The Weyl curvature conjecture and black hole entropy

The universe today, with structure such as stars, galaxies and black holes, seems to have evolved from a very homogeneous initial state. From this it appears as if the entropy of the universe is decreasing, in violation of the second law of thermodynamics. It has been suggested by Roger Penrose \cite{grossmann:penrose:wcc} that this inconsistency can be solved if one assigns an entropy to the spacetime geometry. He also pointed out that the Weyl tensor has the properties one would expect to find in a description of a gravitational entropy. In this article we make an attempt to use this so-called Weyl curvature conjecture to describe the Hawking-Bekenstein entropy of black holes and the entropy of horizons due to a cosmological constant.Comment: 10 pages, 2 figures, typesetting revtex

Constructing Lifshitz solutions from AdS

Under general assumptions, we show that a gravitational theory in d+1 dimensions admitting an AdS solution can be reduced to a d-dimensional theory containing a Lifshitz solution with dynamical exponent z=2. Working in a d=4, N=2 supergravity setup, we prove that if the AdS background is N=2 supersymmetric, then the Lifshitz geometry preserves 1/4 of the supercharges, and we construct the corresponding Killing spinors. We illustrate these results in examples from supersymmetric consistent truncations of type IIB supergravity, enhancing the class of known 4-dimensional Lifshitz solutions of string theory. As a byproduct, we find a new AdS4 x S1 x T(1,1) solution of type IIB.Comment: 29 pages, no figures; v2 minor corrections, a reference adde

Influence of Supporting Cells on Neuronal Degeneration After Hair Cell Loss

In sensorineural hearing loss, hair cell loss is often followed by loss of cochlear nerve fibers, which can continue for years after the insult. The degree and time course of neuronal loss varies, but the reasons for this variation are unclear. The present study addresses this issue with a quantitative analysis of hair cell, supporting cell, and neuronal survival in animals with long-term survival of up to 5.5 years from two types of drug-induced hair cell loss: aminoglycoside antibiotics and platinum-containing chemotherapeutics. To complement the analysis of the effects of organ of Corti damage on neuronal survival, cases of primary neuronal degeneration, via auditory nerve section, are also assessed. Analysis shows that (1) long-term neuronal survival is enhanced when supporting cells in the inner hair cell (IHC) area remain intact; (2) after hair cell loss, the time course of neuronal loss is slower in the apex than in the base; (3) primary loss of cochlear nerve fibers does not lead to secondary degeneration of sensory cells or supporting cells in the organ of Corti; and (4) after auditory nerve section, there can be a massive reinnervation of the IHC region, especially in the apex. Results are consistent with the idea that supporting cells participate in the regulation of neuronal survival and neuronal sprouting in the organ of Corti