I-Sheng Yang

Conditionally extended validity of perturbation theory: Persistence of AdS stability islands

Approximating nonlinear dynamics with a truncated perturbative expansion may be accurate for a while, but it, in general, breaks down at a long time scale that is one over the small expansion parameter. There are interesting cases in which such breakdown does not happen. We provide a mathematically general and precise definition of those cases, in which we prove that the validity of truncated theory trivially extends to the long time scale. This enables us to utilize numerical results, which are only obtainable within finite times, to legitimately predict the dynamics when the expansion parameter goes to zero, and thus the long time scale goes to infinity. In particular, this shows that existing noncollapsing solutions in the AdS (in)stability problem persist to the zero-amplitude limit, opposing the conjecture by Dias, Horowitz, Marolf, and Santos that predicts a shrinkage to measure zero [O.J. Dias et al., Classical Quantum Gravity 29, 235019 (2012)]. We also point out why the persistence of collapsing solutions is harder to prove, and how the recent interesting progress by Bizon, Maliborski, and Rostoworowski has not yet proven this [P. Bizon, M. Maliborski, and A. Rostworowski, arXiv:1506.03519].

Secret loss of unitarity due to the classical background

We show that a quantum subsystem can become significantly entangled with a classical background through a process with little or none semi-classical back-reactions. We study two quantum harmonic oscillators coupled to each other in a time-independent Hamiltonian. We compare it to its semi-classical approximation in which one of the oscillators is treated as the classical background. In this approximation, the remaining quantum oscillator has an effective Hamiltonian which is time-dependent, and its evolution appears to be unitary. However, in the fully quantum model, the two oscillators can entangle with each other. Thus the unitarity of either individual oscillator is never guaranteed. We derive the critical time scale after which the unitarity of either individual oscillator is irrevocably lost. In particular, we give an example that in the adiabatic limit, unitarity is lost before other relevant questions can be addressed.

Geometry of the Infalling Causal Patch

The firewall paradox states that an observer falling into an old black hole must see a violation of unitarity, locality, or the equivalence principle. Motivated by this remarkable conflict, we analyze the causal structure of black hole spacetimes in order to determine whether all the necessary ingredients for the paradox fit within a single observers causal patch. We particularly focus on the question of whether the interior partner modes of the outgoing Hawking quanta can, in principle, be measured by an infalling observer. Since the relevant modes are spread over the entire sphere, we answer a simple geometrical question: can any observer see an entire sphere behind the horizon? We find that for all static black holes in 3 + 1 and higher dimensions, with any value of the cosmological constant, no single observer can see both the early Hawking radiation and the interior modes with low angular momentum. We present a detailed description of the causal patch geometry of the Schwarzschild black hole in 3 + 1 dimensions, where an infalling observer comes closest to being able to measure the relevant modes.

A self-consistency check for unitary propagation of Hawking quanta

The black hole information paradox presumes that quantum field theory in curved space–time can provide unitary propagation from a near-horizon mode to an asymptotic Hawking quantum. Instead of invoking conjectural quantum-gravity effects to modify such an assumption, we propose a self-consistency check. We establish an analogy to Feynman’s analysis of a double-slit experiment. Feynman showed that unitary propagation of the interfering particles, namely ignoring the entanglement with the double-slit, becomes an arbitrarily reliable assumption when the screen upon which the interference pattern is projected is infinitely far away. We argue for an analogous self-consistency check for quantum field theory in curved space–time. We apply it to the propagation of Hawking quanta and test whether ignoring the entanglement with the geometry also becomes arbitrarily reliable in the limit of a large black hole. We present curious results to suggest a negative answer, and we discuss how this loss of naive unitarity in...

Coherent cascade conjecture for collapsing solutions in global AdS

We analyze the gravitational dynamics of a classical scalar field coupled to gravity in asymptotically AdS spacetime, which leads to black hole formation on the shortest nonlinear time scale for some initial conditions. We show that the observed collapse cannot be described by the well-known process of a random-phase cascade in the theory of weak turbulence. This implies that the dynamics on this time scale is highly sensitive to the phases of modes. We explore the alternative possibility of a coherent phase cascade and analytically find stationary solutions with completely coherent phases and power-law energy spectra. We show that these power-law spectra lead to diverging geometric backreaction, which is the likely precursor to black hole formation. In

Gauge dependence of the AdS instability problem

4+1

Gravitational rotation of polarization: Clarifying the gauge dependence and prediction for a double pulsar

dimensions, our stationary solution has the same power-law energy spectrum as the final state right before collapse observed in numerical simulations. We conjecture that our stationary solutions describe the system shortly before collapse in other dimensions, and predict the energy spectrum.

Pulsar acceleration shifts from nearby supernova explosion

Previous work on the anti–de Sitter (AdS) instability problem within the two-time framework (TTF) has found an “oscillating singularity” whose presence depends on the gauge choice. We give a physical interpretation of this singularity as a diverging redshift between the boundary and the center of AdS. This signals a genuine breakdown of the linearized gravity. One can also identify the diverging redshift through a backreaction calculation purely in the boundary gauge, where the TTF result stays regular.

Instability corners in AdS space

From the basic concepts of general relativity, we investigate the rotation of the polarization angle by a moving gravitational lens. Particularly, we clarify the existing confusion in the literature by showing and explaining why such rotation must explicitly depend on the relative motion between the observer and the lens. We update the prediction of such effect on the double pulsar PSR J0737-3039 and estimate a rotation angle of

Inflation on a Slippery Slope

\sim 10^{-7}rad