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In this thesis, we have constructed new analytical solutions for initial data of the Einstein equations. Such solutions are valuable for gaining a better understanding of problems involving strong gravitational and/or electromagnetic interactions in general relativity. In this process, we have examined an inhomogeneous cosmological model consisting a lattice of regularly arranged, charged black holes with initial data corresponding to the maximum expansion of a cosmological solution. We have also refined the method in such a way that the values of the mass and charge of the sources can be prescribed beforehand subject to certain constraints dictated by the field equations. Then we studied a two dimensional 'equatorial' cross-section of the initial data space and presented the behaviour of the local curvature for the slices of the Platonic bodies 8, 16, 24, 120 and compared black hole lattices with a Friedmann universe of a unit radius. We see that the black hole lattice is not close to this, or any other, round sphere as far as its local curvature is concerned. For all Platonic solutions, the black hole regions are located where the curvature assumes its minimum value, and it strikes the eye that they are well isolated from each other and do not distort each other noticeably. On the other hand, we confirm that black holes themselves are remarkably round in the strong curvature regions. The recent surge of interest in these solutions was driven by the cosmological averaging problem. Is it likely to affect our understanding of the dark side of the universe in a significant way? We feel that the right way to go may well be to find other interesting toy models, where agreement can be reached quickly.

Gamma-ray bursts (GRBs) are the brightest events in the Universe, for a short time outshining the rest of the Universe combined, as they explode with isotropic equivalent luminosities up to $10^{54}$ erg s$^{-1}$. These events are believed to be connected to supernovae and to binary compact object mergers, such as binary neutron stars or neutron star -- black hole systems. The origin of the so-called prompt emission in GRBs remains an unsolved problem, although some progress is being made. Spectral analysis of prompt emission has traditionally been performed with the Band function, an empirical model with no physical interpretation, and it is just recently that physical models have started to be fitted to data. This thesis presents spectral analysis of GRB data from the Fermi Gamma-ray Space Telescope using a physical model for subphotospheric dissipation. The model is developed using a numerical code and implemented as a table model in {\scriptsize XSPEC}. Paper \rom{1} presents the model and provides a proof-of-concept of fitting GRB data with such a model. Specifically, two GRBs are fitted and compared with the corresponding Band function fits. In paper \rom{2}, a sample of 37 bursts are fitted with an extended version of the model and improved analysis tools. Overall, about a third of the fitted spectra can be described by the model. From these fits it is concluded that the scenario of subphotospheric dissipation can describe all spectral shapes present in the sample. The key characteristic of the spectra that are not fitted by the model is that they are very luminous. Within the context of the model, this suggests that the assumption of internal shocks as a dissipation mechanism cannot explain the full population of GRBs. Alternatively, additional emission components may required. The thesis concludes that subphotospheric dissipation is viable as a possible origin of GRB prompt emission. Furthermore, it shows the importance of using physically motivated models when analysing GRBs. / <p>QC 20170221</p>

The first stars, known as Population III (Pop III) stars, formed when the Universe was about 100 Myr to 200 Myr old. In contrast to the present-day Universe, star formation took place in a basically metal-free environment. Despite several decades of research, Pop III stars have not yet been directly observed.  This work investigates the prospects of the ArmazoNes high Dispersion Echelle Spectrograph (ANDES), used with the Extremely Large Telescope (ELT) to observe the supernova ejecta of Pop III stars. If those supernova ejecta enrich a pristine gas cloud, the imprints in the absorption spectrum from a background source may be observable.  First, the prospects of the unique identification of Pop III stars in contrast to non-Pop III stars is studied by using theoretical yields and abundance ratios of supernova simulations. The elements C, O and Si, used in a previous proposal for ANDES, can help to differentiate pair-instability supernovae of Pop III stars from any population and mixture of core-collapse supernovae. The inclusion of N, Al, Mg or Fe supports the discrimination of core-collapse supernovae from different populations.  Second, with a new code to simulate synthetic spectra with resolution and noise relevant for ANDES, the potential to identify a Pop III star is studied. Besides the suggested absorption lines of C, O and Si in the previous ANDES science document, the strong lines of Mg and Fe are potential indicators.

The origin of supermassive black holes (SMBHs,∼ 10^9M⊙) in the first billion years of cosmic history remains a mystery. Direct Collapse Black Holes (DCBHs,∼ 10^4M⊙) are considered one of the most promising hypotheses for the progenitor of SMBHs, as they are believed to provide a favorable starting point as massive seeds for SMBH formation. Based on the models of Pacucci et al. (2016), the DCBHs at birth are expected to exhibit an unusual steep (red) spectral energy distribution (SED) in the 1-5 micrometer range. In this study,we investigate degeneracies between DCBHs and dusty galaxies using synthetic data from the Pacucci model. Furthermore, we employ James Webb Space Telescope (JWST) photometric data obtainedfrom the Cosmic Evolution Early Release Science (CEERS) survey,which has been processed and reduced by Gabriel Brammer using the Grizli pipeline. By analyzing this JWST photometric data, we aim to identify potential DCBH candidates for further spectroscopic observations. We find that the dusty galaxies over a wide range ofredshift could mimic the SED shape of DCBHs, and that obscured active galactic nuclei (AGN) could potentially act as interlopers as well. The similarities in certain observational characteristics between DCBHs and dusty galaxies/AGN can obscure their distinct identities. In a localized region of the Extended Groth Strip field, we identify 12, 17, and 77 objects in three catalogues with increasing aperture sizesthat show relatively good fits with the DCBH models. However, upon further examination of their images, we do not find any candidatesthat are particularly compelling or convincing.

Sunspot oscillations, intricate three-dimensional wave-like motions in the solar atmosphere, result from the complex interplay between plasma and magnetic fields. This study delves into the behaviour of these oscillations, exploring their simultaneous excitation and evaluating their impact on solar phenomena like coronal heating, energy transport, and solar flares. Utilising magnetohydrodynamic models, my work replicates and extends a computational study by Stangalini et al. I confirm the existence of multiple resonant modes inside the sunspot's umbra in active region AR 12546, characterised by a powerful magnetic field. I also demonstrate the model's sensitivity to the sunspot umbra's shape as it influences the physical characteristics of eigenfunctions. An extension of the study involves introducing an inhomogeneous distribution of the sound and Alfvén speed while assuming a vertical magnetic field. This advancement from a previously constant model yields substantial variations in results, notably distinguishing between slow and fast modes. The sound speed towards the sunspot centre notably constrains the slow modes. Additionally, analysing the power spectral density of vertical velocity in sunspots verifies the presence of five-minute oscillations, with more vital occurrences in the quiet sun and diminishing towards the centre of the sunspot. Examination of active region evolution over time reveals apparent magnetic polarity changes. This research significantly contributes to our understanding of sunspot dynamics. It introduces a novel model incorporating an inhomogeneous sound distribution and Alfvén speed, an advancement from prior approaches. This innovation adds depth to the comprehension of solar phenomena, paving the way for further investigations.

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The aim of this project was to investigate the radial velocity variations of the Sun as observed from the Earth. This was accomplished by observing Doppler shifts of spectral lines in the region around 6300 Å. Telluric O2 lines were used as reference. The results indicate that during the day, the radial velocity increases and reaches a peak some time in the afternoon. Over spring, the radial velocity slowly declines. These results were compared to predicted values from JPL, NASA, and when accounting for the errors, they mostly agree with the predictions.