New Solutions of Tolman-Oppenheimer-Volkov-Equation and of Kerr Spacetime with Matter and the Corresponding Star Models

The Tolman-Oppenheimer-Volkov (TOV) equation is solved with a new ansatz: the external boundary condition with mass M0 and radius R1 is dual to the internal boundary condition with density ρbc and inner radius ri, and the two boundary conditions yield the same result. The inner boundary condition is imposed with a density ρbc and an inner radius ri, which is zero for the compact neutron stars, but non-zero for the shell-stars: stellar shell-star and galactic (supermassive) shell-star. Parametric solutions are calculated for neutron stars, stellar shell-stars, and galactic shell-stars. From the results, an M-R-relation and mass limits for these star models can be extracted. A new method is found for solving the Einstein equations for Kerr space-time with matter (extended Kerr space-time), i.e. rotating matter distribution in its own gravitational field. Then numerical solutions are calculated for several astrophysical models: white dwarf, neutron star, stellar shell-star, and galactic shell-star. The results are that shell-star star models closely resemble the behaviour of abstract black holes, including the Bekenstein-Hawking entropy, but have finite redshifts and escape velocity v c and no singularity.

Impact of Mixed Fillers on the Physico-mechanical Properties of Flex­ible Polyether Foam

The effect of proportional blend of periwinkle and African star apple seed shell as bio-fillers in flexible polyether foam was studied.Flexible polyether foam samples incorporated with these bio-fillers at varying percentages;10%(S1),20%(S2),30%(S3),40%(S4)and 50%(S5)were produced respectively,while 0%(S0)which had no filler was used as control during the experiment.The mechanical properties of the produced foam samples were determined via density,compression set,indentation hardness,tensile strength and elongation at break tests.The cream time,rise time and height of the foam as parameters for characterising the produced foam samples were determined too.Flammability test was also carried out.The microstructure of the foam samples was analysed as well by using the scanning electron microscope.The results of the experiment showed that the density of the foam samples progressively increased from 19.20(S0)-26.45(S5)as the quantity of the filler increased.The indentation hardness result also showed an increase on addition of the filler.The foam’s loading ability also increased on incorporation of the filler but S3 showed remarkable recovery after compression.The tensile strength and elongation at break of the foam decreased on addition of the filler.The morphological analysis ascertained the effect of the progressive introduction of the filler on the surface morphology of the foam.The flammability of the foam was found to decrease as the filler load increased.Since these fillers are of organic origin,readily available,cheap and eco-friendly,they provide a means of making biodegradable foam,and reducing the flammability of foam.Thus,reducing environmental pollution whilst enhancing the mechanical property of foam.