In this note, we explore the possibility that certain high-energy holographic CFT states correspond to black hole microstates with a geometrical behind-the-horizon region, modelled by a portion of a second asymptotic region terminating at an end-of-theworld (ETW) brane. We study the time-dependent physics of this behind-the-horizon region, whose ETW boundary geometry takes the form of a closed FRW spacetime. We show that in many cases, this behind-the-horizon physics can be probed directly by looking at the time dependence of entanglement entropy for sufficiently large spatial CFT subsystems. We study in particular states defined via Euclidean evolution from conformal boundary states and give specific predictions for the behavior of the entanglement entropy in this case. We perform analogous calculations for the SYK model and find qualitative agreement with our expectations.A fascinating possibility is that for certain states, we might have gravity localized to the ETW brane as in the Randall-Sundrum II scenario for cosmology. In this case, the effective description of physics beyond the horizon could be a big bang/big crunch cosmology of the same dimensionality as the CFT. In this case, the d-dimensional CFT describing the black hole microstate would give a precise, microscopic description of the d-dimensional cosmological physics. seancooper@phas.ubc.ca, rozali@phas.ubc.ca, bswingle@umd.edu, mav@phas.ubc.ca, cwaddell@phas.ubc.ca, daw@phas.ubc.ca 2 Some authors have argued that quantum effects should modify these expectations: the "fuzzball" proposal [1,2,3,4] suggests that microstate geometries are actually horizonless, while proponents of the "firewall" scenario [5,6] argued that consistency with unitarity and the equivalence principle imply that the geometry must end in some type of singularity at or just beyond the horizon. But many authors have given counter-arguments suggesting a more conventional picture.

In this note, we study the first law of entanglement in a boundary conformal field theory (BCFT) dual to warped AdS cut off by a brane. Exploiting the symmetry of boundary-centered half-balls in the BCFT, and using Wald's covariant phase space formalism in the presence of boundaries, we derive constraints from the first law for a broad range of covariant bulk Lagrangians. We explicitly evaluate these constraints for Einstein gravity, and find a local equation on the brane which is precisely the Neumann condition of Takayanagi [arXiv:1105.5165] at linear order in metric perturbations. This is analogous to the derivation of Einstein's equations from the first law of entanglement entropy. This machinery should generalize to give local linearized equations of motion for higher-derivative bulk gravity with additional fields. arXiv:1912.05746v1 [hep-th]

An important reason for providing midterm assessments is to give students early feedback on their progress. Ideally, students will carefully analyze their performance and use the feedback provided to adjust their study strategies or approaches to engaging with the course materials. In our experience, however, only a small fraction of students seek advice from instructors or advisors after an unsatisfactory performance. Research has shown that many students have negative perceptions of office hours, and some students find them inconvenient or have misconceptions about the purpose of office hours. In addition, it is difficult for instructors to provide detailed and individualized advice to a large number of students in a weekly office hour. To address this challenge, we automatically provide additional grades that inform students on their performance in four basic question categories that are related to levels in Bloom’s taxonomy. We also provide a table with specific recommendations for how to improve in each of these categories. These recommendations are based on experience: from conversations with students, we have learned that unsatisfying performance can often be traced back to a lack of effective exam preparation. Many students study by reading solutions to in-class activities or homework rather than reworking problems. We also noticed that struggling students often fail at a fundamental level: they tend to read definitions superficially as symbols instead of interpreting them and exploring their meaning.