A Note on the Symmetry Reduction of SU(2) on Horizons of Various Topologies

It is known that the SU(2) degrees of freedom manifest in the description of the gravitational field in loop quantum gravity are generally reduced to U(1) degrees of freedom on an $S^2$ isolated horizon. General relativity also allows black holes with planar, toroidal, or higher genus topology for their horizons. These solutions also meet the criteria for an isolated horizon, save for the topological criterion, which is not crucial. We discuss the relevant corresponding symmetry reduction for black holes of various topologies (genus 0 and $\geq 2$) here and discuss its ramifications to black hole entropy within the loop quantum gravity paradigm. Quantities relevant to the horizon theory are calculated explicitly using a generalized ansatz for the connection and densitized triad, as well as utilizing a general metric admitting hyperbolic sub-spaces. In all scenarios, the internal symmetry may be reduced to combinations of U(1).Comment: 13 pages, two figures. Version 2 has several references updated and added, as well as some minor changes to the text. Accepted for publication in Class. Quant. Gra

The status and challenge of global fire modelling

Biomass burning impacts vegetation dynamics, biogeochemical cycling, atmospheric chemistry, and climate, with sometimes deleterious socio-economic impacts. Under future climate projections it is often expected that the risk of wildfires will increase. Our ability to predict the magnitude and geographic pattern of future fire impacts rests on our ability to model fire regimes, using either well-founded empirical relationships or process-based models with good predictive skill. While a large variety of models exist today, it is still unclear which type of model or degree of complexity is required to model fire adequately at regional to global scales. This is the central question underpinning the creation of the Fire Model Intercomparison Project (FireMIP), an international initiative to compare and evaluate existing global fire models against benchmark data sets for present-day and historical conditions. In this paper we review how fires have been represented in fire-enabled dynamic global vegetation models (DGVMs) and give an overview of the current state of the art in fire-regime modelling. We indicate which challenges still remain in global fire modelling and stress the need for a comprehensive model evaluation and outline what lessons may be learned from FireMIP

The status and challenge of global fire modelling

Biomass burning impacts vegetation dynamics, biogeochemical cycling, atmospheric chemistry, and climate, with sometimes deleterious socio-economic impacts. Under future climate projections it is often expected that the risk of wildfires will increase. Our ability to predict the magnitude and geographic pattern of future fire impacts rests on our ability to model fire regimes, using either well-founded empirical relationships or process-based models with good predictive skill. While a large variety of models exist today, it is still unclear which type of model or degree of complexity is required to model fire adequately at regional to global scales. This is the central question underpinning the creation of the Fire Model Intercomparison Project (FireMIP), an international initiative to compare and evaluate existing global fire models against benchmark data sets for present-day and historical conditions. In this paper we review how fires have been represented in fire-enabled dynamic global vegetation models (DGVMs) and give an overview of the current state of the art in fire-regime modelling. We indicate which challenges still remain in global fire modelling and stress the need for a comprehensive model evaluation and outline what lessons may be learned from FireMIP