We consider the thermodynamic properties of (d + 1)-dimensional spacetimes with NUT charges. Such spacetimes are asymptotically locally anti de Sitter (or flat), with non-trivial topology in their spatial sections, and can have fixed point sets of the Euclidean time symmetry that are either (d − 1)-dimensional (called "bolts") or of lower dimensionality (pure "NUTs"). We compute the free energy, conserved mass, and entropy for 4, 6, 8 and 10 dimensions for each, using both Noether charge methods and the AdS/CFT-inspired counterterm approach. We then generalize these results to arbitrary dimensionality. We find in 4k + 2 dimensions that there are no regions in parameter space in the pure NUT case for which the entropy and specific heat are both positive, and so all such spacetimes are thermodynamically unstable. For the pure NUT case in 4k dimensions a region of stability exists in parameter space that decreases in size with increasing dimensionality. All bolt cases have some region of parameter space for which thermodynamic stability can be realized.

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson-(A)dS metrics, with the added feature of having Lorentzian signatures. They are asymptotic to (A)dS d+1 /Z p . In the AdS case their energy is negative relative to that of pure AdS. We present perturbative evidence in 5 dimensions that such metrics are the states of lowest energy in their asymptotic class, and present a conjecture that this is generally true for all such metrics. In the dS case these solutions have a cosmological horizon. We show that their mass at future infinity is less than that of pure dS.

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson-(anti)-de Sitter ((A)dS) metrics, with the added feature of having Lorentzian signatures. They provide an affirmative answer to the open question as to whether or not there exist solutions with negative cosmological constant that asymptotically approach AdS 5 /Γ, but have less energy than AdS 5 /Γ. We present evidence that these solutions are the lowest-energy states within their asymptotic class.Weakly coupled non-abelian gauge theories on non-simply connected manifolds can have ground states of much lower energy than one might naively expect. For example, a U(N) gauge theory on a torus of m-dimensions whose typical length is L can have its lowest energy states of order 1/ (NL) (instead of 1/L) if N of the fields are arranged to be periodic after traversing one circle N times [1]. By introducing such locally flat but globally nontrivial connections, the effective size of the compact space is thereby increased by a factor of N, correspondingly reducing the spectrum of states. A string-theoretic interpretation of this phenomenon is that of the low-energy excitations of one D-brane wrapped N times around a circle, where the U(N) gauge theory describes the low energy excitations of N D-branes wrapped on the torus.The N 2 open strings connecting distinct D-branes in the latter case become N multiply identified open strings on a circle of length NL in the former case, yielding a configuration with lower energy states.

We show that the class of four-dimensional Taub-Bolt(NUT) spacetimes with positive cosmological constant for some values of NUT charges are stable and have entropies that are greater than that of de Sitter spacetime, in violation of the entropic N-bound conjecture. We also show that the maximal mass conjecture, which states "any asymptotically dS spacetime with mass greater than dS has a cosmological singularity" , can be violated as well. Our calculation of conserved mass and entropy is based on an extension of the path integral formulation to asymptotically de Sitter spacetimes.

We apply a recent proposal for defining conserved mass in asymptotically de Sitter spacetimes to the class of Taub-Bolt-dS spacetimes. We compute the action, entropy and conserved mass of these spacetimes, and find that in certain instances the mass and entropy can exceed that of pure de Sitter spacetime, in violation of recent suggestive conjectures to the contrary.The search for a holographic dual to de Sitter spacetime has led to a number of suggestive results and conjectures concerning gravitational thermodynamics and its underlying quantumgravitational description. Intriguing evidence that de Sitter (dS) spacetime has maximal entropy first came from calculations of cosmological black hole pair production [1] and was recently formulated in terms of the N-bound [2], which states that any spacetime with positive cosmological constant Λ = 3ℓ −2 has observable entropy S ≤ S dS = πℓ 2 . From this followed the notion that dS spacetime also had maximal mass/energy, expressed in the form of a conjecture [3] that any asymptotically dS spacetime with mass greater than pure dS has a cosmological singularity.The physical meaning of a conserved mass/energy outside the cosmological horizon of an asymptotically dS spacetime requires clarification [4], since asymptotically dS spacetimes do not have spatial infinity the way that their flat or anti de Sitter (AdS) counterparts do. Moreover one cannot define a global timelike Killing vector; rather there is a timelike Killing vector field ∂/∂t inside the dS cosmological horizon that becomes spacelike outside of it. Recently, however, a proposal to extend the Brown-York prescription to asymptotically dS spacetime [5,6,7,8] yielded suggestive information about the stress tensor and conserved charges of the hypothetical dual Euclidean conformal field theory (CFT) on their spacelike boundaries, providing intriguing evidence for a holographic duality similar to the AdS/CFT correspondence. The specific prescription in *