Abstract
The angular ADM reduction of the BTZ spacetime yields a Liouville-type theory. The analysis of the resulting Liouville theory naturally leads to the identification of the stretched horizon. The dynamics associated with the stretched horizon has a feature that seems consistent with the unsmooth horizon; the quantum gravity effects are essential for the unsmoothness. We show that the “anomaly” term in the stress–energy tensor is responsible for the Planck scale energy experienced by an infalling observer.
Highlights
Given the unrenormalizability of the 4D Einstein–Hilbert action, the semi-classical description has been widely used in the black hole literature. (See, e.g., [1,2] for reviews.) This description led to the discovery of Hawking radiation and many other useful results, and we believe it is essential to go beyond it to solve Black Hole Information (BHI) problem and surrounding issues
We show that the central charge term induces the invariant quantity above to generate the Planck scale energy density at the stretched horizon, a behavior consistent with the idea of the unsmooth horizon [30,4]
The additional ADM reduction along r has led to the natural identification of the stretched horizon
Summary
Given the unrenormalizability of the 4D Einstein–Hilbert action, the semi-classical description has been widely used in the black hole literature. (See, e.g., [1,2] for reviews.) This description led to the discovery of Hawking radiation and many other useful results, and we believe it is essential to go beyond it to solve Black Hole Information (BHI) problem and surrounding issues. By applying the procedure in the Hamilton–Jacobi formulation, it was shown that the 5D AdS gravity admits a class of solutions with a “moduli field”, which in turn was identified as the abelian worldvolume (i.e., the hypersurface at a fixed r ) gauge field [10,11]. This may be viewed as the way in which the actual dualization of the bulk theory to the boundary theory should generally work.. We take the Liouville theory resulting from the φ-reduction and analyze its implications for black hole physics.
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