Quantum corrections to the entropy of charged rotating black holes

Hawking radiation from a black hole can be viewed as quantum tunneling of particles through the event horizon. Using this approach we provide a general framework for studying corrections to the entropy of black holes beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law thermodynamics, we study charged rotating black holes and explicitly work out the corrections to entropy and horizon area for the Kerr-Newman and charged rotating BTZ black holes. It is shown that the results for other geometries like the Schwarzschild, Reissner-Nordstr\"{o}m and anti-de Sitter Schwarzschild spacetimes follow easily

Algebraic approach to quantum black holes: logarithmic corrections to black hole entropy

The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As shown previously, for a neutral non-rotating black hole, such eigenvalues must be $2^{n}$-fold degenerate if one constructs the black hole stationary states by means of a pair of creation operators subject to a specific algebra. We show that the algebra of these two building blocks exhibits $U(2)\equiv U(1)\times SU(2)$ symmetry, where the area operator generates the U(1) symmetry. The three generators of the SU(2) symmetry represent a {\it global} quantum number (hyperspin) of the black hole, and we show that this hyperspin must be zero. As a result, the degeneracy of the $n$-th area eigenvalue is reduced to $2^{n}/n^{3/2}$ for large $n$, and therefore, the logarithmic correction term $-3/2\log A$ should be added to the Bekenstein-Hawking entropy. We also provide a heuristic approach explaining this result, and an evidence for the existence of {\it two} building blocks.Comment: 15 pages, Revtex, to appear in Phys. Rev.

Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data -- the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2 supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner-Nordstrom black holes in ordinary Einstein-Maxwell theory.Comment: LaTeX file, 66 page

Higher order WKB corrections to black hole entropy in brick wall formalism

We calculate the statistical entropy of a quantum field with an arbitrary spin propagating on the spherical symmetric black hole background by using the brick wall formalism at higher orders in the WKB approximation. For general spins, we find that the correction to the standard Bekenstein-Hawking entropy depends logarithmically on the area of the horizon. Furthermore, we apply this analysis to the Schwarzschild and Schwarzschild-AdS black holes and discuss our results.Comment: 21 pages, published versio

Ground Water Dependence of Endangered Ecosystems: Nebraska’s Eastern Saline Wetlands

Many endangered or threatened ecosystems depend on ground water for their survival. Nebraska’s saline wetlands, home to a number of endangered species, are ecosystems whose development, sustenance, and survival depend on saline ground water discharge at the surface. This study demonstrates that the saline conditions present within the eastern Nebraska saline wetlands result from the upwelling of saline ground water from within the underlying Dakota Aquifer and deeper underlying formations of Pennsylvanian age. Over thousands to tens of thousands of years, saline ground water has migrated over regional scale flowpaths from recharge zones in the west to the present-day discharge zones along the saline streams of Rock, Little Salt, and Salt creeks in Lancaster and Saunders counties. An endangered endemic species of tiger beetle living within the wetlands has evolved under a unique set of hydrologic conditions, is intolerant to recent anthropogenic changes in hydrology and salinity, and is therefore on the brink of extinction. As a result, the fragility of such systems demands an even greater understanding of the interrelationships among geology, hydrology, water chemistry, and biology than in less imperiled systems where adaptation is more likely. Results further indicate that when dealing with ground water discharge–dependent ecosystems, and particularly those dependent on dissolved constituents as well as the water, wetland management must be expanded outside of the immediate surface location of the visible ecosystem to include areas where recharge and lateral water movement might play a vital role in wetland hydrologic and chemical mixing dynamics