Connection between horizons and algebraic type

We study connections between both event and quasilocal horizons and the algebraic type of the Weyl tensor. The relation regarding spacelike future outer trapping horizon is analysed in four dimensions using double-null foliation.Comment: 4 pages, to appear in Proceedings of Spanish relativity meeting 201

Gravitational waves from quasi-spherical black holes

A quasi-spherical approximation scheme, intended to apply to coalescing black holes, allows the waveforms of gravitational radiation to be computed by integrating ordinary differential equations.Comment: 4 revtex pages, 2 eps figure

Strong Cosmic Censorship and Causality Violation

We investigate the instability of the Cauchy horizon caused by causality violation in the compact vacuum universe with the topology $B\times {\bf S}^{1}\times {\bf R}$, which Moncrief and Isenberg considered. We show that if the occurrence of curvature singularities are restricted to the boundary of causality violating region, the whole segments of the boundary become curvature singularities. This implies that the strong cosmic censorship holds in the spatially compact vacuum space-time in the case of the causality violation. This also suggests that causality violation cannot occur for a compact universe.Comment: corrected version, 8 pages, one eps figure is include

Mode coupling in the nonlinear response of black holes

We study the properties of the outgoing gravitational wave produced when a non-spinning black hole is excited by an ingoing gravitational wave. Simulations using a numerical code for solving Einstein's equations allow the study to be extended from the linearized approximation, where the system is treated as a perturbed Schwarzschild black hole, to the fully nonlinear regime. Several nonlinear features are found which bear importance to the data analysis of gravitational waves. When compared to the results obtained in the linearized approximation, we observe large phase shifts, a stronger than linear generation of gravitational wave output and considerable generation of radiation in polarization states which are not found in the linearized approximation. In terms of a spherical harmonic decomposition, the nonlinear properties of the harmonic amplitudes have simple scaling properties which offer an economical way to catalog the details of the waves produced in such black hole processes.Comment: 17 pages, 20 figures, abstract and introduction re-writte

Non-linear instability of Kerr-type Cauchy horizons

Using the general solution to the Einstein equations on intersecting null surfaces developed by Hayward, we investigate the non-linear instability of the Cauchy horizon inside a realistic black hole. Making a minimal assumption about the free gravitational data allows us to solve the field equations along a null surface crossing the Cauchy Horizon. As in the spherical case, the results indicate that a diverging influx of gravitational energy, in concert with an outflux across the CH, is responsible for the singularity. The spacetime is asymptotically Petrov type N, the same algebraic type as a gravitational shock wave. Implications for the continuation of spacetime through the singularity are briefly discussed.Comment: 11 pages RevTeX, two postscript figures included using epsf.st

Geology, geochemistry and geochronology of the Songwe Hill carbonatite, Malawi

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Songwe Hill, Malawi, is one of the least studied carbonatites but has now become particularly important as it hosts a relatively large rare earth deposit. The results of new mapping, petrography, geochemistry and geochronology indicate that the 0.8 km diameter Songwe Hill is distinct from the other Chilwa Alkaline Province carbonatites in that it intruded the side of the much larger (4 x 6 km) and slightly older (134.6 ± 4.4 Ma) Mauze nepheline syenite and then evolved through three different carbonatite compositions (C1–C3). Early C1 carbonatite is scarce and is composed of medium–coarse-grained calcite carbonatite containing zircons with a U–Pb age of 132.9 ± 6.7 Ma. It is similar to magmatic carbonatite in other carbonatite complexes at Chilwa Island and Tundulu in the Chilwa Alkaline Province and others worldwide. The fine-grained calcite carbonatite (C2) is the most abundant stage at Songwe Hill, followed by a more REE- and Sr-rich ferroan calcite carbonatite (C3). Both stages C2 and C3 display evidence of extensive (carbo)-hydrothermal overprinting that has produced apatite enriched in HREE (<2000 ppm Y) and, in C3, synchysite-(Ce). The final stages comprise HREE-rich apatite fluorite veins and Mn-Fe-rich veins. Widespread brecciation and incorporation of fenite into carbonatite, brittle fracturing, rounded clasts and a fenite carapace at the top of the hill indicate a shallow level of emplacement into the crust. This shallow intrusion level acted as a reservoir for multiple stages of carbonatite-derived fluid and HREE-enriched apatite mineralisation as well as LREE-enriched synchysite-(Ce). The close proximity and similar age of the large Mauze nepheline syenite suggests it may have acted as a heat source driving a hydrothermal system that has differentiated Songwe Hill from other Chilwa carbonatites.Thanks are due to A. Lemon, A. Zabula, C. Mcheka, I. Nkukumila (Mkango Resources Ltd.), É. Deady (BGS) and P. Armitage (Paul Armitage Consulting Ltd.) for logistical support and enthusiastic discussions in the field. This contribution benefitted from reviews by Jindřich Kynický and Ray Macdonald, as well as anonymous reviewers, who we thank for their time and insightful comments. This work was funded by a NERC BGS studentship to SBF (NEE/J50318/1; S208), the NERC SoS RARE consortium (NE/M011429/1) and by Mkango Resources Ltd. AGG publishes with the permission of the Executive Director of the British Geological Survey (NERC)

Geology, geochemistry and geochronology of the Songwe Hill carbonatite, Malawi

Songwe Hill, Malawi, is one of the least studied carbonatites but has now become particularly important as it hosts a relatively large rare earth deposit. The results of new mapping, petrography, geochemistry and geochronology indicate that the 0.8 km diameter Songwe Hill is distinct from the other Chilwa Alkaline Province carbonatites in that it intruded the side of the much larger (4 × 6 km) and slightly older (134.6 ± 4.4 Ma) Mauze nepheline syenite and then evolved through three different carbonatite compositions (C1–C3). Early C1 carbonatite is scarce and is composed of medium–coarse-grained calcite carbonatite containing zircons with a U–Pb age of 132.9 ± 6.7 Ma. It is similar to magmatic carbonatite in other carbonatite complexes at Chilwa Island and Tundulu in the Chilwa Alkaline Province and others worldwide. The fine-grained calcite carbonatite (C2) is the most abundant stage at Songwe Hill, followed by a more REE- and Sr-rich ferroan calcite carbonatite (C3). Both stages C2 and C3 display evidence of extensive (carbo)-hydrothermal overprinting that has produced apatite enriched in HREE (<2000 ppm Y) and, in C3, synchysite-(Ce). The final stages comprise HREE-rich apatite fluorite veins and Mn-Fe-rich veins. Widespread brecciation and incorporation of fenite into carbonatite, brittle fracturing, rounded clasts and a fenite carapace at the top of the hill indicate a shallow level of emplacement into the crust. This shallow intrusion level acted as a reservoir for multiple stages of carbonatite-derived fluid and HREE-enriched apatite mineralisation as well as LREE-enriched synchysite-(Ce). The close proximity and similar age of the large Mauze nepheline syenite suggests it may have acted as a heat source driving a hydrothermal system that has differentiated Songwe Hill from other Chilwa carbonatites

Community perspectives on the reintroduction of Eurasian lynx (Lynx lynx) to the UK

The potential for the reintroduction of Eurasian lynx (Lynx lynx) to the UK gained considerable attention in 2017 when the Lynx UK Trust announced their intention to apply for a licence to hold a controlled trial reintroduction of lynx in Kielder Forest, Northumberland, an application which was denied in 2019 by the then Secretary of State Michael Gove MP. The historical extirpation of large carnivores in the UK has resulted in communities, populations and landscapes with little or no experience of coexistence with large predators. Whilst charismatic carnivores have significant cultural symbolism and are often promoted as flagship species for conservation and rewilding, their reintroduction presents challenges for conservation and rewilding in practice, not least in terms of managing often vehement opposition. This article presents findings from the initial consultation process and considers the lessons learnt from the methodological approach. In particular, while the incomplete consultation centred on a community‐based approach, there were several factors which constrained public participation, information sharing and transparent communications integral to this. These are identified and explored here using qualitative data collected during the local consultation, with the intention of informing any similar reintroduction projects

Absorption and quasinormal modes of classical fields propagating on 3D and 4D de Sitter spacetime

We extensively study the exact solutions of the massless Dirac equation in 3D de Sitter spacetime that we published recently. Using the Newman-Penrose formalism, we find exact solutions of the equations of motion for the massless classical fields of spin s=1/2,1,2 and to the massive Dirac equation in 4D de Sitter metric. Employing these solutions, we analyze the absorption by the cosmological horizon and de Sitter quasinormal modes. We also comment on the results given by other authors.Comment: 31 page