Dynamical Black Holes: Approach to the Final State

Abstract

Since black holes can be formed through widely varying processes, the horizon structure is highly complicated in the dynamical phase. Nonetheless, as numerical simulations show, the final state appears to be universal, well described by the Kerr geometry. How are all these large and widely varying deviations from the Kerr horizon washed out? To investigate this issue, we introduce a well-suited notion of horizon multipole moments and equations governing their dynamics, thereby providing a coordinate and slicing independent framework to investigate the approach to equilibrium. In particular, our flux formulas for multipoles can be used as analytical checks on numerical simulations and, in turn, the simulations could be used to fathom possible universalities in the way black holes approach their final equilibrium.

27 pages, 1 figure. Thanks to the referee's suggestion, two remarks at the end of section III.B were added to clarify certain issues addressed to the numerical relativity community. They in turn led to several new references

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Cited by in corpus (22)

• The SXS Collaboration catalog of binary black hole simulations
• Quasinormal modes and their overtones at the common horizon in a binary black hole merger
• Dynamics of marginally trapped surfaces in a binary black hole merger: Growth and approach to equilibrium
• Nearly extremal apparent horizons in simulations of merging black holes
• Non-linear black hole dynamics and Carrollian fluids
• News from horizons in binary black hole mergers
• Charges and Fluxes on (Perturbed) Non-expanding Horizons
• The interior of a binary black hole merger
• Non-Expanding horizons: Multipoles and the Symmetry Group
• Multipole moments on the common horizon in a binary-black-hole simulation
• Quasi-Local Black Hole Horizons: Recent Advances
• Black Hole Spin Axis in Numerical Relativity
• Inside the Final Black Hole: Puncture and Trapped Surface Dynamics
• Tidal deformations of spinning black holes in Bowen-York initial data
• Geometric horizons in binary black hole mergers
• On Super-Translation transition between Quasi-local Black holes
• Thermodynamics of Black Holes, far from Equilibrium
• Magnetized dynamical black holes
• Dynamical horizons and Super-Translation transitions of the horizon
• Dynamical Horizon Segments and Spacetime Isometries
• Dynamical axisymmetric compact objects in General Relativity
• Curvature Invariants and the Geometric Horizon Conjecture in a Binary Black Hole Merger