Instantons, black holes and harmonic functions

Abstract

We find a class of five-dimensional Einstein-Maxwell type Lagrangians which contains the bosonic Lagrangians of vector multiplets as a subclass, and preserves some features of supersymmetry, namely the existence of multi-centered black hole solutions and of attractor equations. Solutions can be expressed in terms of harmonic functions through a set of algebraic equations. The geometry underlying these Lagrangians is characterized by the existence of a Hesse potential and generalizes the very special real geometry of vector multiplets. Our construction proceeds by first obtaining instanton solutions for a class of four-dimensional Euclidean sigma models, which includes those occuring for four-dimensional Euclidean N=2 vector multiplets as a subclass.

58 pages, minor revision: some references added, discussion of first order flow equations extended, remarks on Hamilton-Jacobi formulation added

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• N=2 Extremal Black Holes
• Supersymmetry and Attractors
• Macroscopic Entropy of $N=2$ Extremal Black Holes
• Black Holes and Critical Points in Moduli Space
• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• Effects of D-instantons
• Supergravity flows and D-brane stability
• Non-Supersymmetric Attractors
• Fake Supergravity and Domain Wall Stability
• Instantons and seven-branes in type IIB superstring theory
• Special geometry, cubic polynomials and homogeneous quaternionic spaces
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• Non-Supersymmetric Attractors in String Theory
• A Stringy Cloak for a Classical Singularity
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• New Attractors
• On Euclidean spinors and Wick rotations
• First-order flow equations for extremal black holes in very special geometry
• Non-Supersymmetric Attractor Flow in Symmetric Spaces
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• Generating Geodesic Flows and Supergravity Solutions
• General BPS Black Holes In Five Dimensions
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• Generating branes via sigma-models
• Stationary solutions of N=2 supergravity
• General Static N=2 Black Holes
• Erice Lectures on Black Holes and Attractors
• Quantum Attractor Flows
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• First-order flow equations for extremal and non-extremal black holes
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Cited by in corpus (23)

• Nonextremal black holes in gauged supergravity and the real formulation of special geometry
• Non-extremal Black Holes, Harmonic Functions, and Attractor Equations
• Black holes and black strings of N=2, d=5 supergravity in the H-FGK formalism
• H-FGK formalism for black-hole solutions of N=2, d=4 and d=5 supergravity
• The Hesse potential, the c-map and black hole solutions
• The Freudenthal gauge symmetry of the black holes of N=2,d=4 supergravity
• Non-supersymmetric extremal multicenter black holes with superpotentials
• The FGK formalism for black p-branes in d dimensions
• Domain walls and instantons in N=1, d=4 supergravity
• Five-dimensional vector multiplets in arbitrary signature
• Black holes as generalised Toda molecules
• Non-extremal black hole solutions from the c-map
• Black holes and equivariant charge vectors in N=2,d=4 supergravity
• A Simple Derivation of Supersymmetric Extremal Black Hole Attractors
• All extremal instantons in Einstein-Maxwell-dilaton-axion theory
• Developments in special geometry
• Black hole solutions of N=2, d=4 supergravity with a quantum correction, in the H-FGK formalism
• Euclidean Actions, Instantons, Solitons and Supersymmetry
• BPS dyons and Hesse flow
• Non-extremal black holes from the generalised r-map
• The supersymmetric black holes of N=8 supergravity
• Five-dimensional Nernst branes from special geometry
• Extremal black holes, attractor equations, and harmonic functions