Numerical Methods for Finding Stationary Gravitational Solutions

Abstract

The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly-spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory-Laflamme zero modes of small rotating black holes in AdS${}_5\times S^5$. We also include several tools and tricks that have been useful throughout the literature.

Invited Topical Review for Classical and Quantum Gravity, 153 pages, 11 figures

References in corpus (86)

• Building an AdS/CFT superconductor
• Lectures on Holographic Superfluidity and Superconductivity
• Instability of the massive Klein-Gordon field on the Kerr spacetime
• Near-horizon symmetries of extremal black holes
• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Setting the boundary free in AdS/CFT
• Superradiant instabilities in astrophysical systems
• The 1965 Penrose singularity theorem
• Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship
• Uniqueness theorem for 5-dimensional black holes with two axial Killing fields
• Ergoregion instability of ultra-compact astrophysical objects
• Gravitational Perturbations of Higher Dimensional Rotating Black Holes: Tensor Perturbations
• The Kerr Metric
• Instabilities of Black Strings and Branes
• Head-on collisions of boson stars
• Bosenova collapse of axion cloud around a rotating black hole
• A numerical relativity approach to the initial value problem in asymptotically Anti-de Sitter spacetime for plasma thermalization - an ADM formulation
• An instability of higher-dimensional rotating black holes
• The thermoelectric properties of inhomogeneous holographic lattices
• A holographic view on physics out of equilibrium
• A classification of near-horizon geometries of extremal vacuum black holes
• Symmetries of Higher Dimensional Black Holes
• Complete Phase Diagrams for a Holographic Superconductor/Insulator System
• Renormalization group, secular term resummation and AdS (in)stability
• Gravitational instability of an extreme Kerr black hole
• Renormalization, averaging, conservation laws and AdS (in)stability
• Metal-insulator Transition by Holographic Charge Density Waves
• Rayleigh-Plateau and Gregory-Laflamme instabilities of black strings
• Ricci flow and black holes
• Linear mode stability of Kerr-Newman and its quasinormal modes
• Extremal vacuum black holes in higher dimensions
• The AdS/CFT Correspondence
• Towards a Novel no-hair Theorem for Black Holes
• Non-equilibrium Condensation Process in a Holographic Superconductor
• A scalar field condensation instability of rotating anti-de Sitter black holes
• Ultraspinning instability of rotating black holes
• An explicit harmonic code for black-hole evolution using excision
• Orthogonal black di-ring solution
• The numerical relativity breakthrough for binary black holes
• Electrically charged black hole with scalar hair
• The Quasinormal Modes of Weakly Charged Kerr-Newman Spacetimes
• Instability of Flat Space Enclosed in a Cavity
• A supersymmetric black lens
• Microscopic Theory of Black Hole Superradiance
• Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes
• Stability of Five-dimensional Myers-Perry Black Holes with Equal Angular Momenta
• Nonuniform black strings in various dimensions
• Global solutions of the Einstein-Maxwell equations in higher dimensions
• Holographic Checkerboards
• AdS flowing black funnels: Stationary AdS black holes with non-Killing horizons and heat transport in the dual CFT
• Black holes in a box: towards the numerical evolution of black holes in AdS
• Thermodynamics of the BMN matrix model at strong coupling
• Numerical study of superradiant instability for charged stringy black hole-mirror system
• Conserved quantities and dual turbulent cascades in Anti-de Sitter spacetime
• The Black Ring is Unstable
• Stability of AdS in Einstein Gauss Bonnet Gravity
• Stable non-uniform black strings below the critical dimension
• What drives AdS unstable?
• On the `Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions
• AdS/Ricci-flat correspondence and the Gregory-Laflamme instability
• Holographic Relaxation of Finite Size Isolated Quantum Systems
• A Simple Holographic Insulator
• A Hidden Symmetry of AdS Resonances
• The missing top of AdS resonance structure
• Collapse and Revival in Holographic Quenches
• Flowing Funnels: Heat sources for field theories and the AdS_3 dual of CFT_2 Hawking radiation
• Onset of superradiant instabilities in the composed Kerr-black-hole-mirror bomb
• Testing the nonlinear stability of Kerr-Newman black holes
• Classical Yang-Mills black hole hair in anti-de Sitter space
• Negative modes and the thermodynamics of Reissner-Nordström black holes
• On the nonlinear instability of confined geometries
• Minimally packed phases in holography
• On the stability of AdS black strings
• Hovering Black Holes from Charged Defects
• Superradiant instability of D-dimensional Reissner-Nordström black hole mirror system
• AdS (In)stability: Lessons From The Scalar Field
• Bumpy black holes
• Holographic quantum criticality from multi-trace deformations
• Multi-black hole configurations on the cylinder
• Analytic Evidence for Continuous Self Similarity of the Critical Merger Solution
• Shock waves in strongly coupled plasmas
• Black Droplets
• Cold planar horizons are floppy
• The Schwarzschild-Black String AdS Soliton: Instability and Holographic Heat Transport
• Localized Plasma Balls
• Non-Abelian fields in AdS${}_4$ spacetime: axially symmetric, composite configurations

Cited by in corpus (120)

• Spontaneous scalarisation of charged black holes
• Constraining the mass of dark photons and axion-like particles through black-hole superradiance
• Entanglement islands in higher dimensions
• The Spectra of Gravitational Atoms
• Testing the Weak Gravity -- Cosmic Censorship Connection
• Boson Stars and Oscillatons: A Review
• Strong cosmic censorship in de Sitter space
• Island in Charged Black Holes
• Evidence for an Electrifying Violation of Cosmic Censorship
• Holographic Axion Model: a simple gravitational tool for quantum matter
• AdS Euclidean wormholes
• Charged Fermions and Strong Cosmic Censorship
• Perturbing the perturbed: Stability of quasinormal modes in presence of a positive cosmological constant
• Further evidence for the weak gravity -- cosmic censorship connection
• Constraints on Kerr-Newman black holes from merger-ringdown gravitational-wave observations
• Holographic quenches and anomalous transport
• Stability of the Cauchy horizon in accelerating black-hole spacetimes
• Hairy black holes and the endpoint of AdS${}_4$ charged superradiance
• Colloquium: Hydrodynamics and holography of charge density wave phases
• Eigenvalue repulsions in the quasinormal spectra of the Kerr-Newman black hole
• Scalar Hairy Black Holes in Four Dimensions are Unstable
• Critical phenomena in dynamical scalarization of charged black hole
• Superradiant Instability of Near Extremal and Extremal Four-Dimensional Charged Hairy Black Hole in anti-de Sitter Spacetime
• Strong Cosmic Censorship in Horndeski Theory
• Almost all extremal black holes in AdS are singular
• Eigenvalue repulsions and quasinormal mode spectra of Kerr-Newman: an extended study
• Localised $\mathbf{Ad}{\mathbf{S}}_5\times {\mathbf{S}}^5$ Black Holes
• Reflected Entropy in Double Holography
• Scalar quasinormal modes of Kerr-AdS${}_5$
• Spectral method for metric perturbations of black holes: Kerr background case in general relativity
• Black hole superradiant instability for massive spin-2 fields
• Evidence for the existence of a novel class of supersymmetric black holes with AdS${}_5\times$S${}^5$ asymptotics
• Collapse and Nonlinear Instability of AdS with Angular Momenta
• A new approach and code for spinning black holes in modified gravity
• Crossing a large-$N$ phase transition at finite volume
• Blandford--Znajek monopole expansion revisited: novel non-analytic contributions to the power emission
• Localised and nonuniform thermal states of super-Yang-Mills on a circle
• Sudden breakdown of effective field theory near cool Kerr-Newman black holes
• Rotating Hairy Black Holes in AdS${}_5\times$S${}^5$
• Plausible scenario for a generic violation of the weak cosmic censorship conjecture in asymptotically flat four dimensions
• On Thermodynamics of AdS Black Holes with Scalar Hair
• Static Einstein-Maxwell black holes with no spatial isometries in AdS space
• Bernstein spectral method for quasinormal modes of a generic black hole spacetime and application to instability of dilaton-de Sitter solution
• Evading no-hair theorems: hairy black holes in a Minkowski box
• Rotating multistate boson stars
• Massive vector fields in Kerr--Newman and Kerr--Sen black hole spacetimes
• Einstein-Gauss-Bonnet Black Rings at Large $D$
• Spinning Black Holes with Axion Hair
• Critical behavior of the black hole / black string transition
• Rotating black holes in semiclassical gravity
• Primordial Black Hole Formation during a Strongly Coupled Crossover
• Holographic dual of hot Polchinski-Strassler quark-gluon plasma
• Stability of the microcanonical ensemble in Euclidean Quantum Gravity
• Horndeski stars
• Thermodynamic origin of the Landau instability of superfluids
• A deformed IR: a new IR fixed point for four-dimensional holographic theories
• Superradiant instability of black resonators and geons
• Interior Quasinormal Modes and Strong Cosmic Censorship
• New phases of $\mathcal{N}=4$ SYM at finite chemical potential
• Deforming black holes in AdS
• Lattice Black Branes: Sphere Packing in General Relativity
• Phases of Holographic Hawking Radiation on spatially compact spacetimes
• Phase Transitions and Stability of Eguchi-Hanson-AdS Solitons
• Strong Cosmic Censorship and Eigenvalue Repulsions for rotating de Sitter black holes in higher-dimensions
• The origin of the Reissner-Nordström de Sitter instability
• Gregory-Laflamme encounters Superradiance
• AdS nonlinear instability: breaking spherical and axial symmetries
• Mass-deformed M2 branes in Stenzel space
• Self-interacting multistate boson stars
• Shadows and Properties of Spin-Induced Scalarized Black Holes with and without a Ricci Coupling
• Polarised Black Holes in ABJM
• Weak cosmic censorship with self-interacting scalar and bound on charge to mass ratio
• Extremal black holes that are not extremal: maximal warm holes
• Zero sound and higher-form symmetries in compressible holographic phases
• Attempts at vacuum counterexamples to cosmic censorship in AdS
• Disordered quantum critical fixed points from holography
• Horndeski fermion-boson stars
• Renormalization group in quantum critical theories with Harris-marginal disorder
• Stirring a black hole
• Schwarzschild quasi-normal modes of non-minimally coupled vector fields
• Rotating black holes in Randall-Sundrum II braneworlds
• Overcoming obstacles in nonequilibrium holography
• Notes on ten-dimensional localized black holes and deconfined states in two-dimensional SYM
• Quasinormal modes of slowly rotating Kerr-Newman black holes using the double series method
• The holographic non-abelian vortex
• Black holes Entangled by Radiation
• Conformally Coupled Scalar in Rotating Black Hole Spacetimes
• Holographic Superfluid Solitons with Backreaction
• Hunting for fermionic instabilities in charged AdS black holes
• The holographic vortex lattice using the circular cell method
• Superradiance and black resonator strings encounter helical black strings
• Phase diagram of the charged black hole bomb system
• Black holes and nilmanifolds: quasinormal modes as the fingerprints of extra dimensions?
• Spontaneous Deformation of an AdS Spherical Black Hole
• Instability in charged Gauss-Bonnet-de Sitter black holes
• Extraction of energy from a black hole in Einstein-Maxwell-scalar theory
• Entanglement inside a black hole before the Page time
• Overspinning a rotating black hole in semiclassical gravity with type-A trace anomaly
• Boson stars and solitons confined in a Minkowski box
• Purely metric Horndeski theories and spontaneous curvaturization of black holes
• To go or not to go with the flow: Hawking radiation at strong coupling
• A Tale of Two Saddles
• Hawking radiation, local temperatures, and nonequilibrium thermodynamics of the black holes with non-killing horizon
• Rotating scalarized black holes: the role of the coupling
• Critical lumpy black holes in AdS${}_p\times S^q$
• EFT Corrections to Charged Black Hole Quasinormal Modes
• Black Tunnels and Hammocks
• Deforming black holes with even multipolar differential rotation boundary
• Lattice Black Branes at Large $D$
• Holographic confinement in inhomogenous backgrounds
• Adiabatic corrections to holographic entanglement in thermofield doubles and confining ground states
• Proto-neutron star oscillations including accretion flows
• Deforming black holes with odd multipolar differential rotation boundary
• Charged Static AdS Black Hole Binaries
• Einstein-scalar field solutions in AdS spacetime: clouds, boundary conditions, and scalar multipoles
• Testing the effective action approach to bubble nucleation in holography
• AInstein: Numerical Einstein Metrics via Machine Learning
• The Low Energy Limit of BFSS Quantum Mechanics
• The Canonical Ensemble Reloaded: The Complex-Stability of Euclidean quantum gravity for Black Holes in a Box
• Deforming charged black holes with dipolar differential rotation boundary