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F. Finster N. Kamran J. Smoller S.-T. Yau 《Communications in Mathematical Physics》2002,230(2):201-244
The Cauchy problem is considered for the massive Dirac equation in the non-extreme Kerr–Newman geometry, for smooth initial
data with compact support outside the event horizon and bounded angular momentum. We prove that the Dirac wave function decays
in at least at the rate t
−5/6. For generic initial data, this rate of decay is sharp. We derive a formula for the probability p that the Dirac particle escapes to infinity. For various conditions on the initial data, we show that p = 0, 1 or 0 < p < 1. The proofs are based on a refined analysis of the Dirac propagator constructed in [4].
Received: 20 August 2001 / Accepted: 22 January 2002
RID="*"
ID="*"Present address: NWF I – Mathematik, Universit?t Regensburg, 93040 Regensburg, Germany.?E-mail: felix.finster@mathematik.uni-regensburg.de
RID="**"
ID="**"Research supported by NSERC grant # RGPIN 105490-1998.
RID="***"
ID="***"Research supported in part by the NSF, Grant No. DMS-0103998.
RID="****"
ID="****"Research supported in part by the NSF, Grant No. 33-585-7510-2-30. 相似文献
16.
T. Joseph Sahaya Anand Chua Kok Yau Yeow See Leong Lim Weng Keat Hng May Ting 《Current Applied Physics》2013,13(8):1674-1683
Effects of High Temperature Storage (HTS) and bonding toward microstructure change of intermetallic compound (IMC) at the wire bonding interface of 3 types of bond pad (Al, AlSiCu and NiPdAu) were presented in this paper. Optical and electron microscope analyses revealed that the IMC growth rate of samples under 175 and 200 °C HTS increased in the order of Al > AlSiCu > NiPdAu. Besides, higher HTS and bonding temperatures also promoted higher IMC thickness. The compositional study showed that higher HTS and bonding temperature developed rapid interdiffusion in bonding interface. In the mechanical ball shear test, a decrease of the shear force of Al and AlSiCu bond pads after 500 h HTS was believed due to poorly developed IMC at bonding interface. On the other hand, shear force degradation at 1000 h was due to excessive growth of IMC that in turn causes the formation of defects. For NiPdAu bond pad, increasing trend of shear force with HTS duration at 175 °C implied a good reliability of the Cu wire bonding. The rapid microscopic inspection on Cu wired Al bond pad under HTS 175 °C showed the IMC development from the periphery to the center of the ball bond. However, after 500 h voids started to develop until the crack was observed at 1000 h. 相似文献
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Felix Finster Joel Smoller Shing-Tung Yau 《Communications in Mathematical Physics》1999,205(2):249-262
We consider for j=?, … a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field.
The Einstein–Dirac–Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the
form of the horizon, the only black hole solutions of the EDM equations are the Reissner–Nordstr?m solutions. In other words,
the spinors must vanish identically. Applied to the gravitational collapse of a “cloud” of spin-?-particles to a black hole,
our result indicates that the Dirac particles must eventually disappear inside the event horizon.
Received: 2 November 1998 / Accepted: 23 February 1999 相似文献
19.
We study the limit of quasilocal energy defined in Wang and Yau (Phys Rev Lett 102(2):021101, 2009; Commun Math Phys 288(3):919–942, 2009) for a family of spacelike 2-surfaces approaching null infinity of an asymptotically flat spacetime. It is shown that Lorentzian
symmetry is recovered and an energy-momentum 4-vector is obtained. In particular, the result is consistent with the Bondi–Sachs
energy-momentum at a retarded time. The quasilocal mass in Wang and Yau (Phys Rev Lett 102(2):021101, 2009; Commun Math Phys 288(3):919–942, 2009) is defined by minimizing quasilocal energy among admissible isometric embeddings and observers. The solvability of the Euler-Lagrange
equation for this variational problem is also discussed in both the asymptotically flat and asymptotically null cases. Assuming
analyticity, the equation can be solved and the solution is locally minimizing in all orders. In particular, this produces
an optimal reference hypersurface in the Minkowski space for the spatial or null exterior region of an asymptotically flat
spacetime. 相似文献
20.
Generalized projective chaos synchronization of gyroscope systems subjected to dead-zone nonlinear inputs 总被引:1,自引:0,他引:1
Her-Terng Yau 《Physics letters. A》2008,372(14):2380-2385
This Letter presents a robust control scheme to generalized projective synchronization between two identical two-degrees-of-freedom heavy symmetric gyroscopes with dead zone nonlinear inputs. Because of the nonlinear terms of the gyroscope system, the system exhibits complex and chaotic motions. By the Lyapunov stability theory with control terms, two suitable sliding surfaces are proposed to ensure the stability of the controlled closed-loop system in sliding mode. Then, two sliding mode controllers (SMC) are designed to guarantee the hitting of the sliding surfaces even when the control inputs contain dead-zone nonlinearity. This method allows us to arbitrarily direct the scaling factor onto a desired value. Numerical simulations show that this method works very well for the proposed controller. 相似文献