11,022 research outputs found
Perturbative expansion of N<8 Supergravity
We characterise the one-loop amplitudes for N=6 and N=4 supergravity in four
dimensions. For N=6 we find that the one-loop n-point amplitudes can be
expanded in terms of scalar box and triangle functions only. This
simplification is consistent with a loop momentum power count of n-3, which we
would interpret as being n+4 for gravity with a further -7 from the N=6
superalgebra. For N=4 we find that the amplitude is consistent with a loop
momentum power count of n, which we would interpret as being n+4 for gravity
with a further -4 from the N=4 superalgebra. Specifically the N=4 amplitudes
contain non-cut-constructible rational terms.Comment: 13 pages. v2 adds analytic expression for rational parts of 5-pt
1-loop N=4 SUGRA amplitude; v3 normalisations clarifie
Obtaining One-loop Gravity Amplitudes Using Spurious Singularities
The decomposition of a one-loop scattering amplitude into elementary
functions with rational coefficients introduces spurious singularities which
afflict individual coefficients but cancel in the complete amplitude. These
cancellations create a web of interactions between the various terms. We
explore the extent to which entire one-loop amplitudes can be determined from
these relationships starting with a relatively small input of initial
information, typically the coefficients of the scalar integral functions as
these are readily determined. In the context of one-loop gravity amplitudes, of
which relatively little is known, we find that some amplitudes with a small
number of legs can be completely determined from their box coefficients. For
increasing numbers of legs, ambiguities appear which can be determined from the
physical singularity structure of the amplitude. We illustrate this with the
four-point and N=1,4 five-point (super)gravity one-loop amplitudes.Comment: Minor corrections. Appendix adde
The n-point MHV one-loop Amplitude in N=4 Supergravity
We present an explicit formula for the n-point MHV one-loop amplitude in a
N=4 supergravity theory. This formula is derived from the soft and collinear
factorisations of the amplitude.Comment: 8 pages; v2 References added. Minor changes to tex
Flow visualization experiments in a porous nozzle
An experimental approach is described for the study of nozzle flows with large wall-transpiration rates. Emphasizing a qualitative understanding of the flow, the technique uses the hydraulic analogy, whereby a compressible gas flow is simulated by a water flow having a free surface. For simplicity, the simulated gas flow is taken to be two-dimensional. A nozzle with porous walls in the throat region has been developed for use on a water table. A technique for visualizing the transpired fluid has also been devised. These are discussed, and preliminary results are presented which illustrate the success of the experimental approach
Black Holes in Higher-Derivative Gravity
Extensions of Einstein gravity with higher-order derivative terms arise in
string theory and other effective theories, as well as being of interest in
their own right. In this paper we study static black-hole solutions in the
example of Einstein gravity with additional quadratic curvature terms. A
Lichnerowicz-type theorem simplifies the analysis by establishing that they
must have vanishing Ricci scalar curvature. By numerical methods we then
demonstrate the existence of further black-hole solutions over and above the
Schwarzschild solution. We discuss some of their thermodynamic properties, and
show that they obey the first law of thermodynamics.Comment: Typos corrected, discussion added, figure changed. 4 pages, 6 figure
Lichnerowicz Modes and Black Hole Families in Ricci Quadratic Gravity
A new branch of black hole solutions occurs along with the standard
Schwarzschild branch in -dimensional extensions of general relativity
including terms quadratic in the Ricci tensor. The standard and new branches
cross at a point determined by a static negative-eigenvalue eigenfunction of
the Lichnerowicz operator, analogous to the Gross-Perry-Yaffe eigenfunction for
the Schwarzschild solution in standard dimensional general relativity.
This static eigenfunction has two r\^oles: both as a perturbation away from
Schwarzschild along the new black-hole branch and also as a threshold unstable
mode lying at the edge of a domain of Gregory-Laflamme-type instability of the
Schwarzschild solution for small-radius black holes. A thermodynamic analogy
with the Gubser and Mitra conjecture on the relation between quantum
thermodynamic and classical dynamical instabilities leads to a suggestion that
there may be a switch of stability properties between the old and new
black-hole branches for small black holes with radii below the branch crossing
point.Comment: 33 pages, 8 figure
Spherically Symmetric Solutions in Higher-Derivative Gravity
Extensions of Einstein gravity with quadratic curvature terms in the action
arise in most effective theories of quantised gravity, including string theory.
This article explores the set of static, spherically symmetric and
asymptotically flat solutions of this class of theories. An important element
in the analysis is the careful treatment of a Lichnerowicz-type `no-hair'
theorem. From a Frobenius analysis of the asymptotic small-radius behaviour,
the solution space is found to split into three asymptotic families, one of
which contains the classic Schwarzschild solution. These three families are
carefully analysed to determine the corresponding numbers of free parameters in
each. One solution family is capable of arising from coupling to a
distributional shell of matter near the origin; this family can then match on
to an asymptotically flat solution at spatial infinity without encountering a
horizon. Another family, with horizons, contains the Schwarzschild solution but
includes also non-Schwarzschild black holes. The third family of solutions
obtained from the Frobenius analysis is nonsingular and corresponds to `vacuum'
solutions. In addition to the three families identified from near-origin
behaviour, there are solutions that may be identified as `wormholes', which can
match symmetrically on to another sheet of spacetime at finite radius.Comment: 57 pages, 6 figures; version appearing in journal; minor corrections
and clarifications to v
The design of a research water table
A complete design for a research water table is presented. Following a brief discussion of the analogy between water and compressible-gas flows (hydraulic analogy), the components of the water table and their function are described. The major design considerations are discussed, and the final design is presented
Flow in a discrete slotted nozzle with massive injection
An experimental investigation has been conducted to determine the effect of massive wall injection on the flow characteristics in a slotted nozzle. Some of the experiments were performed on a water table with a slotted-nozzle test section. This has 45 deg and 15 deg half angles of convergence and divergence, respectively, throat radius of 2.5 inches, and throat width of 3 inches. The hydraulic analogy was employed to qualitatively extend the results to a compressible gas flow through the nozzle. Experimental results from the water table include contours of constant Froude and Mach number with and without injection. Photographic results are also presented for the injection through slots of CO2 and Freon-12 into a main-stream air flow in a convergent-divergent nozzle in a wind tunnel. Schlieren photographs were used to visualize the flow, and qualititative agreement between the results from the gas tunnel and water table is good
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