Comment on "some exact quasinormal frequencies of a massless scalar field in Schwarzschild spacetime"

© 2019 American Physical Society. A new branch of quasinormal modes for a massless scalar field propagating on the Schwarzschild spacetime was recently announced [D. Batic, M. Nowakowski, and K. Redway, Phys. Rev. D 98, 024017 (2018)PRVDAQ2470-001010.1103/PhysRevD.98.024017]. We review the quasinormal modes characterization and arguments and identify the flaws in their proof. Then, we preset explicit counterexamples to such arguments. Finally, we study the modes via alternative methods and do not find the new branch. We conclude against their interpretation

Hyperboloidal slicing approach to quasinormal mode expansions: The Reissner-Nordström case

International audienceWe study quasinormal modes of black holes, with a focus on resonant (or quasinormal mode) expansions, in a geometric frame based on the use of conformal compactifications together with hyperboloidal foliations of spacetime. Specifically, this work extends the previous study of Schwarzschild in this geometric approach to spherically symmetric asymptotically flat black-hole spacetimes, in particular Reissner-Nordström. The discussion involves, first, the nontrivial technical developments needed to address the choice of appropriate hyperboloidal slices in the extended setting as well as the generalization of the algorithm determining the coefficients in the expansion of the solution in terms of the quasinormal modes. In a second stage, we discuss how the adopted framework provides a geometric insight into the origin of regularization factors needed in Leaver’s Cauchy-based foliations, as well as into the discussion of quasinormal modes in the extremal black-hole limit

Greenhouse gas emission associated with sugar production in southern Brazil

<p>Abstract</p> <p>Background</p> <p>Since sugarcane areas have increased rapidly in Brazil, the contribution of the sugarcane production, and, especially, of the sugarcane harvest system to the greenhouse gas emissions of the country is an issue of national concern. Here we analyze some data characterizing various activities of two sugarcane mills during the harvest period of 2006-2007 and quantify the carbon footprint of sugar production.</p> <p>Results</p> <p>According to our calculations, 241 kg of carbon dioxide equivalent were released to the atmosphere per a ton of sugar produced (2406 kg of carbon dioxide equivalent per a hectare of the cropped area, and 26.5 kg of carbon dioxide equivalent per a ton of sugarcane processed). The major part of the total emission (44%) resulted from residues burning; about 20% resulted from the use of synthetic fertilizers, and about 18% from fossil fuel combustion.</p> <p>Conclusions</p> <p>The results of this study suggest that the most important reduction in greenhouse gas emissions from sugarcane areas could be achieved by switching to a green harvest system, that is, to harvesting without burning.</p

Hyperboloidal framework for the Kerr spacetime

Motivated by the need of a robust geometrical framework for the calculation of long, and highly accurate waveforms for extreme-mass-ratio inspirals, this work presents an extensive study of the hyperboloidal formalism for the Kerr spacetime and the Teukolsky equation. In a first step, we introduce a generic coordinate system foliating the Kerr spacetime into hypersurfaces of constant time extending between the black-hole horizon and future null infinity, while keeping track of the underlying degrees of freedom. Then, we express the Teukolsky equation in terms of these generic coordinates with focus on applications in both the time and frequency domains. Specifically, we derive a wave-like equation in $2+1$ dimensions, whose unique solution follows directly from the prescription of initial data (no external boundary conditions). Moreover, we extend the hyperboloidal formulation into the frequency domain. A comparison with the standard form of the Teukolsky equations allows us to express the regularisation factors in terms of the hyperboloidal degrees of freedom. In the second part, we discuss several hyperboloidal gauges for the Kerr solution. Of particular importance, this paper introduces the minimal gauge. The resulting expressions for the Kerr metric and underlying equations are simple enough for eventual (semi)-analytical studies. Despite the simplicity, the gauge has a very rich structure as it naturally leads to two possible limits to extremality, namely the standard extremal Kerr spacetime and its near-horizon geometry. When applied to the Teukolsky equation in the frequency domain, we show that the minimal gauge actually provides the spacetime counterpart of the well-known Leaver's formalism. Finally, we recast the hyperboloidal gauges for the Kerr spacetime available in the literature within the framework introduced here.Comment: 30 pages. Match published versio