Boundary conditions for stationary black holes ; Application to Kerr, Martinez-Troncoso-Zanelli and hairy black holes

Abstract

This work proposes a set of equations that can be used to numerically compute spacetimes containing a stationary black hole. The formalism is based on the 3+1 decomposition of General Relativity with maximal slicing and spatial harmonic gauge. The presence of the black hole is enforced using the notion of apparent horizon in equilibrium. This setting leads to the main result of this paper: a set of boundary conditions describing the horizon and that must be used when solving the 3+1 equations. Those conditions lead to a choice of coordinates that is regular even on the horizon itself. The whole procedure is validated with three different examples chosen to illustrate the great versatility of the method. First, the single rotating black holes are recovered up to very high values of the Kerr parameter. Second, non-rotating black holes coupled to a real scalar field, in the presence of a negative cosmological constant (the so-called MTZ black holes), are obtained. Last, black holes with complex scalar hairs are computed. Eventually, prospects for future work, in particular in contexts where stationarity is only approximate, are discussed.

References in corpus (26)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Science Case for the Einstein Telescope
• Tests of General Relativity with the Binary Black Hole Signals from the LIGO-Virgo Catalog GWTC-1
• Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog
• Kerr black holes with scalar hair
• Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
• Stationary Black Holes: Uniqueness and Beyond
• A 3+1 perspective on null hypersurfaces and isolated horizons
• Exact black hole solution with a minimally coupled scalar field
• A new approach to static numerical relativity, and its application to Kaluza-Klein black holes
• Binary black holes in circular orbits. II. Numerical methods and first results
• Binary black holes in circular orbits. I. A global spacetime approach
• Ricci solitons, Ricci flow, and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua
• Circular orbits and spin in black-hole initial data
• Kadath: a spectral solver for theoretical physics
• A new public code for initial data of unequal-mass, spinning compact-object binaries
• A numerical approach to finding general stationary vacuum black holes
• Hairy rotating black holes in cubic Galileon theory
• Gravitational geons in asymptotically anti-de Sitter spacetimes
• Self-gravitating scalar breathers with negative cosmological constant
• On the existence of stationary Ricci solitons
• Scalar field breathers on anti-de Sitter background
• Obstructions towards a generalization of no-hair theorems: I. Scalar clouds around Kerr black holes
• New code for equilibriums and quasiequilibrium initial data of compact objects. II. Convergence tests and comparisons of binary black hole initial data
• Excised black hole spacetimes: quasi-local horizon formalism applied to the Kerr example

Cited by in corpus (3)

• Self-Interacting Gravitational Atoms in the Strong-Gravity Regime
• High precision numerical sequences of rotating hairy black holes
• Fully consistent rotating black holes in the cubic Galileon theory