Abstract
We argue that the proper time from the event horizon to the black hole singularity can be extracted from the thermal expectation values of certain operators outside the horizon. This works for fields which couple to higher-curvature terms, so that they can decay into two gravitons. To extract this proper time, it is necessary to vary the mass of the field.
Highlights
Under some reasonable assumptions, the simplest correlation function — the one-point function of a massive field — contains this information
We argue that the proper time from the event horizon to the black hole singularity can be extracted from the thermal expectation values of certain operators outside the horizon
We are using the fact that we can vary m in order to focus on the m-dependence of the correlator. This is appropriate in the case of black holes in string theory, where we can keep the black hole metric fixed and vary the string length, which varies the mass of the fields
Summary
Containing a single massive field and the simplest higher-derivative coupling to the gravitational field. By analytically continuing in the dimension, we can define finite integrals, as is standard [9] In this case, the resulting function has poles at certain values of ∆. The resulting function has poles at certain values of ∆ These values are the dimensions of multi-graviton operators that have nonzero vacuum expectation values in the black hole background. One possible sequence of operators corresponds to powers of the stress tensor and lead to poles at ∆ = nd, for n ≥ 2. These poles result from enhanced operator mixing when there is a “resonance”. If two dimensions coincide, we can have mixing at leading order in the large-N expansion. In the large-N limit, this is well defined as long as ∆ is not at one of the resonant dimensions
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