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Doctoral Thesis
DOI
10.11606/T.43.2002.tde-11122013-180728
Document
Author
Full name
Luis Alejandro Correa Borbonet
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2002
Supervisor
Committee
Abdalla, Elcio (President)
Berkovits, Nathan Jacob
Rivelles, Victor de Oliveira
Saa, Alberto Vazquez
Shapiro, Ilya Lvovich
Title in Portuguese
Entropia e holografia em teorias da gravitação
Keywords in Portuguese
Entropy
Holographic principle
Theories of gravitation
Abstract in Portuguese
Estudamos a entropia em várias situações na gravidade, verificando se seu comportamento é holográfico, obedecendo à lei de área de Bekenstein. Inicialmente, usando o método da "parede de tijolos", calculamos, em diversos casos, a entropia estatística de um campo escalar num fundo não trivial. Tal fundo é gerado por buracos negros de 4 ou 5 dimensões com cargas. A fórmula da entropia de Bekenstein é geralmente satisfeita, mas algumas correções são discutidas no caso pentadimensional. Este método é também aplicado para soluções tipo buracos negros na gravidade de Lovelock. Resulta que o método de "parede de tijolos", apesar de correto para a teoria de Einstein-Hilbert, pode não ser válido em geral, o que também acontece com a lei área. Algumas propriedades concernentes à teoria de cordas, especialmente a tecnologia das D-branas, são revistas naqueles aspectos necessários para este trabalho. Também estudamos e calculamos o limite superior da entropia para a gravidade de Lovelock. Finalmente, verificamos a validade do princípio holográfico num universo de (4 + n) dimensões numa fase inflacionária assimétrica.
Title in English
Entropy and holography in theories of gravitation.
Keywords in English
Entropy
Holographic principle
Theories of gravitation
Abstract in English
We study the entropy for various situations in gravity, checking whether its behavior is holographic, obeying Bekensteins area law. First, using the brick wall method, we compute the statistical entropy of a scalar field in a nontrivial background in different cases. Such a background is generated by four and five dimensional black holes with charges. The Bekenstein entropy formula is generally obeyed, but corrections are discussed in the latter case. This method is applied also to the black hole solutions of the Lovelock gravity. It turns out that the brickwall method, through correct for the Einstein-Hilbert theory, may fail in general. The same happens to the area law. Some properties concerning string theory, especially the D-branes technology, are reviewed while necessary to this work. Furthermore, we study and compute the upper limit of the entropy for the Lovelock gravity. Finally, we check the validity of the holographic principle in a (4+n) dimensional universe in an asymmetric inflationary phase.
 
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Publishing Date
2014-02-18
 
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