4,253 research outputs found
A Strong Maximum Principle for Weak Solutions of Quasi-Linear Elliptic Equations with Applications to Lorentzian and Riemannian Geometry
The strong maximum principle is proved to hold for weak (in the sense of
support functions) sub- and super-solutions to a class of quasi-linear elliptic
equations that includes the mean curvature equation for spacelike
hypersurfaces in a Lorentzian manifold. As one application a Lorentzian warped
product splitting theorem is given.Comment: 37 pages, 1 figure, ams-latex using eepi
Thermonuclear burst physics with RXTE
Recently we have made measurements of thermonuclear burst energetics and
recurrence times which are unprecedented in their precision, largely thanks to
the sensitivity of the Rossi X-ray Timing Explorer. In the "Clocked Burster",
GS 1826-24, hydrogen burns during the burst via the rapid-proton (rp) process,
which has received particular attention in recent years through theoretical and
modelling studies. The burst energies and the measured variation of alpha (the
ratio of persistent to burst flux) with accretion rate strongly suggests solar
metallicity in the neutron star atmosphere, although this is not consistent
with the corresponding variation of the recurrence time. Possible explanations
include extra heating between the bursts, or a change in the fraction of the
neutron star over which accretion takes place. I also present results from 4U
1746-37, which exhibits regular burst trains which are interrupted by "out of
phase" bursts.Comment: 4 pages, 2 figures, AIP conference proceedings format. To appear in
the proceedings of the "X-ray Timing 2003: Rossi and Beyond" meeting held in
Cambridge, MA, November, 200
Uniqueness of de Sitter space
All inextendible null geodesics in four dimensional de Sitter space dS^4 are
complete and globally achronal. This achronality is related to the fact that
all observer horizons in dS^4 are eternal, i.e. extend from future infinity
scri^+ all the way back to past infinity scri^-. We show that the property of
having a null line (inextendible achronal null geodesic) that extends from
scri^- to scri^+ characterizes dS^4 among all globally hyperbolic and
asymptotically de Sitter spacetimes satisfying the vacuum Einstein equations
with positive cosmological constant. This result is then further extended to
allow for a class of matter models that includes perfect fluids.Comment: 22 pages, 2 figure
A simple proof of the recent generalisations of Hawking's black hole topology theorem
A key result in four dimensional black hole physics, since the early 1970s,
is Hawking's topology theorem asserting that the cross-sections of an "apparent
horizon", separating the black hole region from the rest of the spacetime, are
topologically two-spheres. Later, during the 1990s, by applying a variant of
Hawking's argument, Gibbons and Woolgar could also show the existence of a
genus dependent lower bound for the entropy of topological black holes with
negative cosmological constant. Recently Hawking's black hole topology theorem,
along with the results of Gibbons and Woolgar, has been generalised to the case
of black holes in higher dimensions. Our aim here is to give a simple
self-contained proof of these generalisations which also makes their range of
applicability transparent.Comment: 12 pages, 1 figur
Non-Existence of Black Holes in Certain 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
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
Fingerprinting the impacts of global change on tropical forests
Recent observations of widespread changes in mature tropical forests such as increasing tree growth, recruitment and mortality rates and increasing above-ground biomass suggest that 'global change' agents may be causing predictable changes in tropical forests. However, consensus over both the robustness of these changes and the environmental drivers that may be causing them is yet to emerge. This paper focuses on the second part of this debate. We review (i) the evidence that the physical, chemical and biological environment that tropical trees grow in has been altered over recent decades across large areas of the tropics, and (ii) the theoretical, experimental and observational evidence regarding the most likely effects of each of these changes on tropical forests. Ten potential widespread drivers of environmental change were identified: temperature, precipitation, solar radiation, climatic extremes (including El Niño Southern Oscillation events), atmospheric CO2 concentrations, nutrient deposition, O3/acid depositions, hunting, land-use change and increasing liana numbers. We note that each of these environmental changes is expected to leave a unique 'fingerprint' in tropical forests, as drivers directly force different processes, have different distributions in space and time and may affect some forests more than others (e.g. depending on soil fertility). Thus, in the third part of the paper we present testable a priori predictions of forest responses to assist ecologists in attributing particular changes in forests to particular causes across multiple datasets. Finally, we discuss how these drivers may change in the future and the possible consequences for tropical forests
What’s in It for Me? Reciprocal Exchanges between Underwriters and Venture Capitalists
In this article, we examine the impact of repeat interactions between VCs and underwriters. Past research has suggested that such interactions build trust and may contribute to more equitable treatment of issuing firms. We adopt an alternative perspective and suggest that these repeat interactions are characterized by reciprocal exchanges facilitated by opportunistic behavior from the VC. Our analysis demonstrates that VCs and underwriters interact in order to appropriate greater value from the IPO. This article provides a more complete understanding of repeat interactions between the VC and the underwriter by identifying characteristics of the relationship that have an impact on the value of the IPO
Summary of the recent short-haul systems studies
The results of several NASA sponsored high density short haul air transportation systems studies are reported as well as analyzed. Included are the total STOL systems analysis approach, a companion STOL composites study conducted in conjunction with STOL systems studies, a STOL economic assessment study, an evaluation of STOL aircraft with and without externally blown flaps, an alternative STOL systems for the San Francisco Bay Area, and the quiet, clean experimental engine studies. Assumptions and results of these studies are summarized, their differences, analyzed, and the results compared with those in-house analyses performed by the Systems Studies Division of the NASA-Ames Research Center. Pertinent conclusions are developed and the more significant technology needs for the evaluation of a viable short haul transportation system are identified
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