The entropy of black holes: a primer

After recalling the definition of black holes, and reviewing their energetics and their classical thermodynamics, one expounds the conjecture of Bekenstein, attributing an entropy to black holes, and the calculation by Hawking of the semi-classical radiation spectrum of a black hole, involving a thermal (Planckian) factor. One then discusses the attempts to interpret the black-hole entropy as the logarithm of the number of quantum micro-states of a macroscopic black hole, with particular emphasis on results obtained within string theory. After mentioning the (technically cleaner, but conceptually more intricate) case of supersymmetric (BPS) black holes and the corresponding counting of the degeneracy of Dirichlet-brane systems, one discusses in some detail the ``correspondence'' between massive string states and non-supersymmetric Schwarzschild black holes.Comment: 51 pages, 4 figures, talk given at the "Poincare seminar" (Paris, 6 December 2003), to appear in Poincare Seminar 2003 (Birkhauser

Black Branes in a Box: Hydrodynamics, Stability, and Criticality

We study the effective hydrodynamics of neutral black branes enclosed in a finite cylindrical cavity with Dirichlet boundary conditions. We focus on how the Gregory-Laflamme instability changes as we vary the cavity radius R. Fixing the metric at the cavity wall increases the rigidity of the black brane by hindering gradients of the redshift on the wall. In the effective fluid, this is reflected in the growth of the squared speed of sound. As a consequence, when the cavity is smaller than a critical radius the black brane becomes dynamically stable. The correlation with the change in thermodynamic stability is transparent in our approach. We compute the bulk and shear viscosities of the black brane and find that they do not run with R. We find mean-field theory critical exponents near the critical point.Comment: 23 pages, 3 figures. v2: added comments on first-order phase transitio

Dynamical Cobordisms in General Relativity and String Theory

We describe a class of time-dependent solutions in string- or M-theory that are exact with respect to alpha-prime and curvature corrections and interpolate in physical space between regions in which the low energy physics is well-approximated by different string theories and string compactifications. The regions are connected by expanding "domain walls" but are not separated by causal horizons, and physical excitations can propagate between them. As specific examples we construct solutions that interpolate between oriented and unoriented string theories, and also between type II and heterotic theories. Our solutions can be weakly curved and under perturbative control everywhere and can asymptote to supersymmetric at late times.Comment: 35 pages, 5 figures, LaTeX v2: reference adde

Diagnostic Utility of the Impact of Event Scale-Revised in Two Samples of Survivors of War

The study aimed at examining the diagnostic utility of the Impact of Event Scale-Revised (IES-R) as a screening tool for post-traumatic stress disorder (PTSD) in survivors of war. The IES-R was completed by two independent samples that had survived the war in the Balkans: a sample of randomly selected people who had stayed in the area of former conflict (n = 3,313) and a sample of refugees to Western European countries (n = 854). PTSD was diagnosed using the MINI International Neuropsychiatric Interview. Prevalence of PTSD was 20.1% in the Balkan sample and 33.1% in the refugee sample. Results revealed that when considering a minimum value of specificity of 0.80, the optimally sensitive cut-off score for screening for PTSD in the Balkan sample was 34. In both the Balkan sample and the refugee sample, this cut-off score provided good values on sensitivity (0.86 and 0.89, respectively) and overall efficiency (0.81 and 0.79, respectively). Further, the kappa coefficients for sensitivity for the cut-off of 34 were 0.80 in both samples. Findings of this study support the clinical utility of the IES-R as a screening tool for PTSD in large-scale research studies and intervention studies if structured diagnostic interviews are regarded as too labor-intensive and too costly

Fermionic Wigs for AdS-Schwarzschild Black Holes

We provide the metric, the gravitino fields and the gauge fields to all orders in the fermionic zero modes for D=5 and D=4, N=2 gauged supergravity solutions starting from non-extremal AdS--Schwarzschild black holes. We compute the Brown-York stress--energy tensor on the boundary of AdS_5 / AdS_4 spaces and we discuss some implications of the fermionic corrections to perfect fluid interpretation of the boundary theory. The complete non-linear solution, which we denote as fermionic wig, is achieved by acting with supersymmetry transformations upon the supergravity fields and that expansion naturally truncates at some order in the fermionic zero modes.Comment: 27 pages, Latex2e, no figures, 3 ancillary file

Causality and the AdS Dirichlet problem

The (planar) AdS Dirichlet problem has previously been shown to exhibit superluminal hydrodynamic sound modes. This problem is defined by bulk gravitational dynamics with Dirichlet boundary conditions imposed on a rigid timelike cut-off surface. We undertake a careful examination of this set-up and argue that, in most cases, the propagation of information between points on the Dirichlet hypersurface is nevertheless causal with respect to the induced light cones. In particular, the high-frequency dynamics is causal in this sense. There are however two exceptions and both involve boundary gravitons whose propagation is not constrained by the Einstein equations. These occur in i) AdS$_3$, where the boundary gravitons generally do not respect the induced light cones on the boundary, and ii) Rindler space, where they are related to the infinite speed of sound in incompressible fluids. We discuss implications for the fluid/gravity correspondence with rigid Dirichlet boundaries and for the black hole membrane paradigm.Comment: 29 pages, 5 figures. v2: added refs. v3: minor clarification

Thermodynamic instability of doubly spinning black objects

We investigate the thermodynamic stability of neutral black objects with (at least) two angular momenta. We use the quasilocal formalism to compute the grand canonical potential and show that the doubly spinning black ring is thermodynamically unstable. We consider the thermodynamic instabilities of ultra-spinning black objects and point out a subtle relation between the microcanonical and grand canonical ensembles. We also find the location of the black string/membrane phases of doubly spinning black objects.Comment: 25 pages, 7 figures v2: matches the published versio

Stereoselective handling of perhexiline:Implications regarding accumulation within the human myocardium

Purpose: Perhexiline is a prophylactic anti-ischaemic agent with weak calcium antagonist effect which has been increasingly utilised in the management of refractory angina. The metabolic clearance of perhexiline is modulated by CYP2D6 metaboliser status and stereoselectivity. The current study sought to (1) determine whether the acute accumulation of perhexiline in the myocardium is stereoselective and (2) investigate the relationship between duration of short-term therapy and the potential stereoselective effects of perhexiline within myocardium. Method: Patients (n = 129) from the active arm of a randomised controlled trial of preoperative perhexiline in cardiac surgery were treated with oral perhexiline for a median of 9 days. Correlates of atrial and ventricular concentrations of enantiomers were sought via univariate followed by multivariate analyses. Results: Myocardial uptake of both (+) and (−) perhexiline was greater in ventricles than in atria, and there was more rapid clearance of (−) than (+) perhexiline. The main determinants of atrial uptake of both (+) and (−) perhexiline were the plasma concentrations [(+) perhexiline: β = −0.256, p = 0.015; (−) perhexiline: β = −0.347, p = 0.001] and patients’ age [(+) perhexiline: β = 0.300, p = 0.004; (−) perhexiline: β = 0.288, p = 0.005]. Atrial uptake of (+) enantiomer also varied directly with duration of therapy (β = 0.228, p = 0.025), while atrial uptake of (−) perhexiline varied inversely with simultaneous heart rate (β = −0.240, p = 0.015). Conclusion: (1) Uptake of both perhexiline enantiomers into atrium is greater with advanced age and displays evidence of both saturability and minor stereoselectivity. (2) Atrial uptake of (−) perhexiline may selectively modulate heart rate reduction

Small Hairy Black Holes in Global AdS Spacetime

We study small charged black holes in global AdS spacetime in the presence of a charged massless minimally coupled scalar field. In a certain parameter range these black holes suffer from well known superradiant instabilities. We demonstrate that the end point of the resultant tachyon condensation process is a hairy black hole which we construct analytically in a perturbative expansion in the black hole radius. At leading order our solution is a small undeformed RNAdS black hole immersed into a charged scalar condensate that fills the AdS `box'. These hairy black hole solutions appear in a two parameter family labelled by their mass and charge. Their mass is bounded from below by a function of their charge; at the lower bound a hairy black hole reduces to a regular horizon free soliton which can also be thought of as a nonlinear Bose condensate. We compute the microcanonical phase diagram of our system at small mass, and demonstrate that it exhibits a second order `phase transition' between the RNAdS black hole and the hairy black hole phases.Comment: 68+1 pages, 18 figures, JHEP format. v2 : small typos corrected and a reference adde

Cardy and Kerr

The Kerr/CFT correspondence employs the Cardy formula to compute the entropy of the left moving CFT states. This computation, which correctly reproduces the Bekenstein--Hawking entropy of the four-dimensional extremal Kerr black hole, is performed in a regime where the temperature is of order unity rather than in a high-temperature regime. We show that the comparison of the entropy of the extreme Kerr black hole and the entropy in the CFT can be understood within the Cardy regime by considering a D0-D6 system with the same entropic properties.Comment: 20 pages; LaTeX; JHEP format; v.2 references added, v.3 Section 4 adde