Bounds on the force between black holes

We treat the problem of N interacting, axisymmetric black holes and obtain two relations among physical parameters of the system including the force between the black holes. The first relation involves the total mass, the angular momenta, the distances and the forces between the black holes. The second one relates the angular momentum and area of each black hole with the forces acting on it.Comment: 13 pages, no figure

Assessment of variability sources in grape ripening parameters by using FTIR and multivariate modelling

The variability in grape ripening is associated with the fact that each grape berry undergoes its own biochemical processes. Traditional viticulture manages this by averaging the physicochemical values of hundreds of grapes to make decisions. However, to obtain accurate results it is necessary to evaluate the different sources of variability, so exhaustive sampling is essential. In this article, the factors “grape maturity over time” and “position of the grape” (both in the grapevine and in the bunch/cluster) were considered and studied by analyzing the grapes with a portable ATR-FTIR instrument and evaluating the spectra obtained with ANOVA–simultaneous component analysis (ASCA). Ripeness over time was the main factor affecting the characteristics of the grapes. Position in the vine and in the bunch (in that order) were also significantly important, and their effect on the grapes evolves over time. In addition, it was also possible to predict basic oenological parameters (TSS and pH with errors of 0.3 °Brix and 0.7, respectively). Finally, a quality control chart was built based on the spectra obtained in the optimal state of ripening, which could be used to decide which grapes are suitable for harvest

A lower bound for the mass of axisymmetric connected black hole data sets

We present a generalisation of the Brill-type proof of positivity of mass for axisymmetric initial data to initial data sets with black hole boundaries. The argument leads to a strictly positive lower bound for the mass of simply connected, connected axisymmetric black hole data sets in terms of the mass of a reference Schwarzschild metric

Hairy planar black holes in higher dimensions

We construct exact hairy planar black holes in D-dimensional AdS gravity. These solutions are regular except at the singularity and have stress-energy that satisfies the null energy condition. We present a detailed analysis of their thermodynamical properties and show that the first law is satisfied. We also discuss these solutions in the context of AdS/CFT duality and construct the associated c-function.Comment: 18 pages, no figures; v2: title changed, typos fixe

Horizon area-angular momentum inequality in higher dimensional spacetimes

We consider $n$-dimensional spacetimes which are axisymmetric--but not necessarily stationary (!)--in the sense of having isometry group $U(1)^{n-3}$, and which satisfy the Einstein equations with a non-negative cosmological constant. We show that any black hole horizon must have area A \ge 8\pi |J_+ J_-|^\half, where $J_\pm$ are distinguished components of the angular momentum corresponding to linear combinations of the rotational Killing fields that vanish somewhere on the horizon. In the case of $n=4$, where there is only one angular momentum component $J_+=J_-$, we recover an inequality of 1012.2413 [gr-qc]. Our work can hence be viewed as a generalization of this result to higher dimensions. In the case of $n=5$ with horizon of topology $S^1 \times S^2$, the quantities $J_+=J_-$ are the same angular momentum component (in the $S^2$ direction). In the case of $n=5$ with horizon topology $S^3$, the quantities $J_+, J_-$ are the distinct components of the angular momentum. We also show that, in all dimensions, the inequality is saturated if the metric is a so-called ``near horizon geometry''. Our argument is entirely quasi-local, and hence also applies e.g. to any stably outer marginally trapped surface.Comment: 16 pages, Latex, no figure

Proof of the area-angular momentum-charge inequality for axisymmetric black holes

We give a comprehensive discussion, including a detailed proof, of the area-angular momentum-charge inequality for axisymmetric black holes. We analyze the inequality from several viewpoints, in particular including aspects with a theoretical interest well beyond the Einstein-Maxwell theory.Comment: 31 pages, 2 figure