Symmetries and conformal bridge in Schwarschild-(A)dS black hole mechanics

We show that the Schwarzschild-(A)dS black hole mechanics possesses a hidden symmetry under the three-dimensional Poincaré group. This symmetry shows up after having gauge-fixed the diffeomorphism invariance in the symmetry-reduced homogeneous Einstein-Λ model and stands as a physical symmetry of the system. It dictates the geometry both in the black hole interior and exterior regions, as well as beyond the cosmological horizon in the Schwarzschild-dS case. It follows that one can associate a set of non-trivial conserved charges to the Schwarzschild-(A)dS black hole which act in each causally disconnected regions. In T-region, they act on fields living on spacelike hypersurface of constant time, while in R-regions, they act on time-like hypersurface of constant radius. We find that while the expression of the charges depend explicitly on the location of the hypersurface, the charge algebra remains the same at any radius in R-regions (or time in T-regions). Finally, the analysis of the Casimirs of the charge algebra reveals a new solution-generating map. The $$ \mathfrak{sl}\left(2,\mathrm{\mathbb{R}}\right) $$ sl 2 ℝ Casimir is shown to generate a one-parameter family of deformation of the black hole geometry labelled by the cosmological constant. This gives rise to a new conformal bridge allowing one to continuously deform the Schwarzschild-AdS geometry to the Schwarzschild and the Schwarzschild-dS solutions.

Finding pythons in unexpected places

We argue that novel (highly nonclassical) quantum extremal surfaces play a crucial role in reconstructing the black hole interior even for isolated, single-sided, non-evaporating black holes (i.e. with no auxiliary reservoir). Specifically, any code subspace where interior outgoing modes can be excited will have a quantum extremal surface in its maximally mixed state. We argue that as a result, reconstruction of interior outgoing modes is always exponentially complex. Our construction provides evidence in favor of a strong Python’s lunch proposal: that nonminimal quantum extremal surfaces are the exclusive source of exponential complexity in the holographic dictionary. We also comment on the relevance of these quantum extremal surfaces to the geometrization of state dependence in the typicality arguments for firewalls.

BMS3 Mechanics and the Black Hole Interior

The spacetime in the interior of a black hole can be described by an homogeneous line element, for which the Einstein–Hilbert action reduces to a one-dimensional mechanical model. We have shown in [1] that this model exhibits a symmetry under the (2+1)-dimensional Poincaré group. Here we extend the Poincaré transformations to the infinite-dimensional BMS3 group. Although the black hole model is not invariant under those extended transformations, we can write it as a geometric action for BMS3, where the configuration space variables are elements of the algebra bms3 and the equations of motion transform as coadjoint vectors. The BMS3 symmetry breaks down to its Poincaré subgroup, which arises as the stabilizer of the vacuum orbit. This symmetry breaking is analogous to what happens with the Schwarzian action in AdS2 JT gravity, although in the present case there is no direct interpretation in terms of boundary symmetries. This observation, together with the fact that other lower-dimensional gravitational models (such as the BTZ black hole) possess the same broken BMS3 symmetries, provides yet another illustration of the ubiquitous role played by this group.

Truly two-dimensional black holes under dimensional transitions of spacetime

A sufficiently massive star in the end of its life will inevitably collapse into a black hole as more deconfined degrees of freedom make the core ever softer. One possible way to avoid the singularity in the end is by dimensional phase transition of spacetime. Indeed, the black hole interior, two-dimensional (2D) in nature, can be described well as a perfect fluid of free massless Majorana fermions and gauge bosons under a 2D supersymmetric mirror model with new understanding of emergent gravity from dimensional evolution of spacetime. In particular, the 2D conformal invariance of the black hole gives rise to desired consistent results for the interior microphysics and structures including its temperature, density and entropy.

HPS meets AMPS: how soft hair dissolves the firewall

We build on the observation by Hawking, Perry and Strominger that a global black hole space-time supports a large number of soft hair degrees of freedom to shed new light on the firewall argument by Almheiri, Marolf, Polchinski, and Sully. We propose that the soft hair Goldstone mode is encoded in a classical transition function that connects the asymptotic and near horizon region. The entropy carried by the soft hair is part of the black hole entropy and encoded in the outside geometry. We argue that the infalling observer automatically measures the classical value of the soft mode before reaching the horizon and that this measurement implements a code subspace projection that enables the reconstruction of interior operators. We use the soft hair dynamics to introduce an observer dependent notion of the firewall and show that for an infalling observer it recedes inwards into the black hole interior: the observer never encounters a firewall before reaching the singularity. Our results indicate that the HPS black hole soft hair plays an essential role in dissolving the AMPS firewall.

Six-point functions and collisions in the black hole interior

In the eternal AdS black hole geometry, we consider two signals sent from the boundaries into the black hole interior shared between the two asymptotic regions. We compute three different out-of-time-order six-point functions to quantify various properties of the collision of these signals behind the horizons: (i) We diagnose the strength of the collision by probing the two-signal state on a late time slice with boundary operators. (ii) We quantify two-sided operator growth, which provides a dual description of the signals meeting in the black hole interior, in terms of the quantum butterfly effect and quantum circuits. (iii) We consider an explicit coupling between the left and right CFTs to make the wormhole traversable and extract information about the collision product from behind the horizon. At a technical level, our results rely on the method of eikonal resummation to obtain the relevant gravitational contributions to Lorentzian six-point functions at all orders in the GN-expansion. We observe that such correlation functions display an intriguing factorization property. We corroborate these results with geodesic computations of six-point functions in two- and three-dimensional gravity.

Warped information and entanglement islands in AdS/WCFT

We use the notion of double holography to study Hawking radiation emitted by the eternal BTZ black hole in equilibrium with a thermal bath, but in the form of warped CFT2 degrees of freedom. In agreement with the literature, we find entanglement islands and a phase transition in the entanglement surface, but our results differ significantly from work in AdS/CFT in three major ways: (1) the late-time entropy decreases in time, (2) island degrees of freedom exist at all times, not just at late times, with the phase transition changing whether or not these degrees of freedom include the black hole interior, and (3) the physics involves a field-theoretic IR divergence emerging when the boundary interval is too big relative to the black hole’s inverse temperature. This behavior in the entropy appears to be consistent with the non-unitarity of holographic warped CFT2 and demonstrates that the islands are not a phenomenon restricted to black hole information in unitary setups.

Size and momentum of an infalling particle in the black hole interior

The future interior of black holes in AdS/CFT can be described in terms of a quantum circuit. We investigate boundary quantities detecting properties of this quantum circuit. We discuss relations between operator size, quantum complexity, and the momentum of an infalling particle in the black hole interior. We argue that the trajectory of the infalling particle in the interior close to the horizon is related to the growth of operator size. The notion of size here differs slightly from the size which has previously been related to momentum of exterior particles and provides an interesting generalization. The fact that both exterior and interior momentum are related to operator size growth is a manifestation of complementarity.