In this work, we study the theory of linearized gravity and prove the linear stability of Schwarzschild black holes as solutions of the vacuum Einstein equations. In particular, we prove that solutions to the linearized vacuum Einstein equations centered at a Schwarzschild metric, with suitably regular initial data, remain uniformly bounded and decay to a linearized Kerr metric on the exterior region. Our method employs Hodge decomposition to split the solution into closed and co-closed portions, respectively identified with even-parity and odd-parity solutions in the physics literature. For both portions, we derive Regge-Wheeler type equations for decoupled, gauge-invariant quantities at the level of perturbed connection coefficients. A general framework for the analysis of Regge-Wheeler type equations is presented, identifying sufficient conditions for decay estimates. With the choice of an appropriate gauge in each of the two portions, such decay estimates on these decoupled quantities are used to establish decay of the linearized metric coefficients, completing the proof of linear stability. The initial value problem is formulated on Cauchy data sets, complementing the work of Dafermos-Holzegel-Rodnianski [6], where the linear stability of Schwarzschild is established for characteristic initial data sets.

Supermassive black hole binaries (SMBHBs) are the natural consequence of galaxy mergers and should form frequently in galactic nuclei. Especially at sub-parsec separations, where the binary evolution is slow, SMBHBs should be fairly abundant. However, the observational evidence remains elusive. In this thesis, we focus on periodic variability of quasars as a potential signature of compact SMBHBs. First, we present a systematic search for periodic variability in the photometric database of the Palomar Transient Factory. Our search in a large sample of ~35,000 quasars returned 50 candidates, 33 of which remain significant after the reanalysis of extended light curves including data from the Catalina Real-Time Transient Survey and the intermediate PTF. Our candidates have periods of a few hundred days. Next, we focus on independent signatures that could verify the binary nature of the candidates. We present a case study of quasar PKS 1302-102, the first candidate that emerged from the large time-domain surveys. We search for multiple periodic components in the variability with a characteristic frequency pattern predicted by hydrodynamical simulations of circumbinary disks. We do not find compelling evidence for a secondary period. Additionally, in compact SMBHBs, relativistic Doppler boost should be significant and may dominate the variability. This model was suggested as a smoking-gun signature for quasar PKS 1302-102, since it is not expected in quasars with a single BH and it offers a robust prediction, which can be tested with multi-wavelength data. With a control sample of non-periodic quasars, we test whether this signature is distinct from the intrinsic multi-wavelength variability of quasars. We concluded that the Doppler boost does not provide a sharp test for SMBHBs.

Higher dimensional black holes are studied in the extra large dimensions scenario. Bulk fermion quasi-normal modes and bulk fermion Hawking emission is calculated. It is found that bulk emission dominates brane emission for d > 5. / To address the Planck phase an effective field theory is investigated. Lepton family number violating processes are elucidated and the corrections to the muon magnetic moment from these channels are calculated. Bounds are placed on the couplings of the theory. / A discrete symmetry between quarks and leptons, and left- right- chirality fields, is orbifolded in 5 dimensions. Using split fermions a one generational standard model extension is found. / An investigation of entanglement in black holes and accelerated motion is presented. It is found that in a certain system the acceleration between two spinors enhances the rate of their disentanglement.

In the following, we build on previous work done on higher derivative gravity, in particular Lovelock gravity. The latter is a family of theories in higher space-time dimensions in which interactions involving higher powers of curvature are introduced, but the equations of motion remain second order in derivatives. We develop a new theory involving cubic terms in the curvature. We then show that the equations of motion for graviton fluctuations remain second order. The curvature cubed term is shown not to be a topological object, contrary to the belief that dimensionally extended Euler densities provided the only stable dimensionally continued theories of gravity (Lovelock gravity). Black hole solutions are studied in this new gravitational framework.

In the following, we build on previous work done on higher derivative gravity, in particular Lovelock gravity. The latter is a family of theories in higher space-time dimensions in which interactions involving higher powers of curvature are introduced, but the equations of motion remain second order in derivatives. We develop a new theory involving cubic terms in the curvature. We then show that the equations of motion for graviton fluctuations remain second order. The curvature cubed term is shown not to be a topological object, contrary to the belief that dimensionally extended Euler densities provided the only stable dimensionally continued theories of gravity (Lovelock gravity). Black hole solutions are studied in this new gravitational framework.

Thesis (Ph. D.)--University of Alberta, 2009. / Title from pdf file main screen (viewed on Jan. 5, 2010). "A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Department of Physics, University of Alberta." Includes bibliographical references.

Thesis (Ph. D.)--Open University. BLDSC no. DXN041011.

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 110-116). Available also in a digital version from Dissertation Abstracts.

This dissertation addresses the co-evolutionary relationship between central super-massive black holes and host galaxies. This relationship is suggested by observed correlations between black hole mass (M[subscript BH]) and properties of the host galaxy bulge. We first discuss investigation of the relationship between MBH and host galaxy velocity dispersion, [sigma subscript asterisk], for quasars in the Sloan Digital Sky Survey (SDSS). We derive MBH from the broad emission line width and continuum luminosity, and [sigma subscript asterisk] from the width of narrow forbidden emission lines. For redshifts z < 0.5, our results agree with the locally-observed M[subscript BH]- [sigma subscript asterisk] relationship. For 0.5 < z < 1.2, the M[subscript BH]- [sigma subscript asterisk] relationship appears to evolve with redshift in the sense that bulges are too small for their black holes. Part of this apparent trend can be attributed to observational biases, including a Malmquist bias involving the quasar luminosity. Accounting for these biases, we find approximately a factor of two evolution in the M[subscript BH]- [sigma subscript asterisk] relationship between the present and redshift z [approximately equal] 1. The second topic involves a search for the largest velocity dispersion galaxies in the SDSS. Black holes in quasars can have M[subscript BH]exceeding 5 billion M[mass compared to the sun], implying [sigma subscript asterisk] > 500 km s−1 by the local M[subscript BH]- [sigma subscript asterisk] relationship. We present high signal-to-noise HET observations for eight galaxies at redshift z < 0.3 from the SDSS showing large [sigma subscript asterisk] while appearing to be single galaxies in HST images. The maximum velocity dispersion we find is [sigma subscript asterisk] = 444 km s−1, suggesting either that quasar black hole masses are overestimated or that the black hole - bulge relationship changes at high black hole mass. The third topic involves work contributed to co-authored papers, including: (1) evidence for recoiling black holes in SDSS quasars, (2) the [sigma][O III] - [sigma subscript asterisk] relationship in active galactic nuclei (AGN), and (3) accretion disk temperatures and continuum colors in quasars. Lastly, we discuss research in progress, including: (1) possible physical influences on the width of narrow emission lines of SDSS AGN, including the gravitational effect of the black hole, and (2) a search for binary AGN in the SDSS using double-peaked [O III] emission lines. / text

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