Approximate analytical description of apparent horizons for initial data with momentum and spin

Abstract

We construct analytical initial data for a slowly moving and rotating black hole for generic orientations of the linear momentum and the spin. We solve the Hamiltonian constraint approximately and work out the properties of the apparent horizon and show the dependence of its shape on the angle between the spin and the linear momentum. In particular a dimple, whose location depends on the mentioned angle, arises on the 2-sphere geometry of the apparent horizon. We exclusively work in the case of conformally flat initial metrics.

arXiv comment11 pages, 1 figure, v2 matches the published form

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• Observation of Gravitational Waves from a Binary Black Hole Merger
• The Dynamics of General Relativity
• A simple construction of initial data for multiple black holes
• Evolving the Bowen-York initial data for spinning black holes
• Approximate initial data for binary black holes
• Non-stationary Energy in General Relativity
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Cited by in corpus (3)

• Basics of Apparent Horizons in Black Hole Physics
• Perturbative solution of the Einstein Constraints with Spin and Momentum Far Away From a Binary Source in the Bowen-York formalism
• Perturbative Analytical Construction of Bowen-York Initial Data for Binary Black Holes up to Third Order in Spin and Linear Momentum