Black Hole Formation and Space-Time Fluctuations in Two Dimensional Dilaton Gravity and Complementarity

Abstract

We study black hole formation in a model of two dimensional dilaton gravity and 24 massless scalar fields with a boundary. We find the most general boundary condition consistent with perfect reflection of matter and the constraints. We show that in the semiclassical approximation and for the generic value of the parameter which characterizes the boundary conditions, the boundary starts receeding to infinity at the speed of light whenever the total energy of the incoming matter flux exceeds a certain critical value. This is also the critical energy which marks the onset of black hole formation. We then compute the quantum fluctuations of the boundary and of the rescaled scalar curvature and show that as soon as the incoming energy exceeds this critical value, an asymptotic observer using normal time resolutions will always measure large fluctuations of space-time near the horizon, even though the freely falling observer does not. This is an aspect of black hole complementarity relating directly the quantum gravity effects.

(Some typographical errors corrected and some equations added to clarify the nature of the singularity in the in the semiclassical solution), 30 pagers, TIFR/TH/94-01, IC/94/16

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Cited by in corpus (7)

• Black Hole Horizons and Complementarity
• Breakdown of the semiclassical approximation at the black hole horizon
• Conformally Invariant Boundary Conditions for Dilaton Gravity
• Quantum gravity effects in the CGHS model of collapse to a black hole
• Exact solutions and critical chaos in dilaton gravity with a boundary
• Quantum gravity effects at a black hole horizon
• Critical energy flux and mass in solvable theories of 2d dilaton gravity