The Kerr solution: A geometrical construction

1975 ◽  
Vol 29 (2) ◽  
pp. 322-339 ◽  
Author(s):  
P. A. Hogan
Keyword(s):  
Kerr Solution ◽  
Geometrical Construction

The Kerr solution

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Kerr Black Hole ◽  
Geodesic Equation ◽  
Einstein Equations ◽  
Kerr Metric ◽  
Kerr Solution ◽  
Axially Symmetric ◽  
Observable Universe ◽  
Einstein Vacuum Equations ◽  
Einstein Vacuum ◽  
The Many

This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals. Finally, the chapter turns to the Kerr black hole, as well as its curvature singularity, horizons, static limit, and maximal extension.

Application of L-systems to geometrical construction of chamise and juniper shrubs

2014 ◽  
Vol 273 ◽  
pp. 86-95 ◽  
Author(s):  
Dallan R. Prince ◽  
Marianne E. Fletcher ◽  
Chen Shen ◽  
Thomas H. Fletcher
Keyword(s):  
Geometrical Construction ◽  
L Systems

Cooperative Pair Driven Quenching of Yb3+ Emission in Nanocrystalline ZrO2:Yb3+

2009 ◽  
Vol 5 ◽  
pp. 121-134 ◽  
Author(s):  
O. Meza ◽  
L.A. Diaz-Torres ◽  
P. Salas ◽  
E. De la Rosa ◽  
C. Ángeles-Chávez ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Crystalline Phase ◽  
Luminescence Quenching ◽  
Interaction Parameters ◽  
Transfer Model ◽  
Geometrical Construction ◽  
Transfer Processes ◽  
Nir Emission ◽  
Energy Transfer Model ◽  
Cooperative Energy

The concentration luminescence quenching of the NIR emission of Yb3+ in nanocrystalline ZrO2 is studied. It is found that the quenching is dominated by cooperative energy transfer processes from isolated Yb3+ ions to Yb-Yb pairs (Yb dimers). The Yb dimer concentration depends on the crystallite phase and size, which on time depends on Yb concentration. An extended energy transfer model was developed to predict the IR and cooperative visible fluorescence emissions by taking in to account the crystalline phase, the nanocrystals size, and the geometrical construction of Yb dimers. Our model succeeds to fit simultaneously both experimental VIS and NIR emissions, and the corresponding interaction parameters are reported.

scholarly journals Tunable three-way topological energy-splitter

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Mehul P. Makwana ◽  
Gregory Chaplain
Keyword(s):  
Time Reversal ◽  
Rectangular Lattice ◽  
Geometrical Construction ◽  
Beam Splitters ◽  
The Third ◽  
Symmetric Square ◽  
Hall States

AbstractStrategically combining four structured domains creates the first ever three-way topological energy-splitter; remarkably, this is only possible using a square, or rectangular, lattice, and not the graphene-like structures more commonly used in valleytronics. To achieve this effect, the two mirror symmetries, present within all fully-symmetric square structures, are broken; this leads to two nondistinct interfaces upon which valley-Hall states reside. These interfaces are related to each other via the time-reversal operator and it is this subtlety that allows us to ignite the third outgoing lead. The geometrical construction of our structured medium allows for the three-way splitter to be adiabatically converted into a wave steerer around sharp bends. Due to the tunability of the energies directionality by geometry, our results have far-reaching implications for applications such as beam-splitters, switches and filters across wave physics.

Flight phase and altitude-dependent geometrical vertical flight plan optimization minimizing the total number of vertical plan segments

2019 ◽  
Vol 233 (13) ◽  
pp. 4825-4838
Author(s):  
Bogdan Dumitru Dancila ◽  
Benoit Beulze ◽  
Ruxandra Mihaela Botez
Keyword(s):  
Flight Path ◽  
Segment Length ◽  
Test Cases ◽  
Geometrical Construction ◽  
Performance Models ◽  
Flight Phase ◽  
Flight Plan ◽  
Plan Optimization ◽  
Trade Offs ◽  
Aircraft Performance

This paper presents a new method for the geometrical construction of an optimal vertical flight plan associated to a provided lateral flight plan defined as a succession of waypoints characterized by their along-the-track distance relative to the first waypoint and their constraints. The principal objective of the proposed method is the minimization of the total number of vertical flight plan segments, whose slope values closest match the values set for their corresponding flight phase and altitude. The main advantage of the proposed method is that it constructs the optimized vertical flight plan employing faster—and less-intensive computations than methods based solely on aircraft performance models. Also, the proposed algorithm has the advantage of generating ground-fixed predicted vertical flight plans which, when flown, are less sensitive to varying wind conditions, thus, smaller trajectory deviations than those computed using solely the model-based algorithms. Two implementations corresponding to different trade-offs between conflicting preferred gradient and minimal segment length constraints were compared. The results show that a vertical flight path segment’s construction and resulting configuration is dependent on the configuration of the vertical flight plan segments that precede it. The results also show that for a majority of the test cases, the resulting flight plans computed using the two implementations were identical. Moreover, even when the flight plans were not completely identical, many of the corresponding segments were identical.

scholarly journals SURFACES WITH PULLEYS AND KHOVANOV HOMOLOGY

2011 ◽  
Vol 20 (07) ◽  
pp. 1021-1040 ◽  
Author(s):  
B. AUDOUX
Keyword(s):  
Finite Number ◽  
Khovanov Homology ◽  
Geometrical Construction

In this paper, we define surfaces with pulleys which are unions of 1- and 2-dimensional manifolds, glued together on a finite number of ℤ/3ℤ-labeled points of their interiors. Then, by seeing them as cobordisms, we give a refinement of Bar-Natan's geometrical construction of Khovanov homology which can be applied to different notions of refined links as links in I-bundle or braid-like links.

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