A Carroll-covariant energy-momentum-news complex at future null infinity yields Ward identities that generalise the Bondi loss equations, with an anomalous Carroll boost.
Variational Principle for Gravity with Null and Non-null boundaries: A Unified Boundary Counter-term
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abstract
It is common knowledge that the Einstein-Hilbert action does not furnish a well-posed variational principle. The usual solution to this problem is to add an extra boundary term to the action, called a counter-term, so that the variational principle becomes well-posed. When the boundary is spacelike or timelike, the Gibbons-Hawking-York counter-term is the most widely used. For null boundaries, we had proposed a counter-term in a previous paper. In this paper, we extend the previous analysis and propose a counter-term that can be used to eliminate variations of the "off-the-surface" derivatives of the metric on any boundary, regardless of its spacelike, timelike or null nature.
years
2026 3representative citing papers
An entropy functional yields the Brown-York tensor via conjugate momentum projection, unifying null and timelike hypersurfaces and reproducing equations in scalar-tensor gravity.
A covariant virtual work and d'Alembert-Lagrange formulation is introduced for general relativity, recovering the Einstein equations from vanishing virtual work and the cosmological constant from an isoperimetric admissibility constraint.
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The Energy-Momentum-News Complex near Future Null Infinity
A Carroll-covariant energy-momentum-news complex at future null infinity yields Ward identities that generalise the Bondi loss equations, with an anomalous Carroll boost.
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Entropic route to Brown-York tensor: A unified framework for null and timelike hypersurfaces
An entropy functional yields the Brown-York tensor via conjugate momentum projection, unifying null and timelike hypersurfaces and reproducing equations in scalar-tensor gravity.
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Covariant virtual work and the d'Alembert-Lagrange formulation of general relativity
A covariant virtual work and d'Alembert-Lagrange formulation is introduced for general relativity, recovering the Einstein equations from vanishing virtual work and the cosmological constant from an isoperimetric admissibility constraint.