Time Evolution of Entropy in Gravitational Collapse

We study the time evolution of the entropy of a collapsing spherical domain wall, from the point of view of an asymptotic observer, by investigating the entropy of the entire system (i.e. domain wall and radiation) and induced radiation alone during the collapse. By taking the difference, we find the entropy of the collapsing domain wall, since this is the object which will form a black hole. We find that for large values of time (times larger than $t/R_s\approx8$), the entropy of the collapsing domain wall is a constant, which is of the same order as the Bekenstein-Hawking entropy.Comment: 9 pages, 6 figure

The postcranial skeleton of the Early Triassic parareptile Sauropareion anoplus, with a discussion of possible life history

The skeletal anatomy of the Early Triassic (Induan) procolophonid reptile Sauropareion anoplusis described on the basis of three partial skeletons from Vangfontein, Middelburg District, South Africa. Together these three specimens preserve the large majority of the pectoral and pelvic girdles, articulated forelimbs and hindlimbs, and all but the caudal portion of the vertebral column, elements hitherto undescribed. Our phylogenetic analysis of the Procolophonoidea is consonant with previous work, positing S. anoplus as the sister taxon to a clade composed of all other procolophonids exclusive of Coletta seca. Previous studies have suggested that procolophonids were burrowers, and this seems to have been the case for S. anoplus, based on comparisons with characteristic skeletal anatomy of living digging animals, such as the presence of a spade−shaped skull, robust phalanges, and large unguals

Alpha taxonomy of the Russian Permian procolophonoids

European Russia has been the source of many procolophonoid taxa from both the Permian and Triassic, and a Permian or− igin for the procolophonoid family Procolophonidae has been based on the Russian taxon Microphon exiguus. Recently, this taxon was reclassified as a seymouriamorph and, in its place, the taxa Nyctiphruretus, Suchonosaurus, and Kinelia from the Middle and Upper Permian of Russia were suggested as “procolophons”, using evolutionary−systematic classifi− cation methods. In recent phylogenies, however, Nyctiphruretus has been recovered as a non–procolophonoid para− reptile, whereas Kinelia and Suchonosaurus have never been included in a phylogenetic study. Re−examination indicates that Suchonosaurus is a member of the procolophonoid subfamily Procolophonidae based on the shape of the maxillary bone and the external naris, the laterally visible maxillary depression, and the number and type of maxillary teeth. Kinelia, on the other hand, is excluded from the Procolophonoidea because of its subpleurodont dental attachment and lack of any procolophonoid features. Thus, Suchonosaurus is the only confirmed Permian procolophonid from the Permian of Rus− sia. Additionally, re−examination of the holotype of Microphon exiguus confirms that it is identical to the seymouria− morph specimens recently included in the genus Microphon and that it lacks procolophonoid features. The earliest un− equivocal record of the subfamily Procolophonidae is confirmed from the Late Permian of Russia, making Russia the only region where, with certainty, both Permian and Triassic procolophonids have been discovered