Abstract
In this work, we investigate how single-sided and eternal black holes in AdS can host an enormous number of semiclassical excitations in their interior, which is seemingly not reflected in the Bekenstein Hawking entropy. In addition to the paradox in the entropy, we argue that the treatment of such excitations using effective field theory also violates black holes’ expected spectral properties. We propose that these mysteries are resolved because apparently orthogonal semiclassical bulk excitations have small inner products between them; and consequently, a vast number of semiclassical excitations can be constructed using the Hilbert space which describes black hole’s interior. We show that there is no paradox in the dual CFT description and comment upon the initial bulk state, which leads to the paradox. Further, we demonstrate our proposed resolution in the context of small N toy matrix models, where we model the construction of these large number of excitations. We conclude by discussing why this resolution is special to black holes.
Highlights
The Bekenstein-Hawking entropy is a thermodynamic coarse-grained measure which states that the entropy of the black hole is proportional to its area [1, 2]
In this work, we investigate how single-sided and eternal black holes in AdS can host an enormous number of semiclassical excitations in their interior, which is seemingly not reflected in the Bekenstein Hawking entropy
We propose that these mysteries are resolved because apparently orthogonal semiclassical bulk excitations have small inner products between them; and a vast number of semiclassical excitations can be constructed using the Hilbert space which describes black hole’s interior
Summary
The Bekenstein-Hawking entropy is a thermodynamic coarse-grained measure which states that the entropy of the black hole is proportional to its area [1, 2]. Specific spacelike slices which go inside the black hole interior become very large in volume for a choice of boundary time These slices can host a considerable number of semiclassical excitations far higher than what the Bekenstein-Hawking entropy suggests, which leads to the paradox. On these late time slices, we will fit in a high number of semiclassical bulk excitations placed spatially far apart from each other such that they have zero spatial overlap, and are independent of each other The number of such excitations is much more extensive than what is stated by the Bekenstein-Hawking entropy, which leads to our paradox. We construct states resembling excitations placed far apart from each other on the Cauchy slice in these matrix models
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