The Cardy-Verlinde Formula and Charged Topological AdS Black Holes

We consider the brane universe in the bulk background of the charged topological AdS black holes. The evolution of the brane universe is described by the Friedmann equations for a flat or an open FRW-universe containing radiation and stiff matter. We find that the temperature and entropy of the dual CFT are simply expressed in terms of the Hubble parameter and its time derivative, and the Friedmann equations coincide with thermodynamic formulas of the dual CFT at the moment when the brane crosses the black hole horizon. We obtain the generalized Cardy-Verlinde formula for the CFT with an R-charge, for any values of the curvature parameter k in the Friedmann equations.Comment: 10 pages, LaTeX, references adde

Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy

We present a class of exact analytic and static, spherically symmetric black hole solutions in the semi-classical Einstein equations with Weyl anomaly. The solutions have two branches, one is asymptotically flat and the other asymptotically de Sitter. We study thermodynamic properties of the black hole solutions and find that there exists a logarithmic correction to the well-known Bekenstein-Hawking area entropy. The logarithmic term might come from non-local terms in the effective action of gravity theories. The appearance of the logarithmic term in the gravity side is quite important in the sense that with this term one is able to compare black hole entropy up to the subleading order, in the gravity side and in the microscopic statistical interpretation side.Comment: Revtex, 10 pages. v2: minor changes and to appear in JHE

Thermodynamic Geometry and Critical Behavior of Black Holes

Based on the observations that there exists an analogy between the Reissner-Nordstr\"om-anti-de Sitter (RN-AdS) black holes and the van der Waals-Maxwell liquid-gas system, in which a correspondence of variables is $(\phi, q) \leftrightarrow (V,P)$, we study the Ruppeiner geometry, defined as Hessian matrix of black hole entropy with respect to the internal energy (not the mass) of black hole and electric potential (angular velocity), for the RN, Kerr and RN-AdS black holes. It is found that the geometry is curved and the scalar curvature goes to negative infinity at the Davies' phase transition point for the RN and Kerr black holes. Our result for the RN-AdS black holes is also in good agreement with the one about phase transition and its critical behavior in the literature.Comment: Revtex, 18 pages including 4 figure

Holographic Thermodynamic on the Brane in Topological Reissner-Nordstr\"om de Sitter Space

We consider the brane universe in the bulk background of the topological Reissner-Nordstr\"om de Sitter black holes. We show that the thermodynamic quantities (including entropy) of the dual CFT take usual special forms expressed in terms of Hubble parameter and its time derivative at the moment, when the brane crosses the black hole horizon or the cosmological horizon. We obtain the generalized Cardy-Verlinde formula for the CFT with an charge and cosmological constant, for any values of the curvature parameter $k$ in the Friedmann equations.Comment: 8 page

Multiple passages of light through an absorption inhomogeneity in optical imaging of turbid media

The multiple passages of light through an absorption inhomogeneity of finite size deep within a turbid medium is analyzed for optical imaging using the ``self-energy'' diagram. The nonlinear correction becomes more important for an inhomogeneity of a larger size and with greater contrast in absorption with respect to the host background. The nonlinear correction factor agrees well with that from Monte Carlo simulations for CW light. The correction is about $50$ in near infrared for an absorption inhomogeneity with the typical optical properties found in tissues and of size of five times the transport mean free path.Comment: 3 figure

Cosmology with minimal length uncertainty relations

We study the effects of the existence of a minimal observable length in the phase space of classical and quantum de Sitter (dS) and Anti de Sitter (AdS) cosmology. Since this length has been suggested in quantum gravity and string theory, its effects in the early universe might be expected. Adopting the existence of such a minimum length results in the Generalized Uncertainty Principle (GUP), which is a deformed Heisenberg algebra between minisuperspace variables and their momenta operators. We extend these deformed commutating relations to the corresponding deformed Poisson algebra in the classical limit. Using the resulting Poisson and Heisenberg relations, we then construct the classical and quantum cosmology of dS and Ads models in a canonical framework. We show that in classical dS cosmology this effect yields an inflationary universe in which the rate of expansion is larger than the usual dS universe. Also, for the AdS model it is shown that GUP might change the oscillatory nature of the corresponding cosmology. We also study the effects of GUP in quantized models through approximate analytical solutions of the Wheeler-DeWitt (WD) equation, in the limit of small scale factor for the universe, and compare the results with the ordinary quantum cosmology in each case.Comment: 11 pages, 4 figures, to appear in IJMP

Influence of Homogeneous Interfaces on the Strength of 500 nm Diameter Cu Nanopillars

Interfaces play an important role in crystalline plasticity as they affect strength and often serve as obstacles to dislocation motion. Here we investigate effects of grain and nanotwin boundaries on uniaxial strength of 500 nm diameter Cu nanopillars fabricated by e-beam lithography and electroplating. Uniaxial compression experiments reveal that strength is lowered by introducing grain boundaries and significantly rises when twin boundaries are present. Weakening is likely due to the activation of grain-boundary-mediated processes, while impeding dislocation glide can be responsible for strengthening by twin boundaries