Misner Strings

"   The purpose of this paper is to carry such arguments a step further by demonstrating that Misner strings themselves have an intrinsic entropy. One need not have a bolt present for a spacetime to have gravitational entropy. This result follows from recent work on the conjectured AdS/CFT duality, which equates the bulk gravitational action of an asymptotically AdS spacetime with the quantum effective action of a conformal field theory (CFT) defined on the AdS boundary. Inspired by this correspondence, Balasubramanian and Kraus [8] have proposed adding a term to the boundary at infinity (understood as boundary at some radius r in the large-r limit) which is a functional only of curvature invariants of the induced metric on the boundary (see also ref. [9]). The addition of such terms does not affect the bulk equations of motion because they are intrinsic invariants of the boundary metric. In four dimensions only two invariants exist which (due to dimensionality) can contribute to the Hamiltonian at infinity, and their coefficients are uniquely fixed by demanding that it b  finite for Schwarzchild-AdS spacetime. As I shall demonstrate, this choice of boundary term is sufficient to compute finite values for the actions, Hamiltonian, and entropies for both Taub-bolt-AdS and Taub-NUT-AdS spacetimes. A recent observation by Lau [10] permits an extension of this boundary term to asymptotically flat cases, and I shall demonstrate how it may be used to compute entropies of the Taub-bolt and Taub-NUT spacetimes. Taub-NUT and Taub-NUT-AdS are the first examples of spacetimes without bolts that have gravitational entropy.

Taken from R.B. Mann.