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⠄⠄⢸⣇⠻⣿⣿⣿⣧⣀⢀⣠⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⠄
⠄⢀⢸⣿⣷⣤⣤⣤⣬⣙⣛⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡍⠄⠄⢀⣤⣄⠉⠋⣰
⠄⣼⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢇⣿⣿⡷⠶⠶⢿⣿⣿⠇⢀⣤
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣶⣥⣴⣿⡗
⢀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄
⢸⣿⣦⣌⣛⣻⣿⣿⣧⠙⠛⠛⡭⠅⠒⠦⠭⣭⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠄
⠘⣿⣿⣿⣿⣿⣿⣿⣿⡆⠄⠄⠄⠄⠄⠄⠄⠄⠹⠈⢋⣽⣿⣿⣿⣿⣵⣾⠃⠄
⠄⠘⣿⣿⣿⣿⣿⣿⣿⣿⠄⣴⣿⣶⣄⠄⣴⣶⠄⢀⣾⣿⣿⣿⣿⣿⣿⠃⠄
⠄⠄⠈⠻⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⠄⣿⣿⡀⣾⣿⣿⣿⣿⣛⠛⠁⠄⠄
⠄⠄⠄⠄⠈⠛⢿⣿⣿⣿⠁⠞⢿⣿⣿⡄⢿⣿⡇⣸⣿⣿⠿⠛⠁⠄⠄
🌸🌸🌸🌸🌸🌸🌸🌸______🌸🌸🌸🌸🌸🌸🌸
🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸
🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸
🌸🌸 𝓕𝓻𝓲𝓮𝓷𝓭𝓵𝔂 𝓰𝓾𝔂=)🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸
_ 🌸𝓦𝓮 𝓬𝓪𝓷 𝓫𝓮 𝓯𝓻𝓲𝓮𝓷𝓭𝓼 𝓯𝓸𝓻 𝓯𝓾𝓽𝓾𝓻𝓮 𝓰𝓪𝓶𝓮𝓼^_^🌸
__🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸
____🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸
_______🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸
_________🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸
___________🌸🌸🌸🌸🌸🌸🌸🌸
____________🌸🌸🌸🌸🌸🌸
_____________🌸🌸🌸🌸
_____________🌸🌸
▄███▀░◐░░░▌░░THE PROFILE OF░░░░
░░░░▌░░░░░▐░░░SOMEONE YOU░░░░
░░░░▐░░░░░▐░░░WANT TO ANALLY░░
░░░░▌░░░░░▐▄▄░░░░░░DEVASTATE░░
░░░░▌░░░░▄▀▒▒▀▀▀▀▄░░░░░░░░░░░
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Lemme Smash
▄███▀░◐░░░▌░░THE PROFILE OF░░░░
░░░░▌░░░░░▐░░░SOMEONE YOU░░░░
░░░░▐░░░░░▐░░░WANT TO ANALLY░░
░░░░▌░░░░░▐▄▄░░░░░░DEVASTATE░░
░░░░▌░░░░▄▀▒▒▀▀▀▀▄░░░░░░░░░░░
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Lemme Smash
in light of the possibility of observing such mergers with ground- and space-based gravitational
wave detectors. Much work has gone into developing perturbative, post-Newtonian, and numerical
methods to obtain the spacetime metric of a binary black hole system during the inspiral, plunge,
and ringdown phases of its evolution.
One feature of the merger worth studying is the geometry of the event horizon. The event horizon
is a null surface which serves as a \surface of last return". Any point outside the event horizon is
causally connected to future null in nity, while any point inside is not. Put in plain English, once
you enter the event horizon, you cannot escape.
As Figure 1 demonstrates, the horizon is a three-dimensional surface in a four-dimensional space-
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