Dilaton black holes with a cosmological term

The properties of static spherically symmetric black holes, which carry electric and magnetic charges, and which are coupled to the dilaton in the presence of a cosmological term (Liouville-type potential, or cosmological constant) are reviewed.Comment: 20 pages, phyzzx, v2 contains expanded introduction, additional references etc to coincide with published versio

Multi-scalar black holes with contingent primary hair: Mechanics and stability

We generalize a class of magnetically charged black holes holes non-minimally coupled to two scalar fields previously found by one of us [gr-qc/9910041] to the case of multiple scalar fields. The black holes possess a novel type of primary scalar hair, which we call a contingent primary hair: although the solutions possess degrees of freedom which are not completely determined by the other charges of the theory, the charges necessarily vanish in the absence of the magnetic monopole. Only one constraint relates the black hole mass to the magnetic charge and scalar charges of the theory. We obtain a Smarr-type thermodynamic relation, and the first law of black hole thermodynamics for the system. We further explicitly show in the two-scalar-field case that, contrary to the case of many other hairy black holes, the black hole solutions are stable to radial perturbations.Comment: 10 pages, RevTeX4, 6 figures, graphicx. v2: Substantial new sections and results added from authors' joint unpublished manuscript dated 2000, doubling the length of the paper. v3: references added. v4: Small additions (extra figures etc) to agree with published versio

Specht Polytopes and Specht Matroids

The generators of the classical Specht module satisfy intricate relations. We introduce the Specht matroid, which keeps track of these relations, and the Specht polytope, which also keeps track of convexity relations. We establish basic facts about the Specht polytope, for example, that the symmetric group acts transitively on its vertices and irreducibly on its ambient real vector space. A similar construction builds a matroid and polytope for a tensor product of Specht modules, giving "Kronecker matroids" and "Kronecker polytopes" instead of the usual Kronecker coefficients. We dub this process of upgrading numbers to matroids and polytopes "matroidification," giving two more examples. In the course of describing these objects, we also give an elementary account of the construction of Specht modules different from the standard one. Finally, we provide code to compute with Specht matroids and their Chow rings.Comment: 32 pages, 5 figure