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Master's Dissertation
DOI
10.11606/D.43.2001.tde-01092006-230554
Document
Author
Full name
Davi Giugno
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2001
Supervisor
Committee
Abdalla, Elcio (President)
Matsas, George Emanuel Avraam
Oliveira, Mario Jose de
Title in Portuguese
Buracos negros e termodinâmica
Keywords in Portuguese
buracos negros
gravitação
termodinâmica
Abstract in Portuguese
A finalidade deste trabalho é estabelecer as conexões entre física de buracos negros e termodinâmica, atentando para eventuais semelhanças e diferenças entre ramos aparentemente bem diversos da física moderna. Tais conexões foram inicialmente buscadas e estabelecidas na década de 1970, graças ao trabalho de S. Hawking e Jacob D. Bekenstein, entre outros, e sucessivamente aprofundadas nos anos subseqüentes, notadamente na última década. O mérito maior do primeiro foi estabelecer a emissão de radiação com espectro térmico por buracos negros em geral, mesmo aqueles desprovidos de rotação e carga (buracos negros de Schwarzschild). O segundo encarregou-se de correlacionar leis termodinâmicas clássicas com processos envolvendo buracos negros. Neste trabalho, procuramos inicialmente estudar os buracos negros de Schwarzschild e Kerr-Newman no tocante às suas propriedades gerais, bem como o problema do movimento de partículas nos espaços-tempos em questão, para discutir-se brevemente o problema de extração de energia de buracos negros, como apontado por Penrose e outros. Estabelecidas as propriedades gerais, pode-se enfim derivar a Termodinâmica destes buracos, correlacionando-se entropia e área, e obter expressões para a temperatura de corpo negro dos mesmos - em perfeita consonância com a derivação de Hawking, não abordada aqui, feita através da Teoria Quântica de Campos. Com a temperatura, pode-se estudar as capacidades térmicas, reveladores de propriedades típicas de buracos negros não compartilhadas por sistemas clássicos. A reboque destas, entra a discussão sobre a estabilidade termodinâmica de buracos negros em ensembles canônicos e microcanônicos, através do método das séries lineares, de Poincaré, fechando o presente trabalho. Assim, os capítulos 1 e 2 tratam das soluções de Schwarzschild e Kerr-Newman, respectivamente, abordando-lhes as propriedades gerais e o problema do movimento de partículas, materiais ou não, nessas geometrias. O capítulo 3 estabelece as pontes entre Termodinâmica e buracos negros, sendo crucial para o restante do trabalho. No capítulo 4 estudamos temperaturas e capacidades térmicas de diversos buracos negros, e finalmente no capítulo 5 vem o problema da estabilidade termodinâmica dos buracos negros.
Title in English
Black holes and thermodynamics
Keywords in English
black holes
gravitation
thermodynamics
Abstract in English
In the present work, we have established the connections between black-hole physics and thermodynamics, searching for similarities and differences between these two branches of physicxs, which might look quite far apart. Such links were first sought for and established during the 1970s, thanks to the pioneering work of S. Hawking and Jacob D. Bekenstein, among others, and continuously developed in the following years, notably in the last decade. Hawking's major achievement was the prediction, from arguments based on Quantum Field Theory, that black holes radiate with a thermal spectrum, even the uncharged and nonrotating ones (the Schwarzschild black holes). Bekenstein's biggest merit was to find the link between classical thermodynamical laws and processes involving black holes. In this work, we started with Schwarzschild and Kerr-Newman black holes, working out their general properties, as well as the problem of particle motion in such spacetimes, so that we could briefly discuss the issue of energy extraction from black holes, as established by Penrose and others. Once the general features of these black holes were known, it was possible to derive the black-hole thermodynamics, due to a simple relation between black-hole entropy and area. Expressions for the black-hole temperature were then easily obtained, in perfect agreement with Hawking's own derivation, not considered here. With temperatures at hand, heat capacities could be thoroughly examined, showing intrinsic properties of black holes, not shared by classical systems. The question of thermodynamic stability of black holes arose naturally from heat capacity analysis, and we have analysed black holes in both the microcanonical and canonical ensembles, in the light of Poincaré's linear series method, completing the current work. Chapters 1 and 2 deal with the Schwarzschild and Kerr-Newman solutions, respectively, deriving their general features and working out particle motion in these geometries. Chapter 3 establishes the links between black-hole physics and thermodynamics, being of crucial importance for the subsequent chapters. Chapter 4 provides an extensive study of black-hole temperatures and heat capacities, paving the way for the last chapter, Chapter 5, concerning to thermodynamic stability of black holes.
 
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Publishing Date
2006-09-13
 
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