Physics
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Item Investigations on entanglement entropy in gravity(2018) Speranza, Antony John; Jacobson, Theodore; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Entanglement entropy first arose from attempts to understand the entropy of black holes, and is believed to play a crucial role in a complete description of quantum gravity. This thesis explores some proposed connections between entanglement entropy and the geometry of spacetime. One such connection is the ability to derive gravitational field equations from entanglement identities. I will discuss a specific derivation of the Einstein equation from an equilibrium condition satisfied by entanglement entropy, and explore a subtlety in the construction when the matter fields are not conformally invariant. As a further generalization, I extend the argument to include higher curvature theories of gravity, whose consideration is necessitated by the presence of subleading divergences in the entanglement entropy beyond the area law. A deeper issue in this construction, as well as in more general considerations identifying black hole entropy with entanglement entropy, is that the entropy is ambiguous for gauge fields and gravitons. The ambiguity stems from how one handles edge modes at the entangling surface, which parameterize the gauge transformations that are broken by the presence of the boundary. The final part of this thesis is devoted to identifying the edge modes in arbitrary diffeomorphism-invariant theories. Edge modes are conjectured to provide a statistical description of the black hole entropy, and this work takes some initial steps toward checking this conjecture in higher curvature theories.Item Novel Techniques for Simulation and Analysis of Black Hole Mergers(2011) Boggs, William Darian; Tiglio, Manuel; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation consists of three research topics from numerical relativity: waveforms from inspiral mergers of black hole binaries, recoils from head-on mergers of black holes, and a new computational technique for error-reduction. The first two topics present research from journal articles that I coauthored with my colleagues in the NASA Goddard Numerical Relativity research group. Chapter 2 discusses a heuristic model of black hole binary mergers and the waveforms produced by them, based on simulations of nonspinning black holes. The gravitational radiation is interpreted as the result of an implicit rotating source that generates the radiation modes as the source multipoles rotate coherently. This interpretation of the waveform phase evolution provides a unified physical picture of the inspiral, plunge, and ringdown of the binaries, and it is the basis of an analytic model of the late-time frequency evolution. Chapter 3 presents a study of kicks in head-on black hole mergers, emphasizing the distinct contributions of spin and mass ratio, as well as their combined effects, to these radiation-induced recoils. The simpler dynamics of head-on mergers allow a more clear separation of the two types of kick and a validation of post-Newtonian predictions for the spin scaling of kicks. Finally, Chapter 4 presents a technique I developed to improve the accuracy of the field evolution in numerical relativity simulations. This "moving patches" technique uses local coordinate frames to minimize black hole motion and reduce error due to advection terms. In tests of the technique, I demonstrate reduction in constraint violations and in errors in the orbital frequency derived from the black holes' motions. I also demonstrate an accuracy gain in a new diagnostic quantity based on orbital angular momentum. I developed this diagnostic for evaluating the moving patches technique, but it has broader applicability. Though the moving patches technique has significant performance costs, these limitations are specific to the current implementation, and it promises greater efficiency and accuracy in the future.Item Submillimeter Test of the Gravitational Inverse-Square Law Using a Superconducting Differential Accelerometer(2007-11-21) Prieto, Violeta A; Paik, Ho Jung; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The inverse-square law of gravitation is tested at submillimeter distances. To minimize Newtonian errors, the experiment employs a near null source, a circular disk of large diameter-to-thickness ratio. Two test masses, also disk-shaped, are suspended on the two sides of the source mass at a nominal distance of 180 micrometers. The source mass amplitude of motion is 16.1 micrometers. The signal is detected by a superconducting differential accelerometer. Careful matching and alignment makes the detector highly immune to platform vibrations. To reduce the thermal Brownian motion noise as well as the temperature noise of the instrument, the experiment is cooled to 1.7 K by pumping on liquid helium. In this dissertation, I discuss the assembly, design, and design improvements of the inverse square law experiment. I perform a comprehensive analysis of the errors, identify the problems with the apparatus, and show ways to improve the design of the experiment. With the improved design, it will be possible to achieve a sensitivity of |alpha| = 2 x 10^-3 at lambda = 150 micrometers, which will improve the current experimental limits by one order of magnitude at 150 micrometers and by over two orders of magnitude at shorter distances.