Twistors and Black Holes

Motivated by black hole physics in N=2, D=4 supergravity, we study the geometry of quaternionic-Kahler manifolds M obtained by the c-map construction from projective special Kahler manifolds M_s. Improving on earlier treatments, we compute the Kahler potentials on the twistor space Z and Swann space S in the complex coordinates adapted to the Heisenberg symmetries. The results bear a simple relation to the Hesse potential \Sigma of the special Kahler manifold M_s, and hence to the Bekenstein-Hawking entropy for BPS black holes. We explicitly construct the ``covariant c-map'' and the ``twistor map'', which relate real coordinates on M x CP^1 (resp. M x R^4/Z_2) to complex coordinates on Z (resp. S). As applications, we solve for the general BPS geodesic motion on M, and provide explicit integral formulae for the quaternionic Penrose transform relating elements of H^1(Z,O(-k)) to massless fields on M annihilated by first or second order differential operators. Finally, we compute the exact radial wave function (in the supergravity approximation) for BPS black holes with fixed electric and magnetic charges.Comment: 47 pages, v2: typos corrected, reference added, v3: minor change

Correlation of Eocene-Oligocene marine and continental records: orbital cyclicity, magnetostratigraphy and sequence stratigraphy of the Solent Group, Isle of Wight, UK

The magnetostratigraphy, clay mineralogy, cyclostratigraphy and sequence stratigraphy of the estuarine and continental Solent Group (Isle of Wight, Hampshire Basin, UK), which is of Late Eocene–Early Oligocene age, were investigated. A new magnetostratigraphy for the Solent Group is correlated to the chronostratigraphic standard using limited biostratigraphical data, and it is concluded that the base of the Oligocene falls close to the base of the Bembridge Limestone Formation. A long time-series of clay mineral XRD data was generated, which shows striking variation in illitic clay abundance. Illite is interpreted to have formed in gley palaeosols through repeated wetting and drying in response to high seasonality. High illitic clay values are tuned to c. 400 ka eccentricity maxima to develop an age model. In addition to a very strong c. 400 ka signal in the data, spectral analysis of the clay data also confirms the influence of short eccentricity (c. 100 ka) and obliquity (c. 40 ka) cycles. The succession displays seven conspicuous 10–20 m thick sequences, which represent transitions from transgressive estuarine environments through highstand floodplains to freshwater lakes. The sequences correspond exactly to the long eccentricity (c. 400 ka) cycles. A sea-level curve is derived using the amount of incision as a minimum measure of eustatic fall, but there is no evidence of a major eustatic drop of 30–90 m corresponding to the early Oligocene glaciation of Antarctica. It is likely that incision was suppressed by rapid rates of subsidence

Observations of water-clay reactions in water-sensitive sandstone and mudrocks using an environmental scanning electron microscope

The experimental in situ wetting and drying of water-sensitive mudrocks in an environmental scanning electron microscope (ESEM) is described. Fluids used in the tests were freshwater (tap water) and a KCl-based drilling mud. By examining the extent to which illite-smectite and smectite swell when treated with water, it has been possible to assess the importance of clay swelling as a drilling problem in these rocks. Smectite in mudrocks obtained from fresh outcrop (WH10 and WH13) and illite-smectite in sandstone (Sample B of Baker et al., 1992) reacted with fresh water to form a gel-like mass, a process which was only slowly reversed by drying. Less swelling was observed in the mudrocks containing Mg/Ca smectite than in those containing predominantly Na in the interlayer sites. Samples treated with KCl-based drilling mud showed no clay swelling with the exception of the most smectite-rich mudrock (1554). This is attributed to the clay having a residual coating of oil from the original oil-based mud used in drilling. Either a residue of this mud, or the solvents which were used to remove it from the cuttings prior to their being supplied to us may have interacted with the KCl-based drilling mud. The swelling rate for the samples used was pure Na-smectite>interstratified illite-Na smectite>Ca/Mg smectite>interstratified illite-Ca/Mg smectite

Diagenetic clinoptilolite and opal-CT from the middle Eocene Wittering Formation, Isle of Wight, U.K.

Thinly interbedded estuarine sandstones and mudstones in the middle Eocene Wittering Formation (Bracklesham Group), Isle of Wight, contain authigenic clinoptilolite, opal-CT, and possibly authigenic smectite over a thickness of 8.5 m. The clinoptilolite and opal-CT cements have resulted in these beds being the only ones tightly cemented in the Wittering Formation, the rest being soft sands and muds. The unit contains abundant siliceous sponge spicules, many of which are preserved as voids and were the likely source of the opal-CT. The presence of an organic-rich, rooted paleosol (histosol) immediately overlying the unit is believed to have contributed significantly to the early diagenetic history of the estuarine sediments, in particular the formation of zeolite. Although the pH and dissolved silica of unmodified seawater are too low for zeolite formation, high concentrations of dissolved silica are believed to have resulted from dissolution of siliceous sponge spicules (opal-A) and formation of silica-organic acid complexes. Organic-acid dissolution of feldspars (absent from the zeolite-bearing interval) is the most probable source of alumina and cations for zeolite formation. REE data show that volcanic ash was never present and cannot therefore have been the source of the zeolite. This investigation therefore demonstrates a novel route by which the pore-fluid chemistry required for zeolite formation can be achieved

Serpentine-nontronite-vermiculate mixed-layer clay from the Weches Formation, Claiborne Group, middle Eocene, Northeast Texas

The Weches Formation of the Claiborne Group (Eocene) in northeast Texas consists of clayey sandstones and mudrocks, both with variable proportions of dark green to brown clay peloids deposited in a marginal to open marine setting on the Gulf Coast margin. The composition of the dark green peloids, from two localities, has been investigated using X-ray diffraction, back-scattered electron microscopy with X-ray analysis, electron energy-loss spectroscopy (EELS), Mössbauer spectroscopy, chemical analysis and Fourier transform infrared spectroscopy. These peloids were previously described on the basis of their color as glauconite (Yancey and Davidoff, 1994); our results, however, show that the dark green indurated pellets are predominantly composed of mixed-layer clays with a high proportion of Fe-rich 7 Å serpentine layers coexisting with a mixed-layer phase containing glauconite, nontronite and vermiculite layers, in addition to discrete illite and kaolinte. Analyses by EELS of single particles with a chemical composition consistent with them being the Fe-rich clay indicate that the Fe is >95% ferric, while Mössbauer analyses of the bulk magnetically separated fraction for the same samples indicates a ferric iron content of ∼60-70%, despite the variable relative proportions of expandable and 7 Å layers. Taking into account that there is a significant amount of 2:1 layers containing ferric Fe, we interpret these data as indicating that the Fe in the 7 Å layers has a significant amount of Fe even taking into account the high ferric Fe ratio from the EELS analysis when the coexisting 2:1 layers are considered. Thus, these 1:1 layers are closer to berthierine in composition than to odinite. The vermiculite layers in the Texas clay may indicate partial 'verdinization' of expandable 2:1 clay. A possible reaction is smectite → vermiculite → berthierine-like phase. We estimate a temperature of 20°C for the seawater in which the Texas clay formed, the lower end of the range for modern occurrences of odinite

Serpentine-nontronite-vermiculate mixed-layer clay from the Weches Formation, Claiborne Group, middle Eocene, Northeast Texas

The Weches Formation of the Claiborne Group (Eocene) in northeast Texas consists of clayey sandstones and mudrocks, both with variable proportions of dark green to brown clay peloids deposited in a marginal to open marine setting on the Gulf Coast margin. The composition of the dark green peloids, from two localities, has been investigated using X-ray diffraction, back-scattered electron microscopy with X-ray analysis, electron energy-loss spectroscopy (EELS), Mössbauer spectroscopy, chemical analysis and Fourier transform infrared spectroscopy. These peloids were previously described on the basis of their color as glauconite (Yancey and Davidoff, 1994); our results, however, show that the dark green indurated pellets are predominantly composed of mixed-layer clays with a high proportion of Fe-rich 7 Å serpentine layers coexisting with a mixed-layer phase containing glauconite, nontronite and vermiculite layers, in addition to discrete illite and kaolinte. Analyses by EELS of single particles with a chemical composition consistent with them being the Fe-rich clay indicate that the Fe is >95% ferric, while Mössbauer analyses of the bulk magnetically separated fraction for the same samples indicates a ferric iron content of ∼60-70%, despite the variable relative proportions of expandable and 7 Å layers. Taking into account that there is a significant amount of 2:1 layers containing ferric Fe, we interpret these data as indicating that the Fe in the 7 Å layers has a significant amount of Fe even taking into account the high ferric Fe ratio from the EELS analysis when the coexisting 2:1 layers are considered. Thus, these 1:1 layers are closer to berthierine in composition than to odinite. The vermiculite layers in the Texas clay may indicate partial 'verdinization' of expandable 2:1 clay. A possible reaction is smectite → vermiculite → berthierine-like phase. We estimate a temperature of 20°C for the seawater in which the Texas clay formed, the lower end of the range for modern occurrences of odinite

Marine biodiversity through the Late Cenomanian–Early Turonian: palaeoceanographic controls and sequence stratigraphic biases

Changes in the marine macro- and microfauna, sedimentary geochemistry and surface-water palaeoproductivity through the last 500 000 years of the Cenomanian and first 300 000 years of the Turonian are documented. These are based on the succession at Eastbourne, the thickest and most complete section through the Late Cenomanian and Early Turonian in the Anglo-Paris Basin. Two levels of rapid faunal and geochemical change are identified, one coincident with a significant increase in siliciclastic input at the base of the Plenus Marls Member, and the other with a marked drop in surface water productivity near the top of the same unit. Faunal change is demonstrated to be largely a pattern of immigration-emigration rather than true extinction, and our sequence stratigraphical analysis shows that it was coincident with major sea-lever changes. No evidence is found to support the hypothesis that reduced bottom water oxygenation developed and was responsible for extinctions amongst the benthos in mid-shelf environments. The onset of pure chalk facies is interpreted to mark the breakdown of shelf-break fronts and the spread of oligotrophic oceanic waters over much of the continental shelf, initialed by rising sea-lever. The Cenomanian-Turonian event, far from recording a mass extinction of shelf fauna, is most probably an artifact caused by a significant switch in the nature of the surviving sedimentary record as a result of a major, but perfectly ordinary, oceanographic change