On the `Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions

All known stationary black hole solutions in higher dimensions possess additional rotational symmetries in addition to the stationary Killing field. Also, for all known stationary solutions, the event horizon is a Killing horizon, and the surface gravity is constant. In the case of non-degenerate horizons (non-extremal black holes), a general theorem was previously established [gr-qc/0605106] proving that these statements are in fact generally true under the assumption that the spacetime is analytic, and that the metric satisfies Einstein's equation. Here, we extend the analysis to the case of degenerate (extremal) black holes. It is shown that the theorem still holds true if the vector of angular velocities of the horizon satisfies a certain "diophantine condition," which holds except for a set of measure zero.Comment: 30pp, Latex, no figure

Homocysteine, folate, vitamin B12, and cardiovascular risk in Indians, Malays, and Chinese in Singapore

OBJECTIVE—To examine the hypothesis that the higher rates of coronary heart disease (CHD) in Indians (South Asians) compared with Malays and Chinese is partly attributable to differences in blood concentrations of homocysteine, and related blood concentrations of folate and vitamin B12.
DESIGN—Cross sectional study of the general population.
SETTING—Singapore.
PARTICIPANTS—Random sample of 726 fasting subjects aged 30 to 69( )years.
MAIN RESULTS—Mean plasma total homocysteine concentrations did not show significant ethnic differences; values were Indians (men 16.2 and women 11.5 µmol/l), Malays (men 15.0 and women 12.5 µmol/l), and Chinese (men 15.3 and women 12.2 µmol/l). Similarly, the proportions with high plasma homocysteine (>14.0 µmol/l) showed no important ethnic differences being, Indians (men 60.0 and women 21.9 %), Malays (men 53.9 and women 37.8 %), and Chinese (men 56.6 and women 30.6 %). Mean plasma folate concentrations were lower in Indians (men 8.7 and women 10.9 nmol/l) and Malays (men 8.5 and women 10.8 nmol/l), than Chinese (men 9.7 and women 13.8 nmol/l). Similarly, the proportions with low plasma folate (<6.8 nmol/l) were higher in Indians (men 44.9 and women 36.6 %) and Malays (men 45.3 and women 24.5 %) than Chinese (men 31.4 and women 12.6( )%). Mean plasma vitamin B12 concentrations were lowest in Indians (men 352.5 and women 350.7 pmol/l), then Chinese (men 371.1 and women 373.7 pmol/l), and then Malays (men 430.5 and women 486.0( )pmol/l).
CONCLUSION—While there were ethnic differences for plasma folate and vitamin B12 (in particular lower levels in Indians), there was no evidence that homocysteine plays any part in the differential ethnic risk from CHD in Singapore and in particular the increased susceptibility of Indians to the disease.


Keywords: coronary heart disease; ethnic; homocystein