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Local quantum field theory appears unlikely to be a good effective low energy description of any system containing a black hole, and should probably not attempt to describe particle states whose volume is smaller than their corresponding schwarzschild radius To avoid these difficulties Cohen-Kaplan-Nelson propose a stronger constraint on the ir cutoff 1/l which excludes all states that lie within their Schwarzschild radius. Since the maximum energy density in the effective theory is M4, the constraint on L is L3A4≤LM Thermal energy M~L374≈1L3A4 La 2gm Schwarzschild radius r Ls LTo avoid these difficulties Cohen-Kaplan-Nelson propose a stronger constraint on the IR cutoff 1/L which excludes all states that lie within their Schwarzschild radius. Since the maximum energy density in the effective theory is Λ^4, the constraint on L is Thermal energy ~ ~ Schwarzschild radius Local quantum field theory appears unlikely to be a good effective low energy description of any system containing a black hole, and should probably not attempt to describe particle states whose volume is smaller than their corresponding Schwarzschild radius
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