Observations of Hawking radiation: the Page curve and baby universes

We reformulate recent insights into black hole information in a manner emphasizing operationally-defined notions of entropy, Lorentz-signature descriptions, and asymptotically flat spacetimes. With the help of replica wormholes, we find that experiments of asymptotic observers are consistent with black holes as unitary quantum systems, with density of states given by the Bekenstein-Hawking formula. However, this comes at the cost of superselection sectors associated with the state of baby universes. Spacetimes studied by Polchinski and Strominger in 1994 provide a simple illustration of the associated concepts and techniques, and we argue them to be a natural late-time extrapolation of replica wormholes. The work aims to be self-contained and, in particular, to be accessible to readers who have not yet mastered earlier formulations of the ideas above.

The high accuracy conserved splitting domain decomposition scheme for solving the parabolic equations

In this paper, the high accuracy mass-conserved splitting domain decomposition method for solving the parabolic equations is proposed. In our scheme, the time extrapolation and local multi-point weighted average schemes are used to approximate the interface fluxes on interfaces of sub-domains, while the interior solutions are computed by one dimension high-order implicit schemes in sub-domains. The important feature is that the developed scheme keeps mass conservation and are of second-order convergent in time and fourth-order convergent in space. Numerical experiments confirm the convergence.

Real-time forecast of MUF for radio paths from current data obtained from oblique sounding with continuous chirp signal

We present a technique of MUF real-time forecast based on time extrapolation for maximum observed frequencies smoothed over a long-term forecast along a given path. We have validated the technique of fitting current data from the long-term forecast, using the OPEMI model, transmission curve method for short paths, and method of normal waves for long paths (over 2000 km). This technique has been tested using data obtained at the chirp sounding network of ISTP SB RAS during periods of strong and weak solar activity. The quality of the forecast has been found to significantly improve in comparison to the long-term forecast, with advance intervals of real-time forecast from 15 to 30 min. The sessions, in which the real-time forecast error is less than 10 % for 15-min advance interval, comprise from 67 to 96 % of all sessions depending on season and radio path orientation.