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In this thesis, we study two topics in using gravitational waves (GWs) to probe fundamental physics. The first topic is using black hole (BH) perturbation theory to model GW emissions by binary BH mergers in gravity theories beyond Einstein’s general relativity (GR). The second topic is studying holographic quantum gravity signatures around interferometers in flat spacetime.
For BH perturbation theory beyond GR, we first construct a novel formalism based on Teukolsky’s seminal work in the 1970s. Our modified Teukolsky formalism works for BHs with arbitrary spin in a broad class of beyond-GR theories that admit an effective field theory description. We derive this formalism by following Chandrasekhar’s prescription to make some convenient gauge choices, under which different degrees of curvature perturbations naturally decouple. In the end, we get two decoupled and potentially separable second-order partial differential equations for the Weyl scalars Ψ0 and Ψ4, representing the ingoing and outgoing gravitational radiations of a perturbed BH, respectively. Our formalism works for both linear and nonlinear orders in the beyond-GR couplings. We then apply our formalism to specific examples.
In the first example, we study the isospectrality breaking of quasinormal modes (QNMs) in beyond-GR theories, where the even- and odd-parity QNMs have different frequencies. We apply the modified Teukolsky formalism and the eigenvalue perturbation method to construct a direct connection between the parity features of a theory and its structure of isospectrality breaking. In the second example, we focus on the QNMs of dynamical Chern-Simons gravity up to the first order in the slow-rotation expansion. We first directly compute the scalar field equation and the modified Teukolsky equations for Ψ0 and Ψ4 in the ingoing and outgoing radiation gauges, respectively. We then reduce all the equations to radial ordinary differential equations by projection to the spin-weighted spheroidal harmonics. We find that the scalar field is only coupled to the odd-parity perturbations, which is consistent with the previous studies. We then compute the QNM frequencies for the non-rotating case via the eigenvalue perturbation method. The results from the two gauges are self-consistent and agree well with previous results using metric perturbations. Since this is ongoing work, we briefly discuss the strategy for the rotating case at the end. In the third example, we apply a similar analysis to certain parametrized axisymmetric deviations of non-rotating BHs using a Weyl multipole expansion. We compute the QNM frequencies directly and analyze their connections to the multipole structure of a BH spacetime.
For holographic gravity in flat spacetime, we build an effective model for geometrical spacetime fluctuations driven by entropic fluctuations, or “geontropic fluctuations” for short, in the casual diamond defined by an interferometer. Our model involves a bosonic scalar field with some nontrivial occupation number, called “pixellon.” The pixellon field characterizes all the nonlinear holographic quantum gravity fluctuations within a causal diamond in flat spacetime. We then build up a framework for computing the gauge-invariant observables of geontropic fluctuations for an interferometer with equal arms separated by arbitrary angles. We compute both the power spectral density and angular correlation of length fluctuations in such an interferometer for the pixellon model. We then use the existing or predicted noise spectra of LVK, LISA, GEO-600, and Holometer to constrain the pixellon model. In our follow-up study, we further extend the pixellon model to incorporate configurations of multiple interferometers. We then apply this extended pixellon model to calculate the power spectral density of geontropic fluctuations in Cosmic Explorer, Einstein Telescope, NEMO, and optically-levitated sensors. For Cosmic Explorer, Einstein Telescope, and NEMO, we find that the signal of the pixellon model could exceed the detector’s predicted sensitivity by one or two orders of magnitudes.