Extremal black holes, nilpotent orbits and the true fake superpotential
arXiv:0908.1742 · doi:10.1007/JHEP01(2010)038
Abstract
Dimensional reduction along time offers a powerful way to study stationary solutions of 4D symmetric supergravity models via group-theoretical methods. We apply this approach systematically to extremal, BPS and non-BPS, spherically symmetric black holes, and obtain their "fake superpotential" W. The latter provides first order equations for the radial problem, governs the mass and entropy formula and gives the semi-classical approximation to the radial wave function. To achieve this goal, we note that the Noether charge for the radial evolution must lie in a certain Lagrangian submanifold of a nilpotent orbit of the 3D continuous duality group, and construct a suitable parametrization of this Lagrangian. For general non-BPS extremal black holes in N=8 supergravity, W is obtained by solving a non-standard diagonalization problem, which reduces to a sextic polynomial in whose coefficients are SU(8) invariant functions of the central charges. By consistent truncation we obtain W for other supergravity models with a symmetric moduli space. In particular, for the one-modulus model, is given explicitely as the root of a cubic polynomial. The STU model is investigated in detail and the nilpotency of the Noether charge is checked on explicit solutions.
47 pages + appendices, 7 figures; v2: minor corrections, to appear in JHEP
References in corpus (15)
- Black Hole Microstates and Attractor Without Supersymmetry
- Charge Orbits of Symmetric Special Geometries and Attractors
- Non-Supersymmetric Attractor Flow in Symmetric Spaces
- Universal BPS structure of stationary supergravity solutions
- Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
- On the Moduli Space of non-BPS Attractors for N=2 Symmetric Manifolds
- First Order Description of Black Holes in Moduli Space
- N=8 non-BPS Attractors, Fixed Scalars and Magic Supergravities
- First-order flow equations for extremal and non-extremal black holes
- First order flows for N=2 extremal black holes and duality invariants
- Constituent Model of Extremal non-BPS Black Holes
- Attractors with Vanishing Central Charge
- Exact Solutions and the Attractor Mechanism in Non-BPS Black Holes
- Quasi-conformal actions, quaternionic discrete series and twistors: SU(2,1) and G_2(2)
- 5D Black Holes and Non-linear Sigma Models
Cited by in corpus (65)
- Four-qubit entanglement from string theory
- Integrable Scalar Cosmologies I. Foundations and links with String Theory
- Black holes in N=8 supergravity from SO(4,4) hidden symmetries
- U-duality and non-BPS solutions
- Seed for general rotating non-extremal black holes of N=8 supergravity
- Subtracted Geometry From Harrison Transformations
- Interacting non-BPS black holes
- On the Black-Hole/Qubit Correspondence
- Octonionic black holes
- Extremal solutions of the S3 model and nilpotent orbits of G2(2)
- Black holes in supergravity and integrability
- Fake Superpotential for Large and Small Extremal Black Holes
- Brane orbits
- First-order flows and stabilisation equations for non-BPS extremal black holes
- STU Black Holes as Four Qubit Systems
- Black holes and black strings of N=2, d=5 supergravity in the H-FGK formalism
- The Hesse potential, the c-map and black hole solutions
- Fake supersymmetry versus Hamilton-Jacobi
- Small N=2 Extremal Black Holes in Special Geometry
- Non-supersymmetric extremal multicenter black holes with superpotentials
- Ungauging black holes and hidden supercharges
- Integrability of Supergravity Black Holes and New Tensor Classifiers of Regular and Nilpotent Orbits
- Charge Orbits of Extremal Black Holes in Five Dimensional Supergravity
- Duality covariant non-BPS first order systems
- Grassmannian Connection Between Three- and Four-Qubit Observables, Mermin's Contextuality and Black Holes
- Non-supersymmetric Microstates of the MSW System
- All the timelike supersymmetric solutions of all ungauged d=4 supergravities
- A bubbling bolt
- An inverse scattering formalism for STU supergravity
- Supergravity divergences, supersymmetry and automorphic forms
- Qubits and chirotopes
- Qubits and oriented matroids in four time and four space dimensions
- General black holes, untwisted
- An Inverse Scattering Construction of the JMaRT Fuzzball
- Matrix Norms, BPS Bounds and Marginal Stability in N=8 Supergravity
- Black hole solutions to the -model and their orbits (I)
- Extremal Multicenter Black Holes: Nilpotent Orbits and Tits Satake Universality Classes
- Geroch Group Description of Black Holes
- The attractor mechanism as a distillation procedure
- Rotating black holes, global symmetry and first order formalism
- Topics in Cubic Special Geometry
- Subtracted Geometry from Harrison Transformations: II
- Maurer-Cartan Equations and Black Hole Superpotentials in N =8 Supergravity
- Iwasawa N=8 Attractors
- Black holes as generalised Toda molecules
- Extremal limits of the Cvetic-Youm black hole and nilpotent orbits of G2(2)
- Black holes and equivariant charge vectors in N=2,d=4 supergravity
- Classifying Supersymmetric Solutions in 3D Maximal Supergravity
- Multiple Single-Centered Attractors
- Nilpotent orbits in real symmetric pairs and stationary black holes
- Attractors and first order formalism in five dimensions revisited
- Developments in special geometry
- d-Geometries Revisited
- Comments on fake supersymmetry
- All extremal instantons in Einstein-Maxwell-dilaton-axion theory
- Oxidation of D=3 cosets and Bonnor dualities in
- Non-extremal black holes from the generalised r-map
- Smooth non-extremal D1-D5-P solutions as charged gravitational instantons
- Stationary Black Holes in Supergravity: The Issue of Real Nilpotent Orbits
- non-BPS walls of marginal stability
- Multi-Centered Black Hole Flows
- Geroch Group Description of Bubbling Geometries
- Multi-Centered First Order Formalism
- Brane solutions and integrability: a status report
- On the Stability of Non-Supersymmetric Quantum Attractors in String Theory