• 1. Yes, by construction, numerical relativity solves Einstein's equations as an initial value problem, restricting one selves to globally hyperbolic spacetimes. The Strong Cosmic Censorship Hypothesis asserts that all of spacetime outside black holes is globally hyperbolic.
• 4. For example, Template Banks for Binary black hole searches with Numerical Relativity waveforms.

Only partial answers / attempts at answers, hopefully to get a more extensive discussion started.

• 1. Yes, by construction, numerical relativity solves Einstein's equations as an initial value problem, restricting one selves to globally hyperbolic spacetimes. The Strong Cosmic Censorship Hypothesis asserts that all of spacetime outside black holes is globally hyperbolic.
• 2. Coordinate conditions are fixed on an ingoing null hypersurface, and then propagated outwards. This is a complication for the identification of gravitational waves, which can only be unambiguously definied at future null-infinity, but that asymptotic condition is not imposed on the numerical calculation.
• 4. For example, Template Banks for Binary black hole searches with Numerical Relativity waveforms.

1. Yes, by construction, numerical relativity solves Einstein's equations as an initial value problem, restricting one selves to globally hyperbolic spacetimes. The Strong Cosmic Censorship Hypothesis asserts that all of spacetime outside black holes is globally hyperbolic.

2. For example, Template Banks for Binary black hole searches with Numerical Relativity waveforms,

• 1. Yes, by construction, numerical relativity solves Einstein's equations as an initial value problem, restricting one selves to globally hyperbolic spacetimes. The Strong Cosmic Censorship Hypothesis asserts that all of spacetime outside black holes is globally hyperbolic.
• 4. For example, Template Banks for Binary black hole searches with Numerical Relativity waveforms.