Black hole and naked singularity geometries supported by three-form fields

We investigate static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert-Einstein action with a Lagrangian constructed from a three-form field $A_{\alpha \beta \gamma}$, which is related to the field strength and a potential term. The field equations are derived from a variational principle and are obtained explicitly for a static and spherically symmetric geometry in vacuum. For the case of the vanishing three-form field potential the gravitational field equations can be solved exactly. However, for arbitrary potentials, due to their mathematical complexity, numerical approaches are adopted in studying the behavior of the metric functions and the three-form field. To this effect, the field equations are reformulated in a dimensionless form and are solved numerically by introducing a suitable independent radial coordinate. We detect the formation of a black hole from the presence of a Killing horizon for the time-like Killing vector in the metric tensor components. Several models, corresponding to different functional forms of the three-field potential, namely, the Higgs and exponential type, are considered. In particular, naked singularity solutions are also obtained for the exponential potential case. Finally, the thermodynamic properties of these black hole solutions, such as the horizon temperature, specific heat, entropy and evaporation time due to the Hawking luminosity, are also investigated in detail.Comment: 19 pages, 22 figures; minor modifications, accepted for publication in EPJ

Competition for light and water play contrasting roles in driving diversity-productivity relationships in Iberian forests

Mixed‐species forests generally sequester and store more carbon in above‐ground woody biomass compared to species‐poor systems. However, the mechanisms driving the positive relationship between diversity and above‐ground wood production (AWP) remain unclear. We investigate the role of competition for light and water as possible sources of complementarity among Iberian pine and oak species. Using tree core data from permanent plots, we test the hypotheses that (i) contrasting abilities of pines and oaks to tolerate shade will promote AWP in mixtures, while (ii) drought stress results in less room for complementarity. We found that pine species receive more light, develop larger crowns and grow 138–155% faster when in mixture with oaks. However, this positive effect of species mixing on growth was severely reduced under drought conditions due to increased competition for water with neighbouring oaks. In contrast to pines, oak trees were less responsive to mixing, primarily as a result of their ability to tolerate shade and water shortage. Mixed pine‐oak forests produce an average 48% more above‐ground woody biomass compared to monocultures each year. However, the magnitude of the diversity effect on AWP fluctuates with time, decreasing noticeably in strength during drought years. Synthesis. Complementary light use strategies among neighbouring trees are critical in explaining why above‐ground wood production (AWP) increases in mixed‐species stands. In contrast, drought causes trees in mixture to compete more fiercely for below‐ground resources, leaving less room for complementarity and causing positive diversity effects to lessen in strength. Together, these two mechanisms provide much needed context for AWP–diversity relationships in Mediterranean forests. Whether or not managing for mixed pine‐oak forests proves to be beneficial for AWP is likely to depend on how climate changes in the Iberian Peninsula.European Union Seventh Framework Programme. Grant Numbers: FP7/2007-2013, 265171This is the accepted manuscript version of the following article: Jucker, T., Bouriaud, O., Avacaritei, D., Dănilă, I., Duduman, G., Valladares, F., Coomes, D. A. (2014), Competition for light and water play contrasting roles in driving diversity–productivity relationships in Iberian forests. Journal of Ecology. doi: 10.1111/1365-2745.12276, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/1365-2745.12276/abstract