A complete cosmological solution to the averaged Einstein field equations as found in macroscopic gravity
A formalism for analyzing the complete set of field equations describing macroscopic gravity is presented. Using this formalism, a cosmological solution to the macroscopic gravity equations is determi...
A formalism for analyzing the complete set of field equations describing macroscopic gravity is presented. Using this formalism, a cosmological solution to the macroscopic gravity equations is determi...
A remark on the dimension of the attractor for the Dirichlet problem of the complex Ginzburg–Landau equation
Using the improved lower bound on the sum of the eigenvalues of the Dirichlet Laplacian proven by Melas [Proc. Am. Math. Soc. 131, 631 (2003)], we remark on a modified estimate of the dimension of the...
Using the improved lower bound on the sum of the eigenvalues of the Dirichlet Laplacian proven by Melas [Proc. Am. Math. Soc. 131, 631 (2003)], we remark on a modified estimate of the dimension of the...
Geometry of universal magnification invariants
J. Math. Phys. 50, 082504 (2009); doi:10.1063/1.3204970
Published 26 August 2009
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Recent work in gravitational lensing and catastrophe theory has shown that the sum of the signed magnifications of images near folds, cusps, and also higher catastrophes is zero. Here, it is discussed how Lefschetz fixed point theory can be used to interpret this result geometrically for a subfamily of these catastrophes, namely, the generic case of folds, cusps, elliptic and hyperbolic umbilics, swallowtails, and the elliptic and hyperbolic umbilics in gravitational lensing.
©2009 American Institute of Physics
| History: | Received 3 April 2009; accepted 22 July 2009; published 26 August 2009 |
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http://link.aip.org/link/?JMAPAQ/50/082504/1 |
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KEYWORDS and PACS
- 95.30.Sf
Relativity and gravitation in astrophysics - 98.62.Sb
Gravitational lenses and luminous arcs - 95.35.+d
Dark matter (stellar, interstellar, galactic, and cosmological) - 98.80.Cq
Particle-theory and field-theory models of the early Universe - 02.40.-k
Geometry, differential geometry, and topology - 04.50.-h
Higher-dimensional gravity and other theories of gravity - YEAR: 2009
RELATED DATABASES
PUBLICATION DATA
0022-2488 (print)
1089-7658 (online)
AIP
REFERENCES (16)
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