Instability of the Cauchy horizon of Reissner-Nordstroem black holes

Journal Article · Tue May 15 04:00:00 EDT 1979 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.19.2821· OSTI ID:6217869

Matzner, R A; Zamorano, N; Sandberg, V D

The stability of the inner Reissner-Nordstroem geometry is studied with test massless integer-spin fields. In contrast to previous mathematical treatments we present physical arguments for the processes involved and show that ray tracing and simple first-order scattering suffice to elucidate most of the results. Monochromatic waves which are of small amplitude and ingoing near the outer horizon develop infinite energy densities near the inner Cauchy horizon (as measured by a freely falling observer). Previous work has shown that certain derivatives of the field in a general (nonmonochromatic) disturbance must fall off exponentially near the inner (Cauchy) horizon (r = r/sub -/) if energy densities are to remain finite. Thus the solution is unstable to physically reasonable perturbations which arise outside the black hole because such perturbations, if localized near past null infinity (I/sup -/), cannot be localized near r/sub +/, the outer horizon. The mass-energy of an infalling disturbance would generate multipole moments on the black hole. Price, Sibgatullin, and Alekseev have shown that such moments are radiated away as ''tails'' which travel outward and are rescattered inward yielding a wave field with a time dependence t/sup -p/, p > 0. This decay in time is sufficiently slow that the tails yield infinite energy densities on the Cauchy horizon. (The amplification of the low-frequency tails upon interacting with the time-dependent potential between the horizons is an important feature guaranteeing the infinite energy density.) The interior structure of the analytically extended solution is thus disrupted by finite external disturbances. Guersel et al. have further shown that even perturbations which are localized as they cross the outer horizon produce singularities at the inner horizon. It is shown that this singularity arises when the incoming radiation is first scattered just inside the outer horizon

• Research Organization: Department of Physics, Center for Relativity, The University of Texas at Austin, Austin, Texas 78712
• OSTI ID: 6217869
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 19:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BLACK HOLES
ELEMENTARY PARTICLES
FUNCTIONS
GRAVITATIONAL COLLAPSE
GREEN FUNCTION
MASSLESS PARTICLES
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TIME DEPENDENCE