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

On the topology of stationary black holes

We prove that the domain of outer communication of a stationary, globally hyperbolic spacetime satisfying the null energy condition must be simply connected. Under suitable additional hypotheses, this implies, in particular, that each connected component of a cross-section of the event horizon of a stationary black hole must have spherical topology.Comment: 7 pages, Late

Evidence for a parsec scale X-ray jet from the accreting neutron star Circinus X-1

We analyzed the zero-order image of a 50 ks Chandra gratings observation of Circinus X-1, taken in 2005 during the source's low-flux state. Circinus X-1 is an accreting neutron star that exhibits ultra-relativistic arcsecond-scale radio jets and diffuse arcminute-scale radio jets and lobes. The image shows a clear excess along the general direction of the north-western counter-jet, coincident with the radio emission, suggesting that it originates either in the jet itself or in the shock the jet is driving into its environment. This makes Circinus X-1 the first neutron star for which an extended X-ray jet has been detected. The kinetic jet power we infer is significantly larger than the minimum power required for the jet to inflate the large scale radio nebula.Comment: Added journal reference, corrected on reference and typo in labels for Fig. 1; 5 pages, 3 figures, ApJ Letter, in pres

A uniqueness theorem for the adS soliton

The stability of physical systems depends on the existence of a state of least energy. In gravity, this is guaranteed by the positive energy theorem. For topological reasons this fails for nonsupersymmetric Kaluza-Klein compactifications, which can decay to arbitrarily negative energy. For related reasons, this also fails for the AdS soliton, a globally static, asymptotically toroidal $\Lambda<0$ spacetime with negative mass. Nonetheless, arguing from the AdS/CFT correspondence, Horowitz and Myers (hep-th/9808079) proposed a new positive energy conjecture, which asserts that the AdS soliton is the unique state of least energy in its asymptotic class. We give a new structure theorem for static $\Lambda<0$ spacetimes and use it to prove uniqueness of the AdS soliton. Our results offer significant support for the new positive energy conjecture and add to the body of rigorous results inspired by the AdS/CFT correspondence.Comment: Revtex, 4 pages; Matches published version. More detail in Abstract and one equation corrected. For details of proofs and further results, see hep-th/020408

Non-Existence of Black Holes in Certain Λ<0\Lambda<0 Spacetimes

Assuming certain asymptotic conditions, we prove a general theorem on the non-existence of static regular (i.e., nondegenerate) black holes in spacetimes with a negative cosmological constant, given that the fundamental group of space is infinite. We use this to rule out the existence of regular negative mass AdS black holes with Ricci flat scri. For any mass, we also rule out a class of conformally compactifiable static black holes whose conformal infinity has positive scalar curvature and infinite fundamental group, subject to our asymptotic conditions. In a limited, but important, special case our result adds new support to the AdS/CFT inspired positive mass conjecture of Horowitz and Myers.Comment: 17 pages, Latex. Typos corrected, minor changes to the text. Accepted for publication in Classical and Quantum Gravit

Some Comments on Gravitational Entropy and the Inverse Mean Curvature Flow

The Geroch-Wald-Jang-Huisken-Ilmanen approach to the positive energy problem to may be extended to give a negative lower bound for the mass of asymptotically Anti-de-Sitter spacetimes containing horizons with exotic topologies having ends or infinities of the form $\Sigma_g \times {\Bbb R}$, in terms of the cosmological constant. We also show how the method gives a lower bound for for the mass of time-symmetric initial data sets for black holes with vectors and scalars in terms of the mass, $|Z(Q,P)|$ of the double extreme black hole with the same charges. I also give a lower bound for the area of an apparent horizon, and hence a lower bound for the entropy in terms of the same function $|Z(Q,P)|$. This shows that the so-called attractor behaviour extends beyond the static spherically symmetric case. and underscores the general importance of the function $|Z(Q,P)|$. There are hints that higher dimensional generalizations may involve the Yamabe conjectures.Comment: 13pp. late

Application of fluvial scaling relationships to reconstruct drainage-basin evolution and sediment routing for the Cretaceous and Paleocene of the Gulf of Mexico

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.Fluvial systems represent a key component in source-to-sink analysis of ancient sediment-dispersal systems. Modern river channels and channel-related deposits possess a range of scaling relationships that reflect drainage-basin controls on water and sediment flux. For example, channel-belt sand-body thicknesses scale to bankfull discharge, and represent a reliable first-order proxy for contributing drainage-basin area, a proxy that is more robust if climatic regimes can be independently constrained. A database of morphometrics from Quaternary channel belts provides key modern fluvial system scaling relationships, which are applied to Cretaceous- to Paleocene-age fluvial deposits. This study documents the scales of channel-belt sand bodies within fluvial successions from the northern Gulf of Mexico passive-margin basin fill from well logs, and uses scaling relationships developed from modern systems to reconstruct the scale of associated sediment-routing systems and changes in scale through time. We measured thicknesses of 986 channel-belt sand bodies from 248 well logs so as to estimate the scales of the Cretaceous (Cenomanian) Tuscaloosa-Woodbine, Paleocene–early Eocene Wilcox, and Oligocene Vicksburg-Frio fluvial systems. These data indicate that Cenozoic fluvial systems were significantly larger than their Cenomanian counterparts, which is consistent with Cretaceous to Paleocene continental-scale drainage reorganization that routed water discharge and sediment from much of the continental United States to the Gulf of Mexico. At a more detailed level, Paleocene–early Eocene Wilcox fluvial systems were larger than their Oligocene counterparts, which could reflect decreases in drainage-basin size and/or climatic change within the continental interior toward drier climates with less runoff. Additionally, these data suggest that the paleo–Tennessee River, which now joins the Ohio River in the northernmost Mississippi embayment of the central United States, was an independent fluvial system, flowing southwest to the southern Mississippi embayment, or directly to the Gulf of Mexico, through the early Eocene. Changes in scaling relationships through time, and interpreted changes in the scales of contributing drainage basins, are generally consistent with previously published regional paleogeographic maps, as well as with newly published maps of paleodrainage from detrital-zircon provenance and geochronological studies. As part of a suite of metrics derived from modern systems, scaling relationships make it possible to more fully understand and constrain the scale of ancient source-to-sink systems and their changes through time, or cross-check interpretations made by other means

Topology of Event Horizons and Topological Censorship

We prove that, under certain conditions, the topology of the event horizon of a four dimensional asymptotically flat black hole spacetime must be a 2-sphere. No stationarity assumption is made. However, in order for the theorem to apply, the horizon topology must be unchanging for long enough to admit a certain kind of cross section. We expect this condition is generically satisfied if the topology is unchanging for much longer than the light-crossing time of the black hole. More precisely, let $M$ be a four dimensional asymptotically flat spacetime satisfying the averaged null energy condition, and suppose that the domain of outer communication \C_K to the future of a cut $K$ of \Sm is globally hyperbolic. Suppose further that a Cauchy surface $\Sigma$ for \C_K is a topological 3-manifold with compact boundary $\partial\S$ in $M$, and $\S'$ is a compact submanifold of \bS with spherical boundary in $\S$ (and possibly other boundary components in $M/\S$). Then we prove that the homology group $H_1(\Sigma',Z)$ must be finite. This implies that either $\partial\S'$ consists of a disjoint union of 2-spheres, or $\S'$ is nonorientable and $\partial\S'$ contains a projective plane. Further, \partial\S=\partial\Ip[K]\cap\partial\Im[\Sp], and $\partial \Sigma$ will be a cross section of the horizon as long as no generator of \partial\Ip[K] becomes a generator of \partial\Im[\Sp]. In this case, if $\S$ is orientable, the horizon cross section must consist of a disjoint union of 2-spheres.}Comment: 11 pages, plain latex (minor revision: $\Sigma$ replaced by its closure in various places.

Channel-belt scaling relationship and application to early Miocene source-to-sink systems in the Gulf of Mexico basin

In past decades, numerous studies have focused on the alluvial sedimentary record of basin fill. Paleo–drainage basin characteristics, such as drainage area or axial river length, have received little attention, mostly because the paleo–drainage system underwent erosion or bypass, and its record is commonly modified and overprinted by subsequent tectonism or erosional processes. In this work, we estimate the drainage areas of early Miocene systems in the Gulf of Mexico basin by using scaling relationships between drainage area and river channel dimensions (e.g., depth) developed in source-to-sink studies. Channel-belt thickness was used to estimate channel depth and was measured from numerous geophysical well logs. Both lower channel-belt thickness and bankfull thickness were measured to estimate the paleo–water depth at low and bankfull stages. Previous paleogeographic reconstruction using detrital zircon and petrographic provenance analysis and continental geomorphic synthesis constrains independent estimates of drainage basin extent. Comparison of results generated by the two independent approaches indicates that drainage basin areas predicted from channel-belt thickness are reasonable and suggests that bankfull thickness correlates best with drainage basin area. The channel bankfull thickness also correlates with reconstructed submarine fan dimension. This work demonstrates application to the deep-time stratigraphic archive, where records of drainage basin characteristics are commonly modified or lost