Abstract:
The question of how to account for the outgoing black hole modes without drawing upon a transplanckian reservoir at the horizon is addressed. It is argued that the outgoing modes must arise via conversion from ingoing modes. It is further argued that the back-reaction must be included to avoid the conclusion that particle creation cannot occur in a strictly stationary background. The process of ``mode conversion" is known in plasma physics by this name and in condensed matter physics as ``Andreev reflection" or ``branch conversion". It is illustrated here in a linear Lorentz non-invariant model introduced by Unruh. The role of interactions and a physical short distance cutoff is then examined in the sonic black hole formed with Helium-II.

Abstract:
It is shown how the results of Deser and Levin on the response of accelerated detectors in anti-de Sitter space can be understood from the same general perspective as other thermality results in spacetimes with bifurcate Killing horizons.

Abstract:
These notes introduce the subject of quantum field theory in curved spacetime and some of its applications and the questions they raise. Topics include particle creation in time-dependent metrics, quantum origin of primordial perturbations, Hawking effect, the trans-Planckian question, and Hawking radiation on a lattice.

Abstract:
Microscopic state counting for a black hole in Loop Quantum Gravity yields a result proportional to horizon area, and inversely proportional to Newton's constant and the Immirzi parameter. It is argued here that before this result can be compared to the Bekenstein-Hawking entropy of a macroscopic black hole, the scale dependence of both Newton's constant and the area must be accounted for. The two entropies could then agree for any value of the Immirzi parameter, if a certain renormalization property holds.

Abstract:
The Schwarzschild metric, its Reissner-Nordstrom-de Sitter generalizations to higher dimensions, and some further generalizations all share the feature that g_{tt} g_{rr}=-1 in Schwarzschild-like coordinates. In this pedagogical note we trace this feature to the condition that the Ricci tensor (and stress-energy tensor in a solution to Einstein's equation) has vanishing radial null-null component, i.e. is proportional to the metric in the t-r subspace. We also show this condition holds if and only if the area-radius coordinate is an affine parameter on the radial null geodesics.

Abstract:
The Einstein equation is derived from the proportionality of entropy and horizon area together with the fundamental relation $\delta Q=TdS$ connecting heat, entropy, and temperature. The key idea is to demand that this relation hold for all the local Rindler causal horizons through each spacetime point, with $\delta Q$ and $T$ interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. This requires that gravitational lensing by matter energy distorts the causal structure of spacetime in just such a way that the Einstein equation holds. Viewed in this way, the Einstein equation is an equation of state. This perspective suggests that it may be no more appropriate to canonically quantize the Einstein equation than it would be to quantize the wave equation for sound in air.

Abstract:
In this short essay we review the arguments showing that black hole entropy is, at least in part, ``entanglement entropy", i.e., missing information contained in correlations between quantum field fluctuations inside and outside the event horizon. Although the entanglement entropy depends upon the matter field content of the theory, it turns out that so does the Bekenstein-Hawking entropy $A/4\hbar G_{ren}$, in precisely the same way, because the effective gravitational constant $G_{ren}$ is renormalized by the very same quantum fluctuations. It appears most satisfactory if the entire gravitational action is ``induced", in the manner suggested by Sakharov, since then the black hole entropy is purebred entanglement entropy, rather than being hybrid with bare gravitational entropy (whatever that might be.)

Abstract:
The rank--1 sector of classical Ashtekar gravity is considered, motivated by the degeneracy of the metric along the Wilson lines in quantum loop states. It is found that the lines behave like 1+1 dimensional spacetimes with a pair of massless complex fields propagating along them. The inclusion of matter and extension to supergravity are also considered.

Abstract:
A derivation of the Hawking effect is given which avoids reference to field modes above some cutoff frequency $\omega_c\gg M^{-1}$ in the free-fall frame of the black hole. To avoid reference to arbitrarily high frequencies, it is necessary to impose a boundary condition on the quantum field in a timelike region near the horizon, rather than on a (spacelike) Cauchy surface either outside the horizon or at early times before the horizon forms. Due to the nature of the horizon as an infinite redshift surface, the correct boundary condition at late times outside the horizon cannot be deduced, within the confines of a theory that applies only below the cutoff, from initial conditions prior to the formation of the hole. A boundary condition is formulated which leads to the Hawking effect in a cutoff theory. It is argued that it is possible the boundary condition is {\it not} satisfied, so that the spectrum of black hole radiation may be significantly different from that predicted by Hawking, even without the back-reaction near the horizon becoming of order unity relative to the curvature.

Abstract:
Einstein-aether theory is general relativity coupled to a dynamical unit timelike vector field. A brief review of current theoretical understanding and observational constraints on the four coupling parameters of the theory is given.