This thesis consists of three separate studies of roles that black holes mightplay in our universe.
In the first part we formulate a statistical method for inferring the cosmologicalparameters of our universe from LIGO/VIRGO measurements of the gravitationalwaves produced by coalescing black-hole/neutron-star binaries. This method isbased on the cosmological distance-redshift relation, with "luminosity distances"determined directly, and redshifts indirectly, from the gravitational waveforms.Using the current estimates of binary coalescence rates and projected "advanced"LIGO noise spectra, we conclude that by our method the Hubble constant shouldbe measurable to within an error of a few percent. The errors for the mean densityof the universe and the cosmological constant will depend strongly on the size ofthe universe, varying from about 10% for a "small" universe up to and beyond100% for a "large" universe. We further study the effects of random gravitationallensing and find that it may strongly impair the determination of the cosmologicalconstant.
In the second part of this thesis we disprove a conjecture that black holes cannotform in an early, inflationary era of our universe, because of a quantum-field-theory inducedinstability of the black-hole horizon. This instability was supposed to arisefrom the difference in temperatures of any black-hole horizon and the inflationarycosmological horizon; it was thought that this temperature difference would makeevery quantum state that is regular at the cosmological horizon be singular atthe black-hole horizon. We disprove this conjecture by explicitly constructing aquantum vacuum state that is everywhere regular for a massless scalar field. Wefurther show that this quantum state has all the nice thermal properties that onehas come to expect of "good" vacuum states, both at the black-hole horizon andat the cosmological horizon.
In the third part of the thesis we study the evolution and implications of a hypotheticalprimordial black hole that might have found its way into the center of theSun or any other solar-type star. As a foundation for our analysis, we generalizethe mixing-length theory of convection to an optically thick, spherically symmetricaccretion flow (and find in passing that the radial stretching of the inflowing fluidelements leads to a modification of the standard Schwarzschild criterion for convection).When the accretion is that of solar matter onto the primordial hole, therotation of the Sun causes centrifugal hangup of the inflow near the hole, resultingin an "accretion torus" which produces an enhanced outflow of heat. We find, however, that the turbulent viscosity, which accompanies the convective transportof this heat, extracts angular momentum from the inflowing gas, thereby bufferingthe torus into a lower luminosity than one might have expected. As a result, thesolar surface will not be influenced noticeably by the torus's luminosity until atmost three days before the Sun is finally devoured by the black hole. As a simpleconsequence, accretion onto a black hole inside the Sun cannot be an answer tothe solar neutrino puzzle.
