 0.78 (i.e. up to a u≡ mass/size) value ≤0.3428), thereby confirmingthe existence of an ultracompact object (uco) thatcorresponds to a mass to size ratio (u ≡ M/a) ≥ 1/3.
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Negi, P.S., Durgapal, M.C. Stable Ultracompact Objects. General Relativity and Gravitation 31, 13–20 (1999). https://doi.org/10.1023/A:1018807219245
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DOI: https://doi.org/10.1023/A:1018807219245