Mathematics – Mathematical Physics
Scientific paper
Jan 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992jmp....33..248w&link_type=abstract
Journal of Mathematical Physics, Vol. 33, No. 1, p. 248 - 255
Mathematics
Mathematical Physics
21
Scientific paper
The usual approach to analyze the linear stability of a static solution of some system of equations consists of searching for linearized solutions which satisfy suitable boundary conditions spatially and which grow exponentially in time. In the case of the n = 1 Einstein-Yang-Mills (EYM) black hole, an interesting situation occurs. There exists a perturbation which grows exponentially in time-and spatially decreases to zero at the horizon-but nevertheless is physically singular on the horizon. Thus, this unstable mode is unacceptable as initial data, and the question arises as to whether the n = 1 EYM black hole is stable. The author analyzes this issue here in the more general case. He proves that there exists smooth initial data of compact support in M which give rise to a solution which grows unboundedly with time. This implies that the n = 1 EYM black hole and other mathematically similar systems are unstable despite the nonexistence of physically acceptable exponentially growing modes.
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