Studies of quadratic gravity with chaos and instability

Deich, Alexander

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https://hdl.handle.net/2142/127257 Copy

Description

Title

Studies of quadratic gravity with chaos and instability

Author(s)

Deich, Alexander

Issue Date

2024-12-05

Director of Research (if dissertation) or Advisor (if thesis)

Yunes, Nicolás

Doctoral Committee Chair(s)

Gammie, Charles

Committee Member(s)

• Noronha-Hostler, Jacquelyn
• Filippini, Jeffrey

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• gravity
• black holes
• chaos
• vlbi
• ligo
• lisa
• lyapunov
• poincare

Abstract

From gravitational wave detectors to very long baseline interferometers, experimental relativity is being born. With the promise of troves of data from the space very near black holes, we are at the cusp of having a sharper view of the most extreme gravitational environments than ever before. In addition, the last half- century of theoretical work has provided a trove of potential modifications to the theory of gravity which we might test with the incoming new data. One approach to testing these theories is to look at what the trajectories of test particles can tell us about the underlying theory, and how we might be able to make observations of those particles with current and future instruments. In particular, the extent to which these trajectories exhibit signs of instability and chaos offer a unique, and in principle independent, test of the metrics which govern their motion. In this dissertation, we focus on how we might test two theories of gravity, dynamical-Chern-Simons (dCS), and scalar-Gauss-Bonnet (sGB). We begin with testing to what extent dynamical chaos may present itself in massive test particle trajectories around black holes in these theories. We show that while these theories may permit chaotic orbits, any features are likely too tiny to be detectable in extreme-mass-ratio inspiral (EMRI) signals in near-future detectors. Then, we look at how the spin expansion order of the metrics may impact the precision of calculated observables. We show that for all but the most rapidly spinning black holes, many astrophysical observables may be calculated with only the first half dozen expansion terms. Finally, we investigate how the instability of photon trajectories in black hole solutions may lead to differences in very-long-baseline interferometer (VLBI) observations of black holes. En route to demonstrating the likely very small differences between these theories, we develop a completely theory-agnostic approach which is sufficiently general to be used for other similar studies.

Graduation Semester

2024-12

Type of Resource

Thesis

Handle URL

https://hdl.handle.net/2142/127257

Copyright and License Information

Copyright 2024 Alexander Deich

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