Uniqueness Theorem for Static Black Hole Solutions of sigma-models in Higher Dimensions

We prove the uniqueness theorem for self-gravitating non-linear sigma-models in higher dimensional spacetime. Applying the positive mass theorem we show that Schwarzschild-Tagherlini spacetime is the only maximally extended, static asymptotically flat solution with non-rotating regular event horizon with a constant mapping.Comment: 5 peges, Revtex, to be published in Class.Quantum Gra

A Mass Bound for Spherically Symmetric Black Hole Spacetimes

Requiring that the matter fields are subject to the dominant energy condition, we establish the lower bound $(4\pi)^{-1} \kappa {\cal A}$ for the total mass $M$ of a static, spherically symmetric black hole spacetime. (${\cal A}$ and $\kappa$ denote the area and the surface gravity of the horizon, respectively.) Together with the fact that the Komar integral provides a simple relation between $M - (4\pi)^{-1} \kappa A$ and the strong energy condition, this enables us to prove that the Schwarzschild metric represents the only static, spherically symmetric black hole solution of a selfgravitating matter model satisfying the dominant, but violating the strong energy condition for the timelike Killing field $K$ at every point, that is, $R(K,K) \leq 0$. Applying this result to scalar fields, we recover the fact that the only black hole configuration of the spherically symmetric Einstein-Higgs model with arbitrary non-negative potential is the Schwarzschild spacetime with constant Higgs field. In the presence of electromagnetic fields, we also derive a stronger bound for the total mass, involving the electromagnetic potentials and charges. Again, this estimate provides a simple tool to prove a ``no-hair'' theorem for matter fields violating the strong energy condition.Comment: 16 pages, LATEX, no figure

The classification of static vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior

We prove non-existence of static, vacuum, appropriately regular, asymptotically flat black hole space-times with degenerate (not necessarily connected) components of the event horizon. This finishes the classification of static, vacuum, asymptotically flat domains of outer communication in an appropriate class of space-times, showing that the domains of outer communication of the Schwarzschild black holes exhaust the space of appropriately regular black hole exteriors.Comment: This version includes an addendum with a corrected proof of non-existence of zeros of the Killing vector at degenerate horizons. A problem with yet another Lemma is pointed out; this problem does not arise if one assumes analyticity of the metric. An alternative solution, that does not require analyticity, has been given in arXiv:1004.0513 [gr-qc] under appropriate global condition

Diversity and habitat characteristics of macrozoobenthos in the mangrove forest of Lubuk Kertang Village, North Sumatra

Mangrove plays an important role in coastal ecosystems including ecological, social, and economic aspects. This study aimed to determine the diversity of macrozoobenthos and water quality based on diversity index (H?), similarity Index (E), and dominance index (D) in the mangrove of Lubuk Kertang Village North Sumatra, Indonesia. The samples of macrozoobenthos (biological parameter) and water quality (physical and chemical parameters) were collected from fifteen plots in three different stations. Macrozoobenthos were collected in 1 m ? 1 m transect in the mangrove forest. The biota was taken by using a shovel, inserted into a plastic bag, and identified. Results showed that eight species of macrozoobenthos were found and classified into three classes of Gastropod, Bivalvia, and Malacostraca. The highest diversity index (H?) of macrozoobenthos was found at Station II (2.39), the highest evenness index (E) was located at Station I (0.54), and the highest dominance index (D) was found at Station II (0.34). Principal component analysis (PCA) was used to determine the habitat characteristics of macrozoobenthos. PCA confirmed that station III was a habitat with suitable characteristics for the life of macrozoobenthos indicating the negative axis. The present study suggested four parameters namely salinity, clay temperature, and dissolved oxygen that should be preserved to support the survival of macrozoobenthos in the mangrove forests. ? 2018, Society for Indonesian Biodiversity. All rights reservedpublishersversionPeer reviewe

THE UNIQUENESS THEOREM FOR ROTATING BLACK HOLE SOLUTIONS OF SELF-GRAVITATING HARMONIC MAPPINGS

We consider rotating black hole configurations of self-gravitating maps from spacetime into arbitrary Riemannian manifolds. We first establish the integrability conditions for the Killing fields generating the stationary and the axisymmetric isometry (circularity theorem). Restricting ourselves to mappings with harmonic action, we subsequently prove that the only stationary and axisymmetric, asymptotically flat black hole solution with regular event horizon is the Kerr metric. Together with the uniqueness result for non-rotating configurations and the strong rigidity theorem, this establishes the uniqueness of the Kerr family amongst all stationary black hole solutions of self-gravitating harmonic mappings.Comment: 18 pages, latex, no figure