Abstract:
We derive the Kerr solution in a pedagogically transparent way, using physical symmetry and gauge arguments to reduce the candidate metric to just two unknowns. The resulting field equations are then easy to obtain, and solve. Separately, we transform the Kerr metric to Schwarzschild frame to exhibit its limits in that familiar setting.

Abstract:
We re-derive, compactly, a TMG decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We can then generalize it to include matter, which is necessarily null.

Abstract:
We re-visit the problem of two (oppositely) charged particles interacting electromagnetically in one dimension with retarded potentials and no radiation reaction. The specific quantitative result of interest is the time it takes for the particles to fall in towards one another. Starting with the non-relativistic form, we answer this question while adding layers of complexity until we arrive at the full relativistic delay differential equation that governs this problem. That case can be solved using the Synge method, which we describe and discuss.

Abstract:
We attempt to generalize the familiar covariantly conserved Bel-Robinson tensor B_{mnab} ~ R R of GR and its recent topologically massive third derivative order counterpart B ~ RDR, to quadratic curvature actions. Two very different models of current interest are examined: fourth order D=3 "new massive", and second order D>4 Lanczos-Lovelock, gravity. On dimensional grounds, the candidates here become B ~ DRDR+RRR. For the D=3 model, there indeed exist conserved B ~ dRdR in the linearized limit. However, despite a plethora of available cubic terms, B cannot be extended to the full theory. The D>4 models are not even linearizable about flat space, since their field equations are quadratic in curvature; they also have no viable B, a fact that persists even if one includes cosmological or Einstein terms to allow linearization about the resulting dS vacua. These results are an unexpected, if hardly unique, example of linearization instability.

Abstract:
We clarify the conditions for Birkhoff's theorem, that is, time-independence in general relativity. We work primarily at the linearized level where guidance from electrodynamics is particularly useful. As a bonus, we also derive the equivalence principle. The basic time-independent solutions due to Schwarzschild and Kerr provide concrete illustrations of the theorem. Only familiarity with Maxwell's equations and tensor analysis is required.

Abstract:
We show succinctly that all metric theories with second order field equations obey Birkhoff's theorem: their spherically symmetric solutions are static.

Abstract:
We exhibit exact solutions of (positive) matter coupled to cosmological TMG; they necessarily evolve to conical singularity/negative mass, rather than physical black hole, BTZ. By providing evidence that the latter constitutes a separate, "superselection", sector not reachable from the physical one, they also provide justification for retaining TMG's original "wrong" G-sign to ensure excitation stability here as well.

Abstract:
The maximally complicated arbitrary-dimensional "maximal" Galileon field equations simplify dramatically for symmetric configurations. Thus, spherical symmetry reduces the equations from the D- to the two-dimensional Monge-Ampere equation, axial symmetry to its cubic extension etc. We can then obtain explicit solutions, such as spherical or axial waves, and relate them to the (known) general, but highly implicit, lower-D solutions.

Abstract:
We construct, and establish the (covariant) conservation of, a 4-index "super-stress tensor" for TMG. Separately, we discuss its invalidity in quadratic curvature models and suggest a generalization.