In this thesis we aim to develop new perspectives on the statistical mechanics of black holes using an information geometric approach (Ruppeiner and Weinhold geometry). The Ruppeiner metric is defined as a Hessian matrix on a Gibbs surface, and provides a geometric description of thermodynamic systems in equilibrium. This Ruppeiner geometry exhibits physically suggestive features; a flat Ruppeiner metric for systems with no interactions i.e. the ideal gas, and curvature singularities signaling critical behavior(s) of the system. We construct a flatness theorem based on the scaling property of the black holes, which proves to be useful in many cases. Another thermodynamic geometry known as the Weinhold geometry is defined as the Hessian of internal energy and is conformally related to the Ruppeiner metric with the system’s temperature as a conformal factor.  We investigate a number of black hole families in various gravity theories. Our findings are briefly summarized as follows: the Reissner-Nordström type, the Einstein-Maxwell-dilaton andBTZ black holes have flat Ruppeiner metrics that can be represented by a unique state space diagram. We conjecture that the state space diagram encodes extremality properties of the black hole solution. The Kerr type black holes have curved Ruppeiner metrics whose curvature singularities are meaningful in five dimensions and higher, signifying the onset of thermodynamic instabilities of the black hole in higher dimensions. All the three-parameter black hole families in our study have non-flat Ruppeiner and Weinhold metrics and their associated curvature singularities occur in the extremal limits. We also study two-dimensional black hole families whose thermodynamic geometries are dependent on parameters that determine the thermodynamics of the black hole in question. The tidal charged black hole which arises in the braneworld gravity is studied. Despite its similarity to the Reissner-Nordström type, its thermodynamic geometries are distinctive. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Submitted. / Geometry and Physics

In this thesis we calculate the Hawking mass numerically for surfaces in Kerr spacetime. The Hawking mass is a useful tool for proving the Penrose inequality and the result does not contradict the inequality. It also does not contradict the assumption that the Hawking mass should be monotonic for surfaces in Kerr spacetime. The Hawking mass is quasi-local and defined by the spin coefficents of Newman and Penrose, so first we give a discussion about quasi-local quantities and then a short description of the Newman-Penrose formalism.

I modify the quasilocal energy formalism of Brown and York into a purely Hamiltonian form. As part of the reformulation, I remove their restriction that the time evolution of the boundary of the spacetime be orthogonal to the leaves of the time foliation. Thus the new formulation allows an arbitrary evolution of the boundary which physically corresponds to allowing general motions of the set of observers making up that boundary. I calculate the rate of change of the quasilocal energy in such situations, show how it transforms with respect to boosts of the boundaries, and use the Lanczos-Israel thin shell formalism to reformulate it from an operational point of view. These steps are performed both for pure gravity and gravity with attendant matter fields. I then apply the formalism to characterize naked black holes and study their properties, investigate gravitational tidal heating, and combine it with the path integral formulation of quantum gravity to analyze the creation of pairs of charged and rotating black holes. I show that one must use complex instantons to study this process though the probabilities of creation remain real and consistent with the view that the entropy of a black hole is the logarithm of the number of its quantum states.

With the long awaited start-up of the LHC, TeV scale physics is now in reach of the particles physicists to explore. There are many questions about the nature to be answered, and many more theories to be tested trying to answer them. The ADD model of extra dimensions is one such model, written to address the large mass hi- erarchy between the two fundamental energy scales in nature, the electroweak and the Planck scales. ADD model predicts stronger gravity at sub-millimeter distance scales, which would then lead to an interesting physical object to be produced at proton collusions at the LHC: Tiny quantum black holes. In this thesis we study the discovery potential of CMS for quantum black hole events for proton-proton collusions at sqrt(s) = 14 TeV. Our study details the trigger response of CMS, various criteria and methods for background rejection, affect of experimental uncertainties on measurements, for different model parameter values.

This thesis is concerned with the study of cosmic strings. We studied the values for the Higgs mass and string coupling for which the gravitational effect of an infinite cosmic string in the context of the Einstein theory is not only locally but also globally weak. We conclude this happens for strings formed at scales less or equal to the Planck one with Higgs mass being less or equal to the boson vectorial mass. Then we examined the metric of an isolated self-gravitating abelian-Higgs vortex in dilatonic gravity for arbitrary coupling of the vortex fields to the dilaton. We looked for solutions in both massless and massive dilaton gravity. We compared our results to existing metrics for strings in Einstein and .Jordan-Brans-Dicke theories. We explored the generalisation of Bogomolnyi arguments for our vortices and commented on the effects on test particles. We then included the presence of an axion field and examined the metric of an isolated self-gravitating axionic-dilatonic string. Finally we studied dilatonic strings through black hole solutions in string theory. We concluded that the horizon of non-extreme charged black holes supports the long-range fields of the Nielsen-Olesen string that can be considered as black hole hair and whose gravitational effect is in general the production of a conical deficit into the metric of the black hole background. We also concluded that the effect of the dilaton on the horizon of these black holes is to generate an additional charge.

Made available in DSpace on 2016-12-12T20:15:53Z (GMT). No. of bitstreams: 1 A-inicio.pdf: 106467 bytes, checksum: 8ecfda3cfa81a009fae7a31b2dea68e8 (MD5) Previous issue date: 2008-10-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this Dissertation we study the scattering of massless monochromatic scalar waves by 5-dimensional (5D) Schwarzschild-Tangherlini black holes. We compute the scattering phase shifts using Prüfer method for high frequencies and high-values of the angular multipole index l. The phase shifts are then used to analyze the glory effect, in comparison with the respective 4D values. In the case of low frequencies th total absorption is completely absent in some cases. The oscillatory behavior of the phase shift for large values of l, typical in the 4D case, now becomes absent. For high frequencies, the total absorption starts at much lower values of l, compared to the 4D case. / Nesta Dissertação estudamos o espalhamento de ondas escalares monocromáticas sem massa por buracos negros de Schwarzschild-Tangherlini em 5 dimensões (5D). Computamos os desvios de fase usando o método de Prüfer para altas freqüências e altos valores do índice de multipolo l. Os desvios de fase são para análise do efeito glória, comparando com os respectivos valores resultantes do caso do espalhamento em 4D. Para baixas freqüências a absorção total em 5D é, em alguns casos, totalmente ausente para l + 0. O comportamento oscilatório do desvio de fase para grandes valores de l, típico em 4D, agora desaparece. Para altas freqüências a absorção total em 5D começa para valores de l muito menores que aqueles respectivos ao caso 4D.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-10-18T18:35:27Z No. of bitstreams: 1 LUIZ CORDEIRO DE LIMA NETO – DISSERTAÇÃO (PPGFísica) 2013.pdf: 963611 bytes, checksum: 83952da12a3c82dcd16e85616b111271 (MD5) / Made available in DSpace on 2018-10-18T18:35:27Z (GMT). No. of bitstreams: 1 LUIZ CORDEIRO DE LIMA NETO – DISSERTAÇÃO (PPGFísica) 2013.pdf: 963611 bytes, checksum: 83952da12a3c82dcd16e85616b111271 (MD5) Previous issue date: 2013-03-26 / Capes / Este trabalho apresenta elementos complementares da formação no nível de mestrado em Física. Discutimos, principalmente, aspectos de Relatividade Geral e Teoria Quân- tica de Campos. Deforma detalhada, explanamos a obtenção das soluções de Reissner- Nordström para as equações de Einstein que mostram a dependência dos buracos negros carregados da sua massa e da sua carga. Analisamos, também, os casos onde a massa difere numericamente da carga conhecidos como casos não-extremos, e os casos onde estas grandezas são equivalentes conhecidos como extremos. Discutimos, também, as leis da mecânica dos buracos negros e a inevitável comparação com as leis usuais da Termodinâmica e, conforme foi demonstrado por Hawking, que essas semelhanças são um fenômeno físico explicado pela a mecânica quântica. Ao rever estes estudos, Unruh percebeu que um observador acelerado em um espaço plano mede radiação térmica. Os estudos apresentados nesta dissertação constituem o embasamento necessário para o trabalho em inúmeras áreas de desenvolvimento da Física na atualidade, visto que os buracos negros carregados (em dimensões extras) possuem uma ligação com a teoria das cordas, uma das teorias mais promissoras para a construção da teoria quântica da gravitação. / This work presents complementary elements of training at the master’s degree level in Physics. We discussed, mainly, aspects of General Relativity and Quantum Field Theory. In details we expounded the obtaining of Reissner-Nordström’s solutions for Einstein’s equations that show the dependence of charged black holes on their massand charge. We also the cases in which the mass differs numerically from charge, known as non- extreme cases, and cases where the sequantities are equivalent, known as extreme. We also discuss the laws of mechanics of black holes and thein evitable comparison with the usual law softhermo dynamics and still, as demonstrated by Hawking, that the se similarities are physical phenomena explained by Quantum Mechanics. By reviewing thes estudies, Unruh realized that an accelerated observerina flat space me asures thermal radiation. The studies presented in this dissertation formed the necessary principles for research in several are as of development of physics now a days, where as the charged black holes (in extradimensions) are connected with the String Theory, one of the most promising theories for construction of the Quantum Theory of Gravitation.

We will consider the scenario of the co-rotation of a fluid star (in specific, a neutron star) and a black hole. The neutron star (or primary)is assumed to have constant angular velocity. The tidal effects on the primary are investigated. First, the centrally condensed approximation is applied, where both bodies are considered as point sources. In the second treatment, the primary is treated as an incompressible and homogeneous fluid mass, which in addition to its own gravity is subject to centrifugal and Coriolis forces, derived from fluid motions. The black hole (or secondary) is treated as a rigid sphere and can be regarded as a point mass. The equilibrium figure is derived. The problem is then adapted to include vorticity and a pseudo-Newtonian potential. The coalescence of neutron star - black hole binaries and their importance to gravitational wave detection is also discussed. / Mathematical Sciences / M. Sc. (Applied Mathematics)

In recent years, advances in deep optical, and especially deep near-infrared imaging with the Hubble Space Telescope (HST) and wide-field ground-based telescopes such as VISTA, have revolutionized our understanding of the cosmological evolution of galaxies and supermassive black-holes (as manifest through active galactic nuclei; AGN). In particular, the dynamic range provided by the survey `wedding cake' of available HST+ground-based optical/IR data offers new opportunities to push the meaningful statistical study of galaxy and AGN evolution out to high redshifts. Much recent attention has focused, unsurprisingly, on using these new data to push studies of galaxy formation back to within a billion years of the Big Bang, and exploring the role of young galaxies in driving cosmic hydrogen reionization during the crucial era corresponding to redshifts z ≃ 6-10. However, these data have not been as thoroughly exploited at intermediate redshifts, and have only recently been used to explore black-hole/AGN evolution. In this thesis I utilise the latest deep optical/near-infrared imaging and spectroscopy to explore three key facets of cosmological evolution. First, I present a new, robust measurement of the evolving rest-frame ultraviolet (UV) galaxy luminosity function (LF) over the key redshift range from z ≃ 2 to z ≃ 4. My results are based on the high dynamic range provided by combining the Hubble Ultra Deep Field (HUDF), CANDELS/GOODS-South, and UltraVISTA/COSMOS surveys. I utilise the unparalleled multi-frequency photometry available in this survey `wedding cake' to compile complete galaxy samples at z ≃ 2; 3; 4 via photometric redshifts (calibrated against the latest spectroscopy). This study is important as the peak of star-formation is shown to happen within a redshift range z = 2 - 4 and determining the exact epoch that the galaxies were forming most of their stars depends significantly on the UV luminosity density which requires robust measurements of the galaxy UV luminosity function and its accurate parameterization. My new determinations of the UV LF extend from M1500 ≃ -22 (AB mag) down to M1500 =-14.5, -15.5 and -16 at z ≃2, 3 and 4 respectively (thus reaching ≃ 3-4 magnitudes fainter than previous blank-field studies at z ≃ 2 - 3). At z ≃ 2 - 3 I find a much shallower faint-end slope (α = -1:32 ± 0:03) than the steeper values (α ≃ -1:7) reported in the literature, and show that this new measurement is robust. By z ≃ 4 the faint-end slope has steepened slightly, to α = -1:43 ± 0:04, and I show that these measurements are consistent with the overall evolutionary trend from z = 0 to z = 8. I then calculate the UV luminosity density (and hence unobscured star-formation density) and show that it peaks at z ≃ 2:5 - 3, when the Universe was ≃ 2:5 Gyr old. Second, I have used these data to revisit the possibility that X-ray AGN played a significant role in cosmic hydrogen reionization which is one of the major processes in the formation of the Universe we see today. Hence, it is really important to understand this phenomenon thoroughly by studying the properties of sources capable of ionising photons, such as star-forming galaxies and high redshift AGNs. Although most recent studies have suggested that the emerging population of young star-forming galaxies can bathe the Universe in sufficient high-energy photons to complete reionization by z ≃ 6, some authors have reasserted the potentially important role of high-redshift AGN in the hydrogen reionization process. In an effort to clarify this situation, I reinvestigate a claimed sample of 22 X-ray detected active galactic nuclei (AGN) at redshifts z > 4, which has reignited the debate as to whether young galaxies or AGN reionized the Universe. These sources lie within the GOODS-S/CANDELS field, and I examine both the robustness of the claimed X-ray detections (within the Chandra 4Ms imaging) and perform an independent analysis of the photometric redshifts of the optical/infrared counterparts. I confirm the reality of only 15 of the 22 reported X-ray detections, and moreover find that only 12 of the 22 optical/infrared counterpart galaxies actually lie robustly at z > 4. I recalculate the evolving far-UV (1500Å) luminosity density produced by AGN at high redshift, and find that it declines rapidly from z ≃ 4 to z ≃ 6, in agreement with several other recent studies of the evolving AGN luminosity function. The associated rapid decline in inferred hydrogen-ionizing emissivity contributed by AGN falls an order-of-magnitude short of the level required to maintain hydrogen ionization at z ≃ 6. I conclude that AGNs make a very minor contribution to cosmic hydrogen reionization. Finally, I have utilized the deep optical/near-infrared survey data to explore the prevalence of quenched/passive galaxies at high redshift. Applying a robust method to isolate passive galaxies from star-forming galaxies is the key to improving our understanding of the quenching process. Focusing primarily on the deep HUDF data-set, I have revisited the effectiveness of simple colour-colour (UVJ) selection techniques in isolating robust samples of quenched galaxies, and find that dust plays a more important role in this selection process than has been previously appreciated. Through careful SED fitting I successfully isolate a sample of apparently dust-free quiescent galaxies in the redshift range 0:5 < z < 4:5 but (at least in the HUDF) fail to find any galaxy which has remained truly quiescent for > 1 Gyr. I conclude by focusing on the properties of a refined/robust sample of apparently quenched galaxies at z > 3, and in particular establishing the contribution of quenched galaxies to stellar-mass density at early times. I conclude with a summary of my findings, and a brief discussion of the most promising avenues for future advances with the next generation of facilities, such as the James Webb Space Telescope (JWST).

The fuzzball model of a black hole is an attempt to resolve the many paradoxes and puzzles of black hole physics that have revealed themselves over the last century. These badly behaved solutions of general relativity have given physicists one of the few laboratories to test candidate quantum theories of gravity. Though little is known about exactly what lies beyond the event horizon, and what the ultimate fate of matter that falls in to a black hole is, we know a few intriguing and elegant semi-classical results that have kept physicists occupied. Among these are the known black hole entropy and the Hawking radiation process.