Black Holes in Klein Space

Abstract

The analytic continuation of the general signature $(1,3)$ Lorentzian Kerr-Taub-NUT black holes to signature $(2,2)$ Kleinian black holes is studied. Their global structure is characterized by a toric Penrose diagram resembling their Lorentzian counterparts. Kleinian black holes are found to be self-dual when their mass and NUT charge are equal for any value of the Kerr rotation parameter $a$. Remarkably, it is shown that the rotation $a$ can be eliminated by a large diffeomorphism; this result also holds in Euclidean signature. The continuation from Lorentzian to Kleinian signature is naturally induced by the analytic continuation of the S-matrix. Indeed, we show that the geometry of linearized black holes, including Kerr-Taub-NUT, is captured by $(2,2)$ three-point scattering amplitudes of a graviton and a massive spinning particle. This stands in sharp contrast to their Lorentzian counterparts for which the latter vanishes kinematically, and enables a direct link to the S-matrix.

arXiv comment23 pages, 5 appendices, 5 figures

References in corpus (59)

• Geometry of the 2+1 Black Hole
• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• MHV Vertices And Tree Amplitudes In Gauge Theory
• Amplitudes, Observables, and Classical Scattering
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• High-energy gravitational scattering and the general relativistic two-body problem
• General Relativity from Scattering Amplitudes
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• On Tree Amplitudes in Gauge Theory and Gravity
• The classical double copy for Taub-NUT spacetime
• Classical black hole scattering from a worldline quantum field theory
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• From Boundary Data to Bound States
• Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings
• The simplest massive S-matrix: from minimal coupling to Black Holes
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Kerr Black Holes as Elementary Particles
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• The self-dual sector of QCD amplitudes
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• On-shell heavy particle effective theories
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• Soft sub-leading divergences in Yang-Mills amplitudes
• Universality of ultra-relativistic gravitational scattering
• Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
• Type D Spacetimes and the Weyl Double Copy
• SUSY in the Sky with Gravitons
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• The Double Copy of Electric-Magnetic Duality
• Conformally Soft Theorem In Gravity
• Soft Photon and Graviton Theorems in Effective Field Theory
• A worldsheet for Kerr
• Separability and Killing Tensors in Kerr-Taub-NUT-de Sitter Metrics in Higher Dimensions
• BMS Symmetry of Celestial OPE
• S-duality and the Double Copy
• $(2,2)$ Scattering and the Celestial Torus
• Classical Solutions and their Double Copy in Split Signature
• Topology and Wilson lines: global aspects of the double copy
• Kleinian Geometry and the N=2 Superstring
• Conformal Block Expansion in Celestial CFT
• Ehlers as EM duality in the double copy
• On the Double Copy for Spinning Matter
• Celestial operator products from the worldsheet
• Monopoles, shockwaves and the classical double copy
• State-Operator Correspondence in Celestial Conformal Field Theory
• Holographic Chiral Algebra: Supersymmetry, Infinite Ward Identities, and EFTs
• Self-Dual Gravity
• Ambidextrous light transforms for celestial amplitudes
• Kerr-Newman stress-tensor from minimal coupling
• Descendants in celestial CFT and emergent multi-collinear factorization
• A Course in Amplitudes
• Soft Radiation from Scattering Amplitudes Revisited
• Post-Newtonian Waveforms from Spinning Scattering Amplitudes
• The Disjointed Thermodynamics of Rotating Black Holes With a NUT Twist
• Quantization Conditions and the Double Copy

Cited by in corpus (3)

• Top-down holography in an asymptotically flat spacetime
• Why is the Weyl double copy local in position space?
• Entanglement Rényi entropies in celestial holography