This doctoral thesis explores the use of high-resolution spectroscopy of active galactic nuclei (AGNs) to probe fundamental physics. It focuses on the study of axion-like particles (ALPs) and the spin of supermassive black holes (SMBHs).

Chapter 1 starts with a review of black holes as mathematical and astronomical objects and provides an account of the knowledge of the physics of the accretion flow onto SMBHs in AGNs as revealed by X-ray observations of AGNs. This is followed with a discussion on the use of X-ray reflection spectroscopy as a probe of the spin of moderately accreting SMBHs, and the use of spin diagnostics to probe the growth of SMBHs over cosmic timescales. Summaries of the Standard Models of cosmology (or the Lambda CDM paradigm) and particle physics are provided. Evidence of the need for physics beyond the Standard Model (BSM) is presented. This introductory chapter concludes by highlighting the role of ALPs as generic predictions in BSM theories and as compelling dark matter candidates and is accompanied by a description of plausible techniques towards their detectability with astronomical sources.

Chapter 2 begins our discussion on astrophysical ALP searches by presenting the tightest bounds to date on the coupling of light ALPs to electromagnetism based on a spectral analysis of high-resolution archival Chandra/Grating observations of the luminous cluster-hosted quasar H 1821+643.

Chapter 3 provides an exploration of how the next-generation Athena X-ray flagship observatory will improve on the current most sensitive limits presented in chapter 2. A promising technique to mitigate the effect of previously ignored systematic uncertainties is discussed. ALP projections from the AXIS probe-class concept proposed to NASA for a 2032 launch are also introduced.

The future of ALP searches with upcoming missions is encouraging due to advances in detector technology. These advances include improvements in effective area, spatial resolution, and spectral resolution when compared with current observatories. In future, probing light ALPs with observations of bright AGNs located at the centres of rich clusters may be the only plausible observational test of string theories and will complement the search for ALP dark matter at light ALP masses.

Chapter 4 presents the application of state-of-the-art X-ray reflection models on the Chandra spectral view of H 1821+643 introduced in chapter 2, pointing out that its colossal, central SMBH is rotating at moderate speeds. This chapter concludes by presenting the observed population of SMBHs whose spin has been estimated from such models.

The observed population seems to feature two subpopulations: a population of low-mass SMBHs with maximal-to-extreme spins and a high-mass population of SMBHs whose spins cluster at moderate values. This notion is aligned with the predictions of semi-analytic and numerical models of hierarchical structure formation and black hole evolution over cosmic timescales. Therefore, assessing this hypothesis with Bayesian statistics may eventually help confirm what drives SMBH growth over cosmic timescales and help distinguish between the relative importance of growth powered by coherent and incoherent accretion and SMBH-SMBH mergers.

Chapter 5 presents closing remarks and outlines possible future research directions.