Flat Information Geometries in Black Hole Thermodynamics

The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the Einstein–Maxwell equations. The picture of state space that we obtain makes some properties such as the occurence of divergent specific heats transparent.Supported by VR.     

Temperature and induced electric field dependence on the phase transition of 9/70/30, 9/65/35 and 9/60/40 PLZT ceramics

In this work, Pb_0.91La_0.09(Zr_1–xTi_x)_0.9775O₃ ceramics where x = 0.3, 0.35 and 0.4 (the composition near MPB) were prepared by solid solution method. After fabrication process, electrical property was measured by LCR meter. Polarization and induced strain behavior of the samples were investigated by using interferometry technique modified with Sawyer–Tower circuit at various temperatures. The results of dielectric, polarization and induced strain properties were due to the Zr/Ti ratios, which changed their behavior when temperature was varied (30–70 °C). The normal to macro-micro domains to relaxor and paraelectric phase transition was demonstrated which is related to linear or nonlinear increase of polarization and induced strain as a function of applied subswitching electric field.     

Geometry of Black Hole Thermodynamics

The Hessian of the entropy function can be thought of as a metric tensor on the state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of this metric gives insight into the underlying statistical mechanical system; the claim is supported by numerous examples. We study this geometry for some families of black holes. It is flat for the BTZ and Reissner–Nordström black holes, while curvature singularities occur for the Reissner–Nordström–anti–de Sitter and Kerr black holes.     

Geometro-thermodynamics of tidal charged black holes

Tidal charged spherically symmetric vacuum brane black holes are characterized by their mass m and tidal charge q, an imprint of the five-dimensional Weyl curvature. For q>0 they are formally identical to the Reissner–Nordström black hole of general relativity. We study the thermodynamics and thermodynamic geometries of tidal charged black holes and discuss similarities and differences as compared to the Reissner–Nordströ m black hole. As a similarity, we show that (for q>0) the heat capacity of the tidal charged black hole diverges on a set of measure zero of the parameter space, nevertheless both the regularity of the Ruppeiner metric and a Poincaré stability analysis show no phase transition at those points. The thermodynamic state spaces being different indicates that the underlying statistical models could be different. We find that the q<0 parameter range, which enhances the localization of gravity on the brane, is thermodynamically preferred. Finally we constrain for the first time the possible range of the tidal charge from the thermodynamic limit on gravitational radiation efficiency at black hole mergers.     

Anti-de Sitter quotients,bubbles of nothing,and black holes

In 3+1 dimensions there are anti-de Sitter quotients which are black holes with toroidal event horizons. By analytic continuation of the Schwarzschild-anti-de Sitter solution (and appropriate identifications) one finds two one parameter families of spacetimes that contain these quotient black holes. One of these families consists of B-metrics (“bubbles of nothing”), the other of black hole spacetimes. All of them have vanishing conserved charges. I. Bengtsson was supported by VR.