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This work provides a comprehensive analysis of modifications to the Einstein–Hilbert action, with a particular focus on Gauss–Bonnet (GB) gravity, and addresses the theoretical challenges in unifying quantum gravity frameworks with the GB gravitational modifications. By developing a novel fourth-order tensor methodology to manage derivative couplings, we establish a stable framework that eliminates higher-order derivative instabilities while enabling modified gravitational phenomena. The model maintains consistency with low-energy string theory constraints and generates testable predictions for black hole thermodynamics and cosmic expansion dynamics. Our results reconcile discrepancies between modified gravity theories and quantum field theory requirements, providing new mathematical tools for analyzing high-energy gravitational interactions. This work bridges critical gaps between theoretical formulations and observational evidence in cosmology, offering a unified approach to modeling gravitational interactions across quantum and cosmological scales.

This Conference Proceedings volume contains the written versions of most of the contributions presented during the 11th International Workshop on Astronomy and Relativistic Astrophysics (IWARA 2024). The Workshop took place in Machupicchu Pueblo (Aguas Calientes), Peru, from September 2–6, 2024. The Workshop provided a setting for discussing recent developments in a wide variety of topics, including Archaeoastronomy and Cognition, the Kerr metric and the Hawking temperature, Damour-Solodukhin-type Wormholes, Stellar Physics and General Relativity, Stochastic Quantum Mechanics in Curved Spaces, Gauss-Bonnet Theory, Quantum Gravity, Black Holes, Fast Radio Bursts, Neutron Stars, Strange Stars, X-ray Binaries, Pulsars, Gravitational Waves, and Dark Matter, among others. Most of these contributions are included in this volume.

MAXI J1820+070, discovered by the Monitor of All-sky X-ray Image (MAXI) in 2018, is a well-known black hole X-ray binary. This study presents a detailed spectral analysis using 2018 observations from the Insight Hard X-ray Modulation Telescope (HXMT). We explored the evolution of the Fe line shape and found it stable at 6.4 keV in the high/soft state, indicating the inner radius of the accretion disk remains at the Innermost Stable Circular Orbit. Additionally, we estimated the black hole spin ($��a_{*}�$) using the continuum fitting method, obtaining a spin of $��a_{*}�{�=�0.122�}_{�-�0.016�}^{�+�0.013�}�$, consistent with previous results. Through these findings, this study has contributed to the spectral analysis and spin parameter estimation of black hole X-ray binary systems, offering valuable insights into black hole behavior and its role in cosmology.

We investigate the emission of gravitational waves from spheroidal magnetized strange stars in two scenarios: an isolated, slowly rotating star and a binary system. For the isolated star, we compute the quadrupole moment and the amplitude of the gravitational waves that may be emitted. In the case of the binary system, we determine the tidal deformation by simultaneously solving the spheroidal structure equations and the Love number equation. Our results are compared with data inferred from the GW170817 event, which is also used to estimate the mass and tidal deformation of the companion star in the binary system. Our model supports the existence of binary systems formed by magnetized strange stars, predicting gravitational wave signals consistent with other models of binary systems composed of magnetized hadronic stars or non-magnetized quark stars.

This review provides a comprehensive discussion of Gauss–Bonnet (GB) gravity, a gravitational theory incorporating higher-order curvature corrections, which can influence gravitational dynamics in higher dimensions. We explore the fundamental motivation for introducing the GB term, particularly in the context of high-energy physics and string theory-inspired scenarios, highlighting its potential in addressing key issues such as singularities, the nature of dark energy, cosmic acceleration, modifications to neutron stars and black holes, and cosmological singularities. Furthermore, we examine emerging research directions and recent advancements in the field, including torsion effects, compact astrophysical phenomena, and modified Gauss–Bonnet models, which further expand the applications of GB gravity in modern theoretical physics and cosmology.

Pulsars, characterized as highly magnetized and rapidly rotating neutron stars, offer a unique laboratory for probing physics under extreme conditions. Magnetars, a subclass of pulsars powered by magnetic field energy, exhibit quantized and highly degenerate Landau levels for relativistic electrons in their crustal ultrastrong magnetic fields. The energy difference between these Landau levels and the field-free system determines the magnetic susceptibility. We first review spin degrees of freedom in relativistic electrons and magnetization mechanisms, then employ quantum statistical methods to calculate the magnetic susceptibility of relativistic electron gases in magnetar crusts. Finally, numerical simulations for the paramagnetic susceptibility oscillatory in superhigh magnetic fields in the magnetar crust was performed. Our results reveal that the magnetization under ultrastrong fields demonstrates oscillatory behavior analogous to the de Haas–van Alphen effect observed in certain low-temperature metals. The total susceptibility, $��\chi �$, comprises a non-oscillatory component ($��{\chi }_m�$) and an oscillatory term ($��{\tilde{\chi }}_m�$), where higher harmonic amplitudes of the oscillatory susceptibility grow with increasing electron density. Notably, the total paramagnetic susceptibility of electrons near the crust-core boundary does not exceed the critical magnetization threshold. However, if an ultrastrong magnetic field exists in the neutron star core, the susceptibility of the electron gas could surpass this critical value, suggesting the potential occurrence of non-equilibrium magnetization processes. This implies a first-order phase transition, akin to gas–liquid transitions, leading to coexisting stable magnetization states or metastable supercooled magnetic phases. A sudden transition from metastable to stable states may release stored magnetic energy, offering a plausible explanation for the observed excess radiation during magnetar giant flares.