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Mark R. Sepanski - One of the best experts on this subject based on the ideXlab platform.
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Factorizations of relative Extremal projectors
P-Adic Numbers Ultrametric Analysis and Applications, 2015Co-Authors: Charles H. Conley, Mark R. SepanskiAbstract:We survey earlier results on factorizations of Extremal projectors and relative Extremal projectors and present preliminary results on non-commutative factorizations of relative Extremal projectors: we deduce the existence of such factorizations for sl_4 and sl_5.
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Infinite commutative product formulas for relative Extremal projectors
Advances in Mathematics, 2005Co-Authors: Charles H. Conley, Mark R. SepanskiAbstract:Abstract Loosely speaking, a relative Extremal projector is a universal projector mapping any appropriate representation onto a certain highest subrepresentation. This paper presents a number of infinite product expansions for the relative Extremal projector, most of which are new even for the Extremal projector. As an application, conditions are given determining when the relative Extremal projector descends to a well-defined operator on a particular representation. The total denominator and related summation formulas are also studied.
Charles H. Conley - One of the best experts on this subject based on the ideXlab platform.
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Factorizations of relative Extremal projectors
P-Adic Numbers Ultrametric Analysis and Applications, 2015Co-Authors: Charles H. Conley, Mark R. SepanskiAbstract:We survey earlier results on factorizations of Extremal projectors and relative Extremal projectors and present preliminary results on non-commutative factorizations of relative Extremal projectors: we deduce the existence of such factorizations for sl_4 and sl_5.
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Infinite commutative product formulas for relative Extremal projectors
Advances in Mathematics, 2005Co-Authors: Charles H. Conley, Mark R. SepanskiAbstract:Abstract Loosely speaking, a relative Extremal projector is a universal projector mapping any appropriate representation onto a certain highest subrepresentation. This paper presents a number of infinite product expansions for the relative Extremal projector, most of which are new even for the Extremal projector. As an application, conditions are given determining when the relative Extremal projector descends to a well-defined operator on a particular representation. The total denominator and related summation formulas are also studied.
James Lucietti - One of the best experts on this subject based on the ideXlab platform.
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On the uniqueness of Extremal vacuum black holes
Classical and Quantum Gravity, 2010Co-Authors: Pau Figueras, James LuciettiAbstract:We prove uniqueness theorems for asymptotically flat, stationary, Extremal, vacuum black hole solutions, in four and five dimensions with one and two commuting rotational Killing fields respectively. As in the non-Extremal case, these problems may be cast as boundary value problems on the two dimensional orbit space. We show that the orbit space for solutions with one Extremal horizon is homeomorphic to an infinite strip, where the two boundaries correspond to the rotational axes, and the two asymptotic regions correspond to spatial infinity and the near-horizon geometry. In four dimensions this allows us to establish the uniqueness of Extremal Kerr amongst asymptotically flat, stationary, rotating, vacuum black holes with a single Extremal horizon. In five dimensions we show that there is at most one asymptotically flat, stationary, Extremal vacuum black hole with a connected horizon, two commuting rotational symmetries and given interval structure and angular momenta. We also provide necessary and sufficient conditions for four and five dimensional asymptotically flat vacuum black holes with the above symmetries to be static (valid for Extremal, non-Extremal and even non-connected horizons).
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a classification of near horizon geometries of Extremal vacuum black holes
arXiv: High Energy Physics - Theory, 2008Co-Authors: Hari K Kunduri, James LuciettiAbstract:We consider the near-horizon geometries of Extremal, rotating black hole solutions of the vacuum Einstein equations, including a negative cosmological constant, in four and five dimensions. We assume the existence of one rotational symmetry in 4d, two commuting rotational symmetries in 5d and in both cases non-toroidal horizon topology. In 4d we determine the most general near-horizon geometry of such a black hole, and prove it is the same as the near-horizon limit of the Extremal Kerr-AdS(4) black hole. In 5d, without a cosmological constant, we determine all possible near-horizon geometries of such black holes. We prove that the only possibilities are one family with a topologically S^1 X S^2 horizon and two distinct families with topologically S^3 horizons. The S^1 X S^2 family contains the near-horizon limit of the boosted Extremal Kerr string and the Extremal vacuum black ring. The first topologically spherical case is identical to the near-horizon limit of two different black hole solutions: the Extremal Myers-Perry black hole and the slowly rotating Extremal Kaluza-Klein (KK) black hole. The second topologically spherical case contains the near-horizon limit of the fast rotating Extremal KK black hole. Finally, in 5d with a negative cosmological constant, we reduce the problem to solving a sixth-order non-linear ODE of one function. This allows us to recover the near-horizon limit of the known, topologically S^3, Extremal rotating AdS(5) black hole. Further, we construct an approximate solution corresponding to the near-horizon geometry of a small, Extremal AdS(5) black ring.
Jun‐qiang Sun - One of the best experts on this subject based on the ideXlab platform.
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Gradient fields of potential energy surfaces
The Journal of Chemical Physics, 1994Co-Authors: Klaus Ruedenberg, Jun‐qiang SunAbstract:While contour plots provide conceptual pictures of potential energy surfaces and exhibit their critical points, quantitative determinations of critical points and reaction paths as well as dynamical calculations require a knowledge of the gradient fields. The corresponding orthogonal trajectory maps are more complex than contour maps, but they provide additional insights. They are found to contain certain frequently occurring structural elements and these patterns are here examined. It is shown that many of them result from local confluences of orthogonal trajectory bundles with gradient Extremals. The analysis leads to the distinction between eight different kinds of such gradient Extremal channels. The most important ones are the streambeds and ridges, the former being typical conceptual prototypes of reaction channels, the latter being prototypes of reaction barriers. Gradient Extremal channels emanate from second order critical points in the directions of all normal modes, but they do not necessarily follow along the entire reaction path of any one reaction. They can also exist unrelated to critical points. The conclusions are exemplified on a number of model potential energy surfaces.
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Gradient Extremals and steepest descent lines on potential energy surfaces
The Journal of Chemical Physics, 1993Co-Authors: Jun‐qiang Sun, Klaus RuedenbergAbstract:Relationships between steepest descent lines and gradient Extremals on potential surfaces are elucidated. It is shown that gradient Extremals are the curves which connect those points where the steepest descent lines have zero curvature. This condition gives rise to a direct method for the global determination of gradient Extremals which is illustrated on the Muller–Brown surface. Furthermore, explicit expressions are obtained for the derivatives of the steepest‐descent‐line curvatures and, from them, for the gradient Extremal tangents. With the help of these formulas, a new gradient Extremal following algorithm is formulated.
Oleg B. Zaslavskii - One of the best experts on this subject based on the ideXlab platform.
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Entropy of an Extremal electrically charged thin shell and the Extremal black hole
Physics Letters B, 2015Co-Authors: José P. S. Lemos, Gonçalo M. Quinta, Oleg B. ZaslavskiiAbstract:Abstract There is a debate as to what is the value of the entropy S of Extremal black holes. There are approaches that yield zero entropy S = 0 , while there are others that yield the Bekenstein–Hawking entropy S = A + / 4 , in Planck units. There are still other approaches that give that S is proportional to r + or even that S is a generic well-behaved function of r + . Here r + is the black hole horizon radius and A + = 4 π r + 2 is its horizon area. Using a spherically symmetric thin matter shell with Extremal electric charge, we find the entropy expression for the Extremal thin shell spacetime. When the shell's radius approaches its own gravitational radius, and thus turns into an Extremal black hole, we encounter that the entropy is S = S ( r + ) , i.e., the entropy of an Extremal black hole is a function of r + alone. We speculate that the range of values for an Extremal black hole is 0 ≤ S ( r + ) ≤ A + / 4 .
