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. / 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.

No description available.

We aim to have a comprehensive understanding of holographic correspondence and to demonstrate how the holographic correspondence (or renormalization) can be applied. Thus this thesis is divided into two parts. The first part is devoted to the former purpose (chapters 1 to 4 including appendix A,B, and C), and the second part is dedicated for the latter purpose (chapter 5 to 7). In Part I, the structure of the AdS/CFT correspondence is analyzed, and the properties of the AdS spacetime is studied in the context of the AdS/CFT correspondence; Here, we investigate the isometry group, the conformal structure, and generation of asymptotic solution near the conformal boundary. This solution yields significant convenience for the process of holographic renormalization. Moreover the properties of the Minkowski spacetime are compared to those of the AdS spacetime. To develop a greater understanding of the Lifshitz/quantum critical theory correspondence, the quantum phase transition is studied. Furthermore The holographic renormalization is briefly reviewed. In part II, the holographic renormalization associated with the Mann-Marolf (MM) counterterm is investigated for the asymptotically Minkowski spacetime in (n+3) dimensions. As a boundary condition, the cylindrical coordinate is considered. The solution of the MM-counterterm is obtained by solving the given algebraic equation, and from the counterterm solution, the boundary stress tensor is calculated. It is proven that the formula for conserved quantities via the boundary stress tensor holds. Next, we investigate deformations of Lifshitz holography with the Gauss-Bonnet term in (n+1) dimensional spacetime. To admit the non-trivial solution of the sub-leading orders, a value of the dynamical critical exponent z is restricted by z= n-1-2(n-2)α̃, where is the (redefined) Gauss-Bonnet coupling constant. Such solution of sub-leading orders correspond to the marginally relevant modes for the massive vector field and are generated by Λ~0, at the asymptotic region. A generic black hole solution, which is characterized by the horizon flux of the vector field and α̃, is considered in the bulk. We explore its thermodynamic properties, which depend on temperature, by varying n and α̃. As a result, the contribution of the marginally relevant mode is found in a function of Λ^z/T, and the relation between the free energy density and the energy density is numerically recovered when the marginally relevant mode is turned off (Λ=0), is obtained.

No description available.

The use of dichromated gelatin (DCG) for the formation of holographic optical elements is investigated. In particular, a study is made of the possible sources of spurious recording and replay in such diffracting media. The formation of spurious gratings due to boundary mismatch, when recording a transmission grating in air, is investigated. Experimental results are treated using a simple linear theory which is capable of predicting the relative modulation strengths of each of six recorded gratings. The efficiencies of each of these gratings is related to Fresnel's Laws of reflection and therefore the beam ratio. A brief experimental study of the beam ratio is made. It is found that linear theories do not explain replay of gratings recorded at high exposure energies. This is because DCG exhibits a saturating recording characteristic. A theoretical model is developed to verify experimental results of modulation versus exposure energy for the recording of single and double exposure transmission gratings and their subsequent harmonics. This gives good agreement for most cases, however, it does not explain fully the replay of a difference grating formed due to nonlinearities in the double exposure hologram. A coupled wave theory is therefore developed to take account of both multiple grating interactions between the two primary recordings and the recording of a third grating with a spatial frequency equal to the difference of the two fundamental frequencies. The model gives good agreement with experimental results for varying replay angles and wavelengths. DCG is finally used as a tool to investigate the formation of noise gratings in silver halide emulsions. In particular, results are presented for experiments which were performed to study the effect of high angular scatter upon the selectivity of the noise grating and the recording of reflection noise gratings.

We aim to have a comprehensive understanding of holographic correspondence and to demonstrate how the holographic correspondence (or renormalization) can be applied. Thus this thesis is divided into two parts. The first part is devoted to the former purpose (chapters 1 to 4 including appendix A,B, and C), and the second part is dedicated for the latter purpose (chapter 5 to 7). In Part I, the structure of the AdS/CFT correspondence is analyzed, and the properties of the AdS spacetime is studied in the context of the AdS/CFT correspondence; Here, we investigate the isometry group, the conformal structure, and generation of asymptotic solution near the conformal boundary. This solution yields significant convenience for the process of holographic renormalization. Moreover the properties of the Minkowski spacetime are compared to those of the AdS spacetime. To develop a greater understanding of the Lifshitz/quantum critical theory correspondence, the quantum phase transition is studied. Furthermore The holographic renormalization is briefly reviewed. In part II, the holographic renormalization associated with the Mann-Marolf (MM) counterterm is investigated for the asymptotically Minkowski spacetime in (n+3) dimensions. As a boundary condition, the cylindrical coordinate is considered. The solution of the MM-counterterm is obtained by solving the given algebraic equation, and from the counterterm solution, the boundary stress tensor is calculated. It is proven that the formula for conserved quantities via the boundary stress tensor holds. Next, we investigate deformations of Lifshitz holography with the Gauss-Bonnet term in (n+1) dimensional spacetime. To admit the non-trivial solution of the sub-leading orders, a value of the dynamical critical exponent z is restricted by z= n-1-2(n-2)α̃, where is the (redefined) Gauss-Bonnet coupling constant. Such solution of sub-leading orders correspond to the marginally relevant modes for the massive vector field and are generated by Λ~0, at the asymptotic region. A generic black hole solution, which is characterized by the horizon flux of the vector field and α̃, is considered in the bulk. We explore its thermodynamic properties, which depend on temperature, by varying n and α̃. As a result, the contribution of the marginally relevant mode is found in a function of Λ^z/T, and the relation between the free energy density and the energy density is numerically recovered when the marginally relevant mode is turned off (Λ=0), is obtained.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 70-72). Also available via the Internet.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 63-66). Also available in electronic version.

In this work, digital holography (DH) is extensively utilized to characterize microparticles. Here, “characterization” refers to the determination of a particle’s shape, size, and, in some cases, its surface structure. A variety of microparticles, such as environmental dust, pollen, volcanic ash, clay, and biological samples, are thoroughly analyzed. In this technique, the microscopically fine interference pattern generated by the coherent superposition of an object and a reference wave fields is digitally recorded using an optoelectronic sensor, in the form of a hologram, and the desired particle property is then computationally extracted by performing a numerical reconstruction to form an image of the particle. The objective of this work is to explore, develop, and demonstrate the feasibility of different experimental arrangements to reconstruct the image of various arbitrary-shaped particles. Both forward- and backward-scattering experimental arrangements are constructed and calibrated to quantify the size of several micron-sized particles. The performance and implications of the technique are validated using the National Institute of Standards and Technology (NIST)-traceable borosilicate glass microspheres of various diameters and a Thorlabs resolution plate. After successful validation and calibration of the system, the resolution limit of the experimental setup is estimated, which is ~10 microns. Particles smaller than 10 microns in size could not be imaged well enough to ensure that what appeared like a single particle was not in fact a cluster. The forward- and backward-scattering holograms of different samples are recorded simultaneously and images of the particles are then computationally reconstructed from these recorded holograms. Our results show that the forward- and backward-scattering images yield different information on the particle surface structure and edge roughness, and thus, reveal more information about a particle profile. This suggests that the two image perspectives reveal aspects of the particle structure not available from a more commonly used forward-scattering based image alone. The results of this work could be supportive to insight more on the particles’ morphology and subsequently important for the advancement of contactree particle characterization technique.

No description available.