We show that three-dimensional massive gravity admits Lifshitz metrics with generic values of the dynamical exponent z as exact solutions. At the point z=3, exact black hole solutions which are asymptotically Lifshitz arise. These spacetimes are thre
e-dimensional analogues of those that were recently proposed as gravity duals for scale invariant fixed points.
A recent paper [arXiv:0801.4566] claims that topologically massive gravity contains only chiral boundary excitations at a particular value of the Chern-Simons coupling. On the other hand, propagating bulk degrees of freedom were found even at the chi
ral point in [arXiv:0803.3998]. The two references use very different methods, making comparison of their respective claims difficult. In this letter, we use the method of [arXiv:0801.4566] to construct a tower of propagating bulk states satisfying standard AdS boundary conditions. Our states have finite norm, with sign opposite to that of right-moving boundary excitations. Our results thus agree with [arXiv:0803.3998] and disagree with [arXiv:0801.4566].
In a recent work, it has been pointed out that certain observables of the massless scalar field theory in a static spherically symmetric background exhibit a universal behavior at large distances. More precisely, it was shown that, unlike what happen
s in the case the coupling to the curvature xi is generic, for the special cases xi=0 and xi = 1/6 the large distance behavior of the expectation value <T^{mu}_{ u}> turns out to be independent of the internal structure of the gravitational source. Here, we address a higher dimensional generalization of this result: We first compute the difference between a black hole and a static spherically symmetric star for the observables <phi^2> and <T^{mu}_{ u}> in the far field limit. Thus, we show that the conformally invariant massless scalar field theory in a static spherically symmetric background exhibits such universality phenomenon in Dgeq 4 dimensions. Also, using the one-loop effective action, we compute <T^{mu}_{ u}> for a weakly gravitating object. These results lead to the explicit expression of the expectation value <T^{mu}_{ u}> for a Schwarzschild-Tangherlini black hole in the far field limit. As an application, we obtain quantum corrections to the gravitational potential in D dimensions, which for D=4 are shown to agree with the one-loop correction to the graviton propagator previously found in the literature.
