The work of this dissertation will study various aspects of the dynamics of compact objects using numerical simulations.We consider BH dynamics within two modified or alternative theories of gravity. Within a family of Einstein-Maxwell-Dilaton-Axion theories, we find that the GW waveforms from binary black hole (BBH) mergers differ from the standard GW waveform prediction of GR for especially large axion values. For more astrophysically realistic (i.e. smaller) values, the differences become negligible and undetectable. Weestablish the existence of a well-posed initial value problem for a second alternative theory fo gravity (quadratic gravity) and demonstrate in spherical symmetry that a linear instability is effectively removed on consideration of the full nonlinear theory.We describe the key components and development of a code for studying BBH mergers for which the mass ratio of the binaries is not close to one. Such intermediate mass ratio inspirals (IMRIs) are much more difficult to simulate and present greater demands on resolution, distributed computing, accuracy and efficiency. To this end, we present a highly-scalable framework that combines a parallel octree-refined adaptive mesh with a wavelet adaptive multiresolution approach. We give results for IMRIs with mass ratios up to 100:1. We study the ejecta from BNS in Newtonian gravity. Using smoothed particle hydrodynamics we develop and present the highly scalable FleCSPH code to simulate such mergers. As part of the ejecta analysis, we consider these mergers and their aftermath as prime candidates for heavy element creation and calculate r-process nucleosynthesis within the post-merger ejecta. Lastly we consider a non-standard, yet increasingly explored, interaction between a BH and a NS that serves as a toy model for primordial black holes (PBH) and their possible role as dark matter candidates. We present results from a study of such systems in which a small BH forms at the center of a NS. Evolving the spherically symmetric system in full GR, we follow the complete dynamics as the small BH consumes the NS from within. Using numerical simulations, we examine the time scale for the NS to collapse into the PBH and show that essentially nothing remains behind. As a result, and in contradiction to other claims in the literature, we conclude that thisis an unlikely site for ejecta and nucleosynthesis, at least in spherical symmetry.

In this thesis a set of recently proposed multigravity theories is analysed. In the special case of bimetric gravity, the theory has been conclusively shown to be ghost-free. On the other hand, for multigravity theories in general, the ghost-issue has not been settled conclusively. Motivated by this fact, the main object of this thesis is to clarify what has been proven so far and what issues that still needs to be addressed. We also provide new calculations and results pointing in the direction that the multigravity theories must be restricted to a set of bimetric Hassan-Rosen couplings in a tree-type structure in order to be consistent. In particular, we prove that for a multivielbein theory of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmathscr%7BN%7D" /> interacting vielbeins, the Lorentz equations of motion is a set of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?(%5Cmathscr%7BN%7D-1)" /> Deser-van Nieuwenhuizen conditions if and only if the theory consists of bimetric Hassan-Rosen couplings in a tree-type structure.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-08T13:15:08Z No. of bitstreams: 1 dantedonizetipereira.pdf: 460175 bytes, checksum: 092f58c5d71aa77ff03d0ae0604294a1 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-06-26T18:10:56Z (GMT) No. of bitstreams: 1 dantedonizetipereira.pdf: 460175 bytes, checksum: 092f58c5d71aa77ff03d0ae0604294a1 (MD5) / Made available in DSpace on 2017-06-26T18:10:56Z (GMT). No. of bitstreams: 1 dantedonizetipereira.pdf: 460175 bytes, checksum: 092f58c5d71aa77ff03d0ae0604294a1 (MD5) Previous issue date: 2013-07-18 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta tese exploramos diferentes aspectos de teorias clássicas e quânticas de campos. Na parte clássica, examinamos o fenômeno da birrefringência eletro-magneto-óptica em ele-trodinâmica não-linear no contexto de meios materiais dielétricos não-lineares como uma correção efetiva à teoria linear maxwelliana do eletromagnetismo. Na parte quântica, seguindo o método do heat kernel em teoria quântica de campos sobre espaços curvos, derivamos e estudamos a estrutura das divergências a 1-loop para a ação efetiva de diferentes modelos. Em particular, no ramo do modelo de Yukawa, exibimos duas novas formas de ambiguidades as quais tomam lugar na ação efetiva de campos fermiônicos através do fenômeno da anomalia multiplicativa não-local. Além disso, analisamos a estrutura das divergências ultravioletas a 1-loop para um modelo recentemente proposto de gravitação massiva livre de fantasmas, e mostramos que esse modelo encontra sérias dificuldades no nível quântico. / In this thesis we explore different aspects in classical and quantum field theories. In the classical part, we examine the phenomenon of electro-magneto-optical birefringence in nonlinear electrodynamics in the context of nonlinear dielectric media as an effective correction to the linear Maxwellian theory of electromagnetism. In the quantum part, following the heat kernel method in quantum field theory on curved spaces, we derive and study the structure of the 1-loop divergences for the effective action of different models. In particular, through the Yukawa model, we show two new forms of ambiguities which take place in the effective action of fermionic fields through the phenomenon of nonlocal multiplicative anomaly. Moreover, we analyzed the structure of ultraviolet divergences at 1-loop for a recently proposed ghost-free massive gravity model, and we show that this model meets serious difficulties at the quantum level.