The Kerr-Schild Double Copy in Lifshitz Spacetime

Abstract

The Kerr-Schild double copy is a map between exact solutions of general relativity and Maxwell's theory, where the nonlinear nature of general relativity is circumvented by considering solutions in the Kerr-Schild form. In this paper, we give a general formulation, where no simplifying assumption about the background metric is made, and show that the gauge theory source is affected by a curvature term that characterizes the deviation of the background spacetime from a constant curvature spacetime. We demonstrate this effect explicitly by studying gravitational solutions with non-zero cosmological constant. We show that, when the background is flat, the constant charge density filling all space in the gauge theory that has been observed in previous works is a consequence of this curvature term. As an example of a solution with a curved background, we study the Lifshitz black hole with two different matter couplings. The curvature of the background, i.e., the Lifshitz spacetime, again yields a constant charge density; however, unlike the previous examples, it is canceled by the contribution from the matter fields. For one of the matter couplings, there remains no additional non-localized source term, providing an example for a non-vacuum gravity solution corresponding to a vacuum gauge theory solution in arbitrary dimensions.

arXiv comment20 pages + references, a reference regarding the KS form of the Lifshitz black holes added

References in corpus (65)

• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• 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
• Gravity as the Square of Gauge Theory
• Black holes and the double copy
• Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
• Radiation and the classical double copy for color charges
• The classical double copy for Taub-NUT spacetime
• From Boundary Data to Bound States
• Observables and amplitudes for spinning particles and black holes
• Kerr Black Holes as Elementary Particles
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• The Kerr-Schild double copy in curved spacetime
• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• Yang-Mills origin of gravitational symmetries
• Gravitational Radiation from Color-Kinematics Duality
• Type D Spacetimes and the Weyl Double Copy
• Spinning particles, axion radiation, and the classical double copy
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• Bound states and the classical double copy
• Gravity as Gauge Theory Squared: A Ghost Story
• A Twistorial Foundation for the Classical Double Copy
• The Double Copy of Electric-Magnetic Duality
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• Exact solutions for the biadjoint scalar field
• Kerr-Schild Double Field Theory and Classical Double Copy
• On Charged Lifshitz Black Holes
• S-duality and the Double Copy
• The Weyl Double Copy for Gravitational Waves
• Screw-symmetric gravitational waves: a double copy of the vortex
• A double copy for $\mathcal{N}=2$ supergravity: a linearised tale told on-shell
• Topology and Wilson lines: global aspects of the double copy
• Double Copy for Celestial Amplitudes
• The classical double copy of non-singular black holes
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• The Classical Double Copy of a Point Charge
• Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO
• The convolutional double copy: a case study with a point
• Extended solutions for the biadjoint scalar field
• Twin Supergravities from Yang-Mills Squared
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Ehlers as EM duality in the double copy
• Weyl doubling
• The Newman-Penrose Map and the Classical Double Copy
• Kerr-Newman from Minimal Coupling
• Kerr-Schild Double Copy and Complex Worldlines
• Monopoles, shockwaves and the classical double copy
• Gravitational shock waves and scattering amplitudes
• Heterotic Kerr-Schild Double Field Theory and Classical Double Copy
• Strings, extended objects, and the classical double copy
• New heavenly double copies
• Gravity as the square of Yang-Mills?
• $D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories
• Classical double copy from Color Kinematics duality: A proof in the soft limit
• Spinning BTZ Black Hole versus Kerr Black Hole : A Closer Look
• Radiation of scalar modes and the classical double copy
• More on the Classical Double Copy in Three Spacetime Dimensions
• Spinor-helicity and the algebraic classification of higher-dimensional spacetimes
• Classical Gravitational Self-Energy from Double Copy