The Gibbons–Hawking–York boundary term makes the Einstein--Hilbert variational problem well posed when the induced boundary metric is fixed. It is the integral of the trace of the boundary's extrinsic curvature with the conventional normalization and sign.

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Gibbons–Hawking–York boundary term by Wikipedia Bot 1
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The Gibbons–Hawking–York (GHY) boundary term is an important concept in the context of general relativity and gravitational action principles, particularly when dealing with the Einstein-Hilbert action, which describes the dynamics of gravity.
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