On the consistency of neutron-star radius measurements from thermonuclear bursts

The radius of neutron stars can in principle be measured via the normalisation of a blackbody fitted to the X-ray spectrum during thermonuclear (type-I) X-ray bursts, although few previous studies have addressed the reliability of such measurements. Here we examine the apparent radius in a homogeneous sample of long, mixed H/He bursts from the low-mass X-ray binaries GS 1826-24 and KS 1731-26. The measured blackbody normalisation (proportional to the emitting area) in these bursts is constant over a period of up to 60s in the burst tail, even though the flux (blackbody temperature) decreased by a factor of 60-75% (30-40%). The typical rms variation in the mean normalisation from burst to burst was 3-5%, although a variation of 17% was found between bursts observed from GS 1826-24 in two epochs. A comparison of the time-resolved spectroscopic measurements during bursts from the two epochs shows that the normalisation evolves consistently through the burst rise and peak, but subsequently increases further in the earlier epoch bursts. The elevated normalisation values may arise from a change in the anisotropy of the burst emission, or alternatively variations in the spectral correction factor, f_c, of order 10%. Since burst samples observed from systems other than GS 1826-24 are more heterogeneous, we expect that systematic uncertainties of at least 10% are likely to apply generally to measurements of neutron-star radii, unless the effects described here can be corrected for.Comment: 9 pages, 6 figures; accepted by Ap

Topological censorship for Kaluza-Klein space-times

The standard topological censorship theorems require asymptotic hypotheses which are too restrictive for several situations of interest. In this paper we prove a version of topological censorship under significantly weaker conditions, compatible e.g. with solutions with Kaluza-Klein asymptotic behavior. In particular we prove simple connectedness of the quotient of the domain of outer communications by the group of symmetries for models which are asymptotically flat, or asymptotically anti-de Sitter, in a Kaluza-Klein sense. This allows one, e.g., to define the twist potentials needed for the reduction of the field equations in uniqueness theorems. Finally, the methods used to prove the above are used to show that weakly trapped compact surfaces cannot be seen from Scri.Comment: minor correction

Outer trapped surfaces are dense near MOTSs

We show that any vacuum initial data set containing a marginally outer trapped surface S and satisfying a "no KIDs" condition can be perturbed near S so that S becomes strictly outer trapped in the new vacuum initial data set. This, together with the results in [9], gives a precise sense in which generic initial data containing marginally outer trapped surfaces lead to geodesically incomplete spacetimes.Comment: 14 pages, minor rewording

Uniqueness of static black-holes without analyticity

We show that the hypothesis of analyticity in the uniqueness theory of vacuum, or electrovacuum, static black holes is not needed. More generally, we show that prehorizons covering a closed set cannot occur in well-behaved domains of outer communications.Comment: 6 pages, 1 figur

The Cosmic Censor Forbids Naked Topology

For any asymptotically flat spacetime with a suitable causal structure obeying (a weak form of) Penrose's cosmic censorship conjecture and satisfying conditions guaranteeing focusing of complete null geodesics, we prove that active topological censorship holds. We do not assume global hyperbolicity, and therefore make no use of Cauchy surfaces and their topology. Instead, we replace this with two underlying assumptions concerning the causal structure: that no compact set can signal to arbitrarily small neighbourhoods of spatial infinity (``$i^0$-avoidance''), and that no future incomplete null geodesic is visible from future null infinity. We show that these and the focusing condition together imply that the domain of outer communications is simply connected. Furthermore, we prove lemmas which have as a consequence that if a future incomplete null geodesic were visible from infinity, then given our $i^0$-avoidance assumption, it would also be visible from points of spacetime that can communicate with infinity, and so would signify a true naked singularity.Comment: To appear in CQG, this improved version contains minor revisions to incorporate referee's suggestions. Two revised references. Plain TeX, 12 page

Radius-expansion burst spectra from 4U 1728-34: an ultracompact binary?

Recent theoretical and observational studies have shown that ashes from thermonuclear burning may be ejected during radius-expansion bursts, giving rise to photoionisation edges in the X-ray spectra. We report a search for such features in Chandra spectra observed from the low-mass X-ray binary 4U 1728-34. We analysed the spectra from four radius-expansion bursts detected in 2006 July, and two in 2002 March, but found no evidence for discrete features. We estimate upper limits for the equivalent widths of edges of a few hundred eV, which for the moderate temperatures observed during the bursts, are comparable with the predictions. During the 2006 July observation 4U 1728-34 exhibited weak, unusually frequent bursts (separated by <2 hr in some cases), with profiles and alpha-values characteristic of hydrogen-poor fuel. Recurrence times as short as those measured are insufficient to exhaust the accreted hydrogen at solar composition, suggesting that the source accretes hydrogen deficient fuel, for example from an evolved donor. The detection for the first time of a 10.77 min periodic signal in the persistent intensity, perhaps arising from orbital modulation, supports this explanation, and suggests that this system is an ultracompact binary similar to 4U 1820-30.Comment: 9 pages, 6 figures, accepted by Ap

Mathematical general relativity: a sampler

We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.Comment: Some updates. A shortened version, to appear in the Bulletin of the AMS, is available online at http://www.ams.org/journals/bull/0000-000-00/S0273-0979-2010-01304-

Regularity of Horizons and The Area Theorem

We prove that the area of sections of future event horizons in space-times satisfying the null energy condition is non-decreasing towards the future under any one of the following circumstances: 1) the horizon is future geodesically complete; 2) the horizon is a black hole event horizon in a globally hyperbolic space-time and there exists a conformal completion with a ``H-regular'' Scri plus; 3) the horizon is a black hole event horizon in a space-time which has a globally hyperbolic conformal completion. (Some related results under less restrictive hypotheses are also established.) This extends a theorem of Hawking, in which piecewise smoothness of the event horizon seems to have been assumed. No assumptions about the cosmological constant or its sign are made. We prove smoothness or analyticity of the relevant part of the event horizon when equality in the area inequality is attained - this has applications to the theory of stationary black holes, as well as to the structure of compact Cauchy horizons. In the course of the proof we establish several new results concerning the differentiability properties of horizons.Comment: final version to appear in Annales Henri Poincare, various changes as suggested by a referee, in particular a section on Krolak's area theorems adde

On the mass aspect function and positive energy theorems for asymptotically hyperbolic manifolds

We prove positivity of energy for a class of asymptotically locally hyperbolic manifolds in dimensions $4\le n \le 7$. The result is established by first proving deformation-of-mass-aspect theorems in dimensions $n\ge 4$. Our positivity results extend to the case $n = 3$ when more stringent conditions are imposed.Comment: trivial typos correcte