Falling through the black hole horizon

We consider the fate of a small classical object, a "stick", as it falls through the horizon of a large black hole (BH). Classically, the equivalence principle dictates that the stick is affected by small tidal forces, and Hawking's quantum-mechanical model of BH evaporation makes essentially the same prediction. If, on the other hand, the BH horizon is surrounded by a "firewall", the stick will be consumed as it falls through. We have recently extended Hawking's model by taking into account the quantum fluctuations of the geometry and the classical back-reaction of the emitted particles. Here, we calculate the strain exerted on the falling stick for our model. The strain depends on the near-horizon state of the Hawking pairs. We find that, after the Page time when the state of the pairs deviates significantly from maximal entanglement (as required by unitarity), the induced strain in our semiclassical model is still parametrically small. This is because the number of the disentangled pairs is parametrically smaller than the BH entropy. A firewall does, however, appear if the number of disentangled pairs near the horizon is of order of the BH entropy, as implicitly assumed in previous discussions in the literature.Comment: 25 pages, 3 figure

Horizons of semiclassical black holes are cold

We calculate, using our recently proposed semiclassical framework, the quantum state of the Hawking pairs that are produced during the evaporation of a black hole (BH). Our framework adheres to the standard rules of quantum mechanics and incorporates the quantum fluctuations of the collapsing shell spacetime in Hawking's original calculation, while accounting for back-reaction effects. We argue that the negative-energy Hawking modes need to be regularly integrated out; and so these are effectively subsumed by the BH and, as a result, the number of coherent negative-energy modes $N_{coh}$ at any given time is parametrically smaller than the total number of the Hawking particles $N_{total}$ emitted during the lifetime of the BH. We find that $N_{coh}$ is determined by the width of the BH wavefunction and scales as the square root of the BH entropy. We also find that the coherent negative-energy modes are strongly entangled with their positive-energy partners. Previously, we have found that $N_{coh}$ is also the number of coherent outgoing particles and that information can be continually transferred to the outgoing radiation at a rate set by $N_{coh}$. Our current results show that, while the BH is semiclassical, information can be released without jeopardizing the nearly maximal inside-out entanglement and imply that the state of matter near the horizon is approximately the vacuum. The BH firewall proposal, on the other hand, is that the state of matter near the horizon deviates substantially from the vacuum, starting at the Page time. We find that, under the usual assumptions for justifying the formation of a firewall, one does indeed form at the Page time. However, the possible loophole lies in the implicit assumption that the number of strongly entangled pairs can be of the same order of $N_{total}$.Comment: Replaced to agree with the published version. Added clarifications and explanations, error corrected in the calculation of the reduced density matrix in Sect. 6, conclusions unchanged. 48 pages, 1 figur

The sound damping constant for generalized theories of gravity

The near-horizon metric for a black brane in Anti-de Sitter (AdS) space and the metric near the AdS boundary both exhibit hydrodynamic behavior. We demonstrate the equivalence of this pair of hydrodynamic systems for the sound mode of a conformal theory. This is first established for Einstein's gravity, but we then show how the sound damping constant will be modified, from its Einstein form, for a generalized theory. The modified damping constant is expressible as the ratio of a pair of gravitational couplings that are indicative of the sound-channel class of gravitons. This ratio of couplings differs from both that of the shear diffusion coefficient and the shear viscosity to entropy ratio. Our analysis is mostly limited to conformal theories but suggestions are made as to how this restriction might eventually be lifted.Comment: 24 page

Emergent horizon, Hawking radiation and chaos in the collapsed polymer model of a black hole

We have proposed that the interior of a macroscopic Schwarzschild black hole (BH) consists of highly excited, long, closed, interacting strings and, as such, can be modeled as a collapsed polymer. It was previously shown that the scaling relations of the collapsed-polymer model agree with those of the BH. The current paper further substantiates this proposal with an investigation into some of its dynamical consequences. In particular, we show that the model predicts, without relying on gravitational effects, an emergent horizon. We further show that the horizon fluctuates quantum mechanically as it should and that the strength of the fluctuations is inversely proportional to the BH entropy. It is then demonstrated that the emission of Hawking radiation is realized microscopically by the quantum-induced escape of small pieces of string, with the rate of escape and the energy per emitted piece both parametrically matching the Hawking temperature. We also show, using standard methods from statistical mechanics and chaos theory, how our model accounts for some other known properties of BHs. These include the accepted results for the scrambling time and the viscosity-to-entropy ratio, which in our model apply not only at the horizon but throughout the BH interior.Comment: 41 pages, 4 figures, added introductory material and figures. Belated updated version to match the published version. Results unchange

Gravitational entropy and thermodynamics away from the horizon

We define, by an integral of geometric quantities over a spherical shell of arbitrary radius, an invariant gravitational entropy. This definition relies on defining a gravitational energy and pressure, and it reduces at the horizon of both black branes and black holes to Wald's Noether charge entropy. We support the thermodynamic interpretation of the proposed entropy by showing that, for some cases, the field theory duals of the entropy, energy and pressure are the same as the corresponding quantities in the field theory. In this context, the Einstein equations are equivalent to the field theory thermodynamic relation TdS=dE+PdV supplemented by an equation of state.Comment: 13 pages, Substantial changes to presentation. Conclusions unchanged, version to be published in PL