Astronomy and Astrophysics – Astrophysics
Scientific paper
Jan 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996phdt........10m&link_type=abstract
Thesis (PH.D.)--THE UNIVERSITY OF CONNECTICUT, 1996.Source: Dissertation Abstracts International, Volume: 57-06, Section: B, pag
Astronomy and Astrophysics
Astrophysics
Scientific paper
Primordial black holes were conjectured, by quantum theory, to have formed in the early universe as a result of the conditions that existed then. At their time of formation these were tiny (probably atomic size) holes which radiated energy at a rate related to their surface temperature. Because nobody has found them yet, it is natural to wonder about their evolution and fate. The original aim of this research was to study the response of these black holes to external gravitational perturbations. This would, hopefully, give one an idea of how the holes evolved since the radiation era. It was, however, soon found out that no theory exists to describe gravitational perturbations of radiating spacetimes, in general. This finding broadened the motivation for the research. Consequently, this dissertation attempts to initiate research in the area of gravitational perturbations of radiating spacetimes. Using the null tetrad calculus of Newman and Penrose the field perturbation equations that describe the problem are derived. It is shown that all the perturbations are sufficiently described by only two scalars which satisfy two partial differential equations. For the self-similar model of a radiating black hole, these equations are found separable! The resulting radial-null equations have singularities which are all shown to be regular. This has made it possible to obtain analytic solutions for the gravitational perturbation field equations. As far as we know, no analytic solutions have been obtained before in perturbation problems involving gravitational fields. The solutions reduce to those of the perturbed Schwarzchild geometry, as the background radiation is switched off. Moreover, their asymptotic form is completely consistent with the peeling theorem of R. Penrose. Both these characteristics are used to validate the theory. The solutions reveal that when gravitational fields propagate in a Vaidya spacetime, they suffer an attenuation in their amplitude. Further, the energy flux calculation at null infinity shows evidence of energy dumping into the black holes. This suggests that these black holes could have grown and cooled down as time went on. On this basis it is possible that some primordial black holes may not have radiated themselves away, after all, but may have evolved to take on the characteristics not unlike those of the astrophysical black hole! This is not to suggest that all astrophysical black holes are primordial. The dissertation ends by suggesting where these black holes might be. Projections for future research are also discussed.
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