Analytical Steps Towards the Observation of High-Spin Black Holes

Abstract

Ongoing astronomical efforts extract physical properties of a black hole from electromagnetic emissions in its vicinity. In this dissertation, we analytically study such emissions from the near-horizon region of high-spin black holes. Given the complexity of the Kerr metric, null geodesics in the spacetime of a rotating black hole are generally studied only numerically. Subsequent modelling involves extensive numerical work. In the case of a high-spin black hole, however, a simplification occurs when we zoom into its near-horizon region. This so-called Near-Horizon Extreme Kerr geometry has an SL(2,R)XU(1) isometry. In particular, the time translation symmetry is enlarged to an SL(2,R) global conformal symmetry, which includes dilations and special-conformal transformations. Our analytical methods are based upon these enhanced symmetries. We first solve for the near-superradiant geodesics that extend from the near-horizon region to a distant observatory, expressing our results in terms of elementary functions. Next we compute the broadening of electromagnetic line emissions from the innermost part of an accretion disk. We obtain an analytic formula for the observed flux, which is independent of the disk model and therefore universal. Finally, we investigate the polarized near-horizon emissions and find patterns of whorls aligned with the black hole's spin.