31 research outputs found
A generalization of Hawking's black hole topology theorem to higher dimensions
Hawking's theorem on the topology of black holes asserts that cross sections
of the event horizon in 4-dimensional asymptotically flat stationary black hole
spacetimes obeying the dominant energy condition are topologically 2-spheres.
This conclusion extends to outer apparent horizons in spacetimes that are not
necessarily stationary. In this paper we obtain a natural generalization of
Hawking's results to higher dimensions by showing that cross sections of the
event horizon (in the stationary case) and outer apparent horizons (in the
general case) are of positive Yamabe type, i.e., admit metrics of positive
scalar curvature. This implies many well-known restrictions on the topology,
and is consistent with recent examples of five dimensional stationary black
hole spacetimes with horizon topology . The proof is inspired
by previous work of Schoen and Yau on the existence of solutions to the Jang
equation (but does not make direct use of that equation).Comment: 8 pages, latex2e, references updated, minor corrections, to appear in
Communications in Mathematical Physic
Quantum Formation of Black Hole and Wormhole in Gravitational Collapse of a Dust Shell
Quantum-mechanical model of self-gravitating dust shell is considered. To
clarify the relation between classical and quantum spacetime which the shell
collapse form, we consider various time slicing on which quantum mechanics is
developed. By considering the static time slicing which corresponds to an
observer at a constant circumference radius, we obtain the wave functions of
the shell motion and the discrete mass spectra which specify the global
structures of spherically symmetric spacetime formed by the shell collapse. It
is found that wormhole states are forbidden when the rest mass is comparable
with Plank mass scale due to the zero-point quantum fluctuations.Comment: 10 pages in twocolumn, 8 figures, RevTeX 3.
Nonexistence of marginally trapped surfaces and geons in 2+1 gravity
We use existence results for Jang's equation and marginally outer trapped
surfaces (MOTSs) in 2+1 gravity to obtain nonexistence of geons in 2+1 gravity.
In particular, our results show that any 2+1 initial data set, which obeys the
dominant energy condition with cosmological constant \Lambda \geq 0 and which
satisfies a mild asymptotic condition, must have trivial topology. Moreover,
any data set obeying these conditions cannot contain a MOTS. The asymptotic
condition involves a cutoff at a finite boundary at which a null mean convexity
condition is assumed to hold; this null mean convexity condition is satisfied
by all the standard asymptotic boundary conditions. The results presented here
strengthen various aspects of previous related results in the literature. These
results not only have implications for classical 2+1 gravity but also apply to
quantum 2+1 gravity when formulated using Witten's solution space quantization.Comment: v3: Elements from the original two proofs of the main result have
been combined to give a single proof, thereby circumventing an issue with the
second proof associated with potential blow-ups of solutions to Jang's
equation. To appear in Commun. Math. Phy
On Vanishing Theorems For Vector Bundle Valued p-Forms And Their Applications
Let be a strictly increasing function
with . We unify the concepts of -harmonic maps, minimal
hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and
introduce -Yang-Mills fields, -degree, -lower degree, and generalized
Yang-Mills-Born-Infeld fields (with the plus sign or with the minus sign) on
manifolds. When and
the -Yang-Mills field becomes an ordinary Yang-Mills field,
-Yang-Mills field, a generalized Yang-Mills-Born-Infeld field with the plus
sign, and a generalized Yang-Mills-Born-Infeld field with the minus sign on a
manifold respectively. We also introduce the energy functional (resp.
-Yang-Mills functional) and derive the first variational formula of the
energy functional (resp. -Yang-Mills functional) with
applications. In a more general frame, we use a unified method to study the
stress-energy tensors that arise from calculating the rate of change of various
functionals when the metric of the domain or base manifold is changed. These
stress-energy tensors, linked to -conservation laws yield monotonicity
formulae. A "macroscopic" version of these monotonicity inequalities enables us
to derive some Liouville type results and vanishing theorems for forms with
values in vector bundles, and to investigate constant Dirichlet boundary value
problems for 1-forms. In particular, we obtain Liouville theorems for
harmonic maps (e.g. -harmonic maps), and Yang-Mills fields (e.g.
generalized Yang-Mills-Born-Infeld fields on manifolds). We also obtain
generalized Chern type results for constant mean curvature type equations for
forms on and on manifolds with the global doubling property
by a different approach. The case and is due to Chern.Comment: 1. This is a revised version with several new sections and an
appendix that will appear in Communications in Mathematical Physics. 2. A
"microscopic" approach to some of these monotonicity formulae leads to
celebrated blow-up techniques and regularity theory in geometric measure
theory. 3. Our unique solution of the Dirichlet problems generalizes the work
of Karcher and Wood on harmonic map
The Strong Energy Condition and the S-Brane Singularity Problem
Recently it has been argued that, because tachyonic matter satisfies the
Strong Energy Condition [SEC], there is little hope of avoiding the
singularities which plague S-Brane spacetimes. Meanwhile, however, Townsend and
Wohlfarth have suggested an ingenious way of circumventing the SEC in such
situations, and other suggestions for actually violating it in the S-Brane
context have recently been proposed. Of course, the natural context for
discussions of [effective or actual] violations of the SEC is the theory of
asymptotically deSitter spacetimes, which tend to be less singular than
ordinary FRW spacetimes. However, while violating or circumventing the SEC is
necessary if singularities are to be avoided, it is not at all clear that it is
sufficient. That is, we can ask: would an asymptotically deSitter S-brane
spacetime be non-singular? We show that this is difficult to achieve; this
result is in the spirit of the recently proved "S-brane singularity theorem".
Essentially our results suggest that circumventing or violating the SEC may not
suffice to solve the S-Brane singularity problem, though we do propose two ways
of avoiding this conclusion.Comment: 13 pages, minor corrections and improvements, references adde
Noncommutative Topological Theories of Gravity
The possibility of noncommutative topological gravity arising in the same
manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to
construct such a theory based on a SL(2,C) complex connection, from which the
Euler characteristic and the signature invariant are obtained. This gives us a
way towards the description of noncommutative gravitational instantons as well
as noncommutative local gravitational anomalies.Comment: 17+1 pages, LaTeX, no figures, some clarifications, comments and
references added, style improve
A Conformally Invariant Holographic Two-Point Function on the Berger Sphere
We apply our previous work on Green's functions for the four-dimensional
quaternionic Taub-NUT manifold to obtain a scalar two-point function on the
homogeneously squashed three-sphere (otherwise known as the Berger sphere),
which lies at its conformal infinity. Using basic notions from conformal
geometry and the theory of boundary value problems, in particular the
Dirichlet-to-Robin operator, we establish that our two-point correlation
function is conformally invariant and corresponds to a boundary operator of
conformal dimension one. It is plausible that the methods we use could have
more general applications in an AdS/CFT context.Comment: 1+49 pages, no figures. v2: Several typos correcte
Extensive Genomic Variation within Clonal Complexes of Neisseria meningitidis
Meningococcal disease is a widely distributed complex disease affecting all age categories. It can cause severe meningitis and septicemia, especially in unvaccinated infants and young children. The causative agent, Neisseria meningitidis (Nm), can be phenotypically and genetically differentiated into serogroups and sequence types (STs) and has a highly dynamic population structure. To obtain a deeper understanding of the epidemiology of Nm, we sequenced seven Nm genomes. Large-scale genomic analysis was conducted with these 7 Nm genomes, 27 additional Nm genomes from GenBank, and 4 other Neisseria genomes. We observed extensive homologous recombination in all gene functional categories among different Nm genomes. Homologous recombination is so frequent that it has resulted in numerous chimeric open reading frames, including genes in the capsule biosynthesis cluster and loci targeted by commercial vaccines. Our results reveal that, despite widespread use, evolutionary relationships inferred from the standard seven-gene multilocus sequence typing (MLST) method could not predict virulence gene content or strain phenotype. In fact, up to 28% of the virulence-associated genes could differ between strains of identical STs. Consistent with previous studies, we found that allelic recombination is also associated with alterations in antibiotic susceptibility. Overall, these findings emphasize the extensive genomic plasticity of Nm and the limitations of standard molecular methods to quantify this genotypic and phenotypic diversity
Risk profiles and one-year outcomes of patients with newly diagnosed atrial fibrillation in India: Insights from the GARFIELD-AF Registry.
BACKGROUND: The Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF) is an ongoing prospective noninterventional registry, which is providing important information on the baseline characteristics, treatment patterns, and 1-year outcomes in patients with newly diagnosed non-valvular atrial fibrillation (NVAF). This report describes data from Indian patients recruited in this registry. METHODS AND RESULTS: A total of 52,014 patients with newly diagnosed AF were enrolled globally; of these, 1388 patients were recruited from 26 sites within India (2012-2016). In India, the mean age was 65.8 years at diagnosis of NVAF. Hypertension was the most prevalent risk factor for AF, present in 68.5% of patients from India and in 76.3% of patients globally (P < 0.001). Diabetes and coronary artery disease (CAD) were prevalent in 36.2% and 28.1% of patients as compared with global prevalence of 22.2% and 21.6%, respectively (P < 0.001 for both). Antiplatelet therapy was the most common antithrombotic treatment in India. With increasing stroke risk, however, patients were more likely to receive oral anticoagulant therapy [mainly vitamin K antagonist (VKA)], but average international normalized ratio (INR) was lower among Indian patients [median INR value 1.6 (interquartile range {IQR}: 1.3-2.3) versus 2.3 (IQR 1.8-2.8) (P < 0.001)]. Compared with other countries, patients from India had markedly higher rates of all-cause mortality [7.68 per 100 person-years (95% confidence interval 6.32-9.35) vs 4.34 (4.16-4.53), P < 0.0001], while rates of stroke/systemic embolism and major bleeding were lower after 1 year of follow-up. CONCLUSION: Compared to previously published registries from India, the GARFIELD-AF registry describes clinical profiles and outcomes in Indian patients with AF of a different etiology. The registry data show that compared to the rest of the world, Indian AF patients are younger in age and have more diabetes and CAD. Patients with a higher stroke risk are more likely to receive anticoagulation therapy with VKA but are underdosed compared with the global average in the GARFIELD-AF. CLINICAL TRIAL REGISTRATION-URL: http://www.clinicaltrials.gov. Unique identifier: NCT01090362