Globular clusters are dense and massive star clusters that are an integral part of any major galaxy. Careful studies of their stars, a single cluster may contain several millions of them, have revealed that the ages of many globular clusters are comparable to the age of the Universe. These remarkable ages make them valuable probes for the exploration of structure formation in the early universe or the assembly of our own galaxy, the Milky Way. A topic of current research relates to the question whether globular clusters harbour massive black holes in their centres. These black holes would bridge the gap from stellar mass black holes, that represent the final stage in the evolution of massive stars, to supermassive ones that reside in the centres of galaxies. For this reason, they are referred to as intermediate-mass black holes. The most reliable method to detect and to weigh a black hole is to study the motion of stars inside its sphere of influence. The measurement of Doppler shifts via spectroscopy allows one to carry out such dynamical studies. However, spectroscopic observations in dense stellar fields such as Galactic globular clusters are challenging. As a consequence of diffraction processes in the atmosphere and the finite resolution of a telescope, observed stars have a finite width characterized by the point spread function (PSF), hence they appear blended in crowded stellar fields. Classical spectroscopy does not preserve any spatial information, therefore it is impossible to separate the spectra of blended stars and to measure their velocities. Yet methods have been developed to perform imaging spectroscopy. One of those methods is integral field spectroscopy. In the course of this work, the first systematic study on the potential of integral field spectroscopy in the analysis of dense stellar fields is carried out. To this aim, a method is developed to reconstruct the PSF from the observed data and to use this information to extract the stellar spectra. Based on dedicated simulations, predictions are made on the number of stellar spectra that can be extracted from a given data set and the quality of those spectra. Furthermore, the influence of uncertainties in the recovered PSF on the extracted spectra are quantified. The results clearly show that compared to traditional approaches, this method makes a significantly larger number of stars accessible to a spectroscopic analysis. This systematic study goes hand in hand with the development of a software package to automatize the individual steps of the data analysis. It is applied to data of three Galactic globular clusters, M3, M13, and M92. The data have been observed with the PMAS integral field spectrograph at the Calar Alto observatory with the aim to constrain the presence of intermediate-mass black holes in the centres of the clusters. The application of the new analysis method yields samples of about 80 stars per cluster. These are by far the largest spectroscopic samples that have so far been obtained in the centre of any of the three clusters. In the course of the further analysis, Jeans models are calculated for each cluster that predict the velocity dispersion based on an assumed mass distribution inside the cluster. The comparison to the observed velocities of the stars shows that in none of the three clusters, a massive black hole is required to explain the observed kinematics. Instead, the observations rule out any black hole in M13 with a mass higher than 13000 solar masses at the 99.7% level. For the other two clusters, this limit is at significantly lower masses, namely 2500 solar masses in M3 and 2000 solar masses in M92. In M92, it is possible to lower this limit even further by a combined analysis of the extracted stars and the unresolved stellar component. This component consists of the numerous stars in the cluster that appear unresolved in the integral field data. The final limit of 1300 solar masses is the lowest limit obtained so far for a massive globular cluster. / Kugelsternhaufen sind dichte, gravitativ gebundene Ansammlungen von teilweise mehreren Millionen Sternen, die ein fester Bestandteil jeder massiven Galaxie sind. Aus der Untersuchung der Kugelsternhaufen in der Milchstraße weiß man, dass das Alter von vielen dieser Objekte vergleichbar ist mit jenem des Universums. Dies macht sie zu wertvollen Forschungsobjekten, beispielsweise um die Entstehung der Milchstraße und die Strukturbildung im frühen Universum zu verstehen. Eine aktuelle wissenschaftliche Fragestellung befasst sich damit, ob Kugelsternhaufen massive schwarze Löcher beherbergen. Diese würden eine Brücke schlagen von den stellaren schwarzen Löchern, die durch den Kollaps massereicher Sterne entstehen, zu den supermassiven schwarzen Löchern, welche man in den Zentren massiver Galaxien beobachtet. Man bezeichnet sie daher auch als mittelschwere schwarze Löcher. Die sicherste Diagnostik, um schwarze Löcher zu detektieren und ihre Masse zu bestimmen ist, die Bewegung der Sterne innerhalb ihrer gravitativen Einflusssphäre zu vermessen. Spektroskopische Untersuchungen vermögen dies über die Dopplerverschiebung von Spektrallinien, sind jedoch in dichten stellaren Feldern wie Kugelsternhaufen schwierig. Aufgrund der Turbulenz in der Atmosphäre und dem endlichen Auflösungsvermögen des Teleskops erscheinen die Sterne in den Beobachtungen nicht punktförmig, sondern mit einer durch die Punktspreizfunktion (PSF) gegebenen Breite. In dichten stellaren Feldern führt dies dazu, dass die Sterne überlappen. Da klassische spektroskopische Verfahren nicht bildgebend sind, lassen sich die Beiträge der Einzelsterne zu einem beobachteten Spektrum nicht trennen und die Geschwindigkeiten der Sterne können nicht vermessen werden. Bildgebende spektroskopische Verfahren, wie etwa die Integralfeld-Spektroskopie, bieten jedoch die Möglichkeit, die PSF zu rekonstruieren und basierend darauf die Spektren überlappender Sterne zu trennen. Im Rahmen der vorgelegten Arbeit wird das Potential der Integralfeld-Spektroskopie in der Beobachtung dichter stellarer Felder zum ersten Mal systematisch analysiert. Hierzu wird eine Methodik entwickelt, die das Extrahieren von Einzelsternspektren über eine Rekonstruktion der PSF aus den vorhandenen Daten erlaubt. Anhand von Simulationen werden Voraussagen darüber gemacht, wie viele Sternspektren aus einem gegebenen Datensatz extrahiert werden können, welche Qualität diese Spektren haben und wie sich Ungenauigkeiten in der rekonstruierten PSF auf die Analyse auswirken. Es zeigt sich hierbei, dass die entwickelte Methodik die spektroskopische Analyse von deutlich mehr Sternen erlaubt als klassische Verfahren. Parallel zu dieser systematischen Studie erfolgt die Entwicklung einer dezidierten Analysesoftware, welche im zweiten Teil der Arbeit auf Daten von drei Kugelsternhaufen angewendet wird, die mit dem PMAS Integralfeld-Spektrographen am Calar Alto Observatorium aufgenommen wurden: M3, M13 und M92. Die Auswertung dieser Daten liefert Spektren für eine Stichprobe von ungefähr 80 Sternen pro Kugelsternhaufen, weit mehr als bisher im Zentrum eines der drei Haufen verfügbar waren. In der weiteren Analyse werden Jeans Modelle für jedes der drei Objekte gerechnet. Diese erlauben basierend auf einer angenommenen Massenverteilung innerhalb des Kugelsternhaufens eine Vorhersage der Geschwindigkeitsdispersion der Sterne. Der Vergleich mit den gemessenen Geschwindigkeiten zeigt, dass in keinem der drei Haufen ein schwarzes Loch benötigt wird, um die Dynamik der zentrumsnahen Sterne zu erklären. Im Gegenteil, die Beobachtungen können zu 99,7-prozentiger Sicherheit ausschließen, dass sich in M13 ein schwarzes Loch mit einer Masse größer 13000 Sonnenmassen befindet. In den anderen beiden Haufen liegt diese Grenze noch bei deutlich geringeren Massen, nämlich bei 2500 Sonnenmassen in M3 und 2000 Sonnenmassen in M92. In M92 ist es außerdem möglich, das Limit noch weiter herabzusetzen durch eine zusätzliche Analyse der unaufgelösten stellaren Komponente. Diese Komponente besteht aus dem integrierten Licht all jener Sterne, die zu schwach und zahlreich sind als dass sie aus den verfügbaren Daten einzeln extrahiert werden könnten. Das endgültige Limit von 1300 Sonnenmassen ist das geringste, welches bisher in einem massiven Kugelsternhaufen gemessen wurde.

As an operational approach to the Bekenstein-Hawking formula S_{BH}=A/4l_{Pl}^{2} for the black hole entropy, we consider the reversible contraction of a spinning thin shell to its event horizon and find that its thermodynamic entropy approaches $S_{\mathrm{BH}}$. In this sense the shell, called a "black shell", imitates and is externally indistinguishable from a black hole. Our work is a generalization of the previous result [10] for the spherical case. We assume the exterior space-time of the shell is given by the Kerr metric and match it to two different interior metrics, a vacuum one and a non-vacuum one. We find the vacuum interior embedding breaks down for fast spinning shells. The mechanism is not clear and worth further exploring. We also examine the case of a Kerr-AdS exterior, without trying to find a detailed interior solution. We expect the same behavior of the shell when the horizon limit is approached.

In multi-hop wireless network (MWN), the mobile nodes relay others’ packets for enabling new applications and enhancing the network deployment and performance. However, the selfish nodes drop the packets because packet relay consumes their resources without benefits, and the malicious nodes drop the packets to launch Denial-of-Service attacks. Packet drop attacks adversely degrade the network fairness and performance in terms of throughput, delay, and packet delivery ratio. Moreover, due to the nature of wireless transmission and multi-hop packet relay, the attackers can analyze the network traffic in undetectable way to learn the users’ locations in number of hops and their communication activities causing a serious threat to the users’ privacy. In this thesis, we propose efficient security protocols for thwarting packet drop attacks and preserving users’ privacy in multi-hop wireless networks. First, we design a fair and efficient cooperation incentive protocol to stimulate the selfish nodes to relay others’ packets. The source and the destination nodes pay credits (or micropayment) to the intermediate nodes for relaying their packets. In addition to cooperation stimulation, the incentive protocol enforces fairness by rewarding credits to compensate the nodes for the consumed resources in relaying others’ packets. The protocol also discourages launching Resource-Exhaustion attacks by sending bogus packets to exhaust the intermediate nodes’ resources because the nodes pay for relaying their packets. For fair charging policy, both the source and the destination nodes are charged when the two nodes benefit from the communication. Since micropayment protocols have been originally proposed for web-based applications, we propose a practical payment model specifically designed for MWNs to consider the significant differences between web-based applications and cooperation stimulation. Although the non-repudiation property of the public-key cryptography is essential for securing the incentive protocol, the public-key cryptography requires too complicated computations and has a long signature tag. For efficient implementation, we use the public-key cryptography only for the first packet in a series and use the efficient hashing operations for the next packets, so that the overhead of the packet series converges to that of the hashing operations. Since a trusted party is not involved in the communication sessions, the nodes usually submit undeniable digital receipts (proofs of packet relay) to a centralized trusted party for updating their credit accounts. Instead of submitting large-size payment receipts, the nodes submit brief reports containing the alleged charges and rewards and store undeniable security evidences. The payment of the fair reports can be cleared with almost no processing overhead. For the cheating reports, the evidences are requested to identify and evict the cheating nodes. Since the cheating actions are exceptional, the proposed protocol can significantly reduce the required bandwidth and energy for submitting the payment data and clear the payment with almost no processing overhead while achieving the same security strength as the receipt-based protocols. Second, the payment reports are processed to extract financial information to reward the cooperative nodes, and contextual information such as the broken links to build up a trust system to measure the nodes’ packet-relay success ratios in terms of trust values. A node’s trust value is degraded whenever it does not relay a packet and improved whenever it does. A node is identified as malicious and excluded from the network once its trust value reaches to a threshold. Using trust system is necessary to keep track of the nodes’ long-term behaviors because the network packets may be dropped normally, e.g., due to mobility, or temporarily, e.g., due to network congestion, but the high frequency of packet drop is an obvious misbehavior. Then, we propose a trust-based and energy-aware routing protocol to route traffics through the highly trusted nodes having sufficient residual energy in order to establish stable routes and thus minimize the probability of route breakage. A node’s trust value is a real and live measurement to the node’s failure probability and mobility level, i.e., the low-mobility nodes having large hardware resources can perform packet relay more efficiently. In this way, the proposed protocol stimulates the nodes not only to cooperate but also to improve their packet-relay success ratio and tell the truth about their residual energy to improve their trust values and thus raise their chances to participate in future routes. Finally, we propose a privacy-preserving routing and incentive protocol for hybrid ad hoc wireless network. Micropayment is used to stimulate the nodes’ cooperation without submitting payment receipts. We only use the lightweight hashing and symmetric-key-cryptography operations to preserve the users’ privacy. The nodes’ pseudonyms are efficiently computed using hashing operations. Only trusted parties can link these pseudonyms to the real identities for charging and rewarding operations. Moreover, our protocol protects the location privacy of the anonymous source and destination nodes. Extensive analysis and simulations demonstrate that our protocols can secure the payment and trust calculation, preserve the users’ privacy with acceptable overhead, and precisely identify the malicious and the cheating nodes. Moreover, the simulation and measurement results demonstrate that our routing protocols can significantly improve route stability and thus the packet delivery ratio due to stimulating the selfish nodes’ cooperation, evicting the malicious nodes, and making informed decisions regarding route selection. In addition, the processing and submitting overheads of the payment-reports are incomparable with those of the receipts in the receipt-based incentive protocols. Our protocol also requires incomparable overhead to the signature-based protocols because the lightweight hashing operations dominate the nodes’ operations.

As an operational approach to the Bekenstein-Hawking formula S_{BH}=A/4l_{Pl}^{2} for the black hole entropy, we consider the reversible contraction of a spinning thin shell to its event horizon and find that its thermodynamic entropy approaches $S_{\mathrm{BH}}$. In this sense the shell, called a "black shell", imitates and is externally indistinguishable from a black hole. Our work is a generalization of the previous result [10] for the spherical case. We assume the exterior space-time of the shell is given by the Kerr metric and match it to two different interior metrics, a vacuum one and a non-vacuum one. We find the vacuum interior embedding breaks down for fast spinning shells. The mechanism is not clear and worth further exploring. We also examine the case of a Kerr-AdS exterior, without trying to find a detailed interior solution. We expect the same behavior of the shell when the horizon limit is approached.

V klasické fyzice m·že být ustavena statická rovnováha v soustavě, která obsahuje extrémně nabité zdroje gravitačního a elektromagnetického pole. Udivujícím faktem je, že tato situace m·že nastat i pro černé díry v relativis- tické fyzice. Tato práce vyšetřuje speciální případ nekonečně dlouhé, extrémně nabité struny, zkoumá geometrii prostoročasu, elektrogeodetiky, vlastnosti zdroje a srovnává řešení se situací v klasické fyzice. Dále se zabýváme analogickou situací v dynamickém prostoročase s kosmologickou konstantou, a řešení porovnáváme s jeho statickou verzí. Nakonec zkoumáme periodické řešení Laplaceovy rovnice, které odpovídá nekonečně mnoha extremálním bodovým zdroj·m rozloženým v pravidelném rozestupu podél přímky. Vyšetřujeme vlastnosti elektrostatického potenciálu a ukazujeme, že v limitě velké vzdálenosti od osy tvořené zdroji pře- chází toto řešení v nabitou strunu. 1

Dans la cochlée, la réponse couplée de sa structure et de son fluide interne peut être représentée sous la forme d’une onde dont les caractéristiques varient en fonction de la position longitudinale. La méthode asymptotique Wentzel-Kramers-Brillouin est adaptée à la modélisation de ce type d’onde. Dans un premier temps, cette méthode est reprise. Un modèle numérique est également développé et les résultats des deux méthodes sont comparés. Dans un deuxième temps, la métohde Wentzel-Kramers-Brillouin est améliorée afin de prendre en compte le couplage entre plusieurs ondes. Le couplage d’un mode propagatif avec des modes évanescents est réalisé et validé. Dans la cochlée, la stimulation des cellules cillées résulte d’un mouvement de cisaillement de la membrane tectoriale et de flexion de la membrane basilaire. Le couplage entre ces deux modes de déformation est encore peu connu et offre une perspective intéressante. Dans un troisième temps, une nouvelle méthode couplant la méthode Wentzel-Kramesr Brillouin et une méthode numérique est développée et validée afin de déterminer des modes transverses de propagation. Cette méthode est appliquée à la mécanique cochléaire et un mode de flexion de la membrane basilaire et un mode relatif à un mouvement de cisaillement de la membrane tectoriale sont déterminés. Enfin, une expérience inspirée des cochlées artificielles est conçue et réalisée. La propagation d’ondes est observée et la tonotopie est mesurée et comparée aux modèles. Afin de limiter la réflexion des ondes et de faciliter la mesure, une combinaison originale du trou noir acoustique avec une lame de largeur variable est utilisée. / The cochlea is the organ of hearing for humans and mammals. It is often modelled as an inhomogeneous waveguide. A travelling wave propagates along the fluid structure coupled waveguide. The mechanical impedance of the structure is varying and provides a frequency place relation. The asymptotic method Wentzel-Kramers-Brillouin allows to solve for the basilar membrane vibration. The evanescents modes are taken into account to provide a better representation compared to the numerical models. As a second step, the finite elements method is used to solve for the transversal modes while the WKB Approximation deals with the longitudinal propagation. The first flexural mode of the basilar membrane is shown. The second propagative mode reveals a shearing motion of the tectorial membrane which can help stimulating the hair cells. An over-size artificial cochlea is designed and built. Thanks to an acoustic black hole, used as a anechoic end, travelling waves are observed on this device. Reflected waves are attenuated and the interferences with incident waves reduced. Mode coupling could be applied not only to evanescent modes but also to propagatives ones. Perspectives for the adaptation of the WKB method to fluid structure inhomogeneous waveguides, and particularly to the immersed acoustic black hole, seem to be very promising.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O fenômeno do colapso gravitacional e a estrutura de estrelas relativísticas são de grande importância em astrofísica desde a formulação da relatividade geral. Alguns trabalhos mais recentes revelam avanços importantes em nosso entendimento da formação de estruturas como buracos negros e singularidades nuas e do comportamento de fluidos exóticos tais como matéria e energia escura, incluindo aqui os fluidos fantasmas. A complexidade do estudo do colapso gravitacional está relacionada à existência de poucas soluções analíticas disponíveis para este fim. Recentemente, soluções auto-similares das equações de campo de Einstein têm atraído grande atenção, não somente pela possibilidade de serem estudadas analiticamente, simplificando o problema, mas também por sua relevância em astrofísica. Neste trabalho, estudamos o colapso gravitacional do fluido anisotrópico com auto-similaridade do segundo e primeiro tipos em espaços-tempos (2 + 1)-dimensionais, com simetria circular. Impondo as equações de estado pr = 0 e pθ = ωρ, onde ρ determina a densidade de energia e pr, pθ as pressões nas direções radial e tangencial do fluido, mostramos que, para soluções com auto-similaridade do segundo tipo, há duas distintas famílias. Para uma delas, as únicas soluções são as que representam fluido de poeira. Todas as soluções para as equações de campo de Einstein são encontradas e suas propriedades locais e globais são estudadas em detalhes. Algumas delas podem ser interpretadas como um processo de colapso gravitacional, em que singularidades nuas e buracos negros são formados. Para a outra família de soluções, temos um modelo cosmológico, com expansão acelerada, que começa em uma singularidade inicial (t = 0), com todas as condições de energia satisfeitas. Nosso propósito foi investigar o papel da não-homogeneidade na aceleração do fluido. Na intenção de estudar as soluções com auto-similaridade do primeiro tipo, mostramos que existe uma solução que representa um processo de colapso gravitacional, resultando em uma estrutura final de buraco negro ou singularidade nua, que podem ser constituídos de um fluido bem comportado ou fantasma.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O fenômeno do colapso gravitacional e a estrutura de estrelas relativísticas são de grande importância em astrofísica desde a formulação da relatividade geral. Alguns trabalhos mais recentes revelam avanços importantes em nosso entendimento da formação de estruturas como buracos negros e singularidades nuas e do comportamento de fluidos exóticos tais como matéria e energia escura, incluindo aqui os fluidos fantasmas. A complexidade do estudo do colapso gravitacional está relacionada à existência de poucas soluções analíticas disponíveis para este fim. Recentemente, soluções auto-similares das equações de campo de Einstein têm atraído grande atenção, não somente pela possibilidade de serem estudadas analiticamente, simplificando o problema, mas também por sua relevância em astrofísica. Neste trabalho, estudamos o colapso gravitacional do fluido anisotrópico com auto-similaridade do segundo e primeiro tipos em espaços-tempos (2 + 1)-dimensionais, com simetria circular. Impondo as equações de estado pr = 0 e pθ = ωρ, onde ρ determina a densidade de energia e pr, pθ as pressões nas direções radial e tangencial do fluido, mostramos que, para soluções com auto-similaridade do segundo tipo, há duas distintas famílias. Para uma delas, as únicas soluções são as que representam fluido de poeira. Todas as soluções para as equações de campo de Einstein são encontradas e suas propriedades locais e globais são estudadas em detalhes. Algumas delas podem ser interpretadas como um processo de colapso gravitacional, em que singularidades nuas e buracos negros são formados. Para a outra família de soluções, temos um modelo cosmológico, com expansão acelerada, que começa em uma singularidade inicial (t = 0), com todas as condições de energia satisfeitas. Nosso propósito foi investigar o papel da não-homogeneidade na aceleração do fluido. Na intenção de estudar as soluções com auto-similaridade do primeiro tipo, mostramos que existe uma solução que representa um processo de colapso gravitacional, resultando em uma estrutura final de buraco negro ou singularidade nua, que podem ser constituídos de um fluido bem comportado ou fantasma.

A colisão de buracos negros é uma das fontes mais importantes de ondas gravitacionais e, em geral, a emissão anisotrópica da radiação causa um recuo do objeto final. Este cenário já é conhecido há décadas, mas foi somente com o recente avanço na relatividade numérica que as velocidades finais dos objetos radiantes foram computadas com precisão. Os valores encontrados podem ser altos o suficiente para exercerem um importante papel no crescimento de buracos negros super massivos via coleção de galáxias e na abundância de núcleos galáticos ativos contendo buracos negros. Este é um autêntico efeito da não linearidade de Relatividade Geral e esta tese fornece uma nova metodologia estudar alguns aspectos da dinâmica da colisão de buracos negros. Consideramos o horizonte como uma tela canônica que codifica as informações da evolução temporal do espaço-tempo. Com esta hipótese, fenômenos como o anti-kick, isto é, uma súbita desaceleração do sistema antes de atingir a velocidade final, são explicado em termos da dissipação das deformações do horizonte. Estudamos primeiramente o Espaço-tempo de Robinson-Trautman. Uma das solução mais simples das equações de Einstein, esta métrica nos fornece um poderoso modelo para investigar tanto a perda de massa quanto o recuo do objeto final. Mostramos que, quando as configurações iniciais tem simetria especular, a massa do buraco negro remanescente e a energia irradiada são completamente determinadas pela condição inicial. Com isso, obtemos as expressões analíticas dos resultados numéricos obtidos anteriormente na literatura. Além disto, com o auxilio do método espectral de Galerkin, analisamos o regime não linear das equações envolvidas e verificamos que se pode estimar a velocidade de recuo final com boa precisão a partir de medidas da assimetria da condição inicial. Introduzimos na seqüência a curvatura efetiva como uma medida das deformações intrínsecas ao horizonte. Além de considerar as deformações gerais, ela também inclui as diferenças entre os hemisférios norte e sul. No espaço-tempo de Robinson-Trautman, essa quantidade se correlaciona de uma forma injetora com a velocidade final. Para superar algumas limitações dessa solução, aplicamos o mesmo procedimento nos resultados da simulação numérica de uma colisão head-on. Neste caso, a curvatura efetiva, está na realidade, correlacionada com a aceleração do sistema. Refinamentos e generalizações desta técnica são também discutidos e propostos para trabalhos futuros. / Colliding black holes are one of the most important sources of gravitational waves and the anisotropic emission of the radiation generally causes the recoil of the final hole. This scenario has been known for decades, but it is only thanks to the recent progress in numerical relativity that the final velocity have been accurately computed. The values found can be large enough to play an important role in the growth of supermassive black holes via mergers of galaxies and on the number of galaxies containing them. This is a genuine nonlinear effect of general relativity and this thesis provides a new methodology to study some features on the dynamics of the collision. We propose that the horizon is a canonical screen, which encodes he information of its surroundings. With this assumption, phenomena such as the anti-kick, namely the sudden deceleration before reaching the final velocity, are explained in terms of the dissipation of the horizons deformation. We first study the Robinson-Trautman spacetime. One of the simplest solutions of Einsteins equations, it provides us with a powerful toymodel to investigate both the mass loss of the system and the recoil of the final object. We show that, for the case of reflectionsymmetric initial configurations, the mass of the remnant black-hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some numerical results that had appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the non-linear regime of the equations involved, we found that the recoil velocity can be estimated with good accuracy from some symmetry measures of the initial data. Then we introduce the effective urvature as a measure of intrinsic deformations on the horizon. Not only does it account for overall deformation, but also for the differences on the north and south hemispheres. In the Robinson-Trautman spacetime, this quantity correlates in an injective way with the final velocity. To overcome some caveats of this solutions, we apply the same procedure to the results given by numerical simulations of a head-on collision. In the case, the effective curvature is actually correlated with the acceleration of the system. Further improvement and generalizations of this technic is also discussed and proposed for future work.

Orientador: Prof. Dr. André Gustavo Scagliusi Landulfo / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, Santo André, 2018. / Nas últimas décadas, pesquisas na área de física de buracos negros mostraram que existe uma relação profunda entre buracos negros, termodinâmica e mecânica quântica. Em particular, buracos negros em um contexto semiclássico parecem possuir uma temperatura TH=k/2p e uma entropia Sbh =A/4, proporcionais à sua gravidade superficial k e à sua área A, respectivamente. Essa surpreendente conexão é reforçada ao analisarmos a validade da chamada Segunda Lei Generalizada da Termodiâmica (SLG), que afirma que a entropia da matéria fora do buraco negro somada à entropia do buraco negro nunca decresce com o tempo. Este trabalho investiga provas gerais da validade da Segunda Lei Generalizada, já que tem um papel central na interpretação de buracos negros como entidadestermodinâmicas. Emseguida, é analisado como podemos usar a SLG para extender um teorema clássico de singularidade para um contexto semiclássico. / In the past few decades, research in black hole physics have shown a deep relation between black holes, thermodynamics, and quantum mechanics. In particular, blackholes in a semiclassical context appear to have a temperatureTH =k/2p and an entropy Sbh = A/4 proportional to its surface gravity k and area A,respectively. This striking connection is strengthened when one analyses the validity of the so called Generalized Second Law of Thermodynamics (GSL), which states that the entropy of matter outside the black hole plus the black hole¿s entropy never decrease with time. This work investigate general proofsofthevalidityofGeneralizedSecondLaw,sinceitplaysacentralroleininterpreting black holes as thermodynamical entities. In addition, it is analyzed how the GSL can be used to extend a classical singularity theorem to a semiclassical context.