Abstract
We initiate a study of gravity focusing on generic null hypersurfaces, non-perturbatively in the Newton coupling. We present an off-shell account of the extended phase space of the theory, which includes the expected spin-2 data as well as spin-0, spin-1 and arbitrary matter degrees of freedom. We construct the charges and the corresponding kinematic Poisson brackets, employing a Beltrami parameterization of the spin-2 modes. We explicitly show that the constraint algebra closes, the details of which depend on the non-perturbative mixing between spin-0 and spin-2 modes. Finally we show that the spin zero sector encodes a notion of a clock, called dressing time, which is dynamical and conjugate to the constraint.
It is well-known that the null Raychaudhuri equation describes how the geometric data of a null hypersurface evolve in null time in response to gravitational radiation and external matter. Our analysis leads to three complementary viewpoints on this equation. First, it can be understood as a Carrollian stress tensor conservation equation. Second, we construct spin-0, spin-2 and matter stress tensors that act as generators of null time reparametrizations for each sector. This leads to the perspective that the null Raychaudhuri equation can be understood as imposing that the sum of CFT-like stress tensors vanishes. Third, we solve the Raychaudhuri constraint non-perturbatively. The solution relates the dressing time to the spin-2 and matter boost charge operators.
Finally we establish that the corner charge corresponding to the boost operator in the dressing time frame is monotonic. These results show that the notion of an observer can be thought of as emerging from the gravitational degrees of freedom themselves. We briefly mention that the construction offers new insights into focusing conjectures.
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Acknowledgments
This paper is the result of a focused research group held at BIRS, Banff, in November 2022, titled “Symmetries of Gravity at the Black Hole Horizon”. We are indebted to BIRS for the warm hospitality and for creating such a stimulating environment. We thank Ted Jacobson, Marc Klinger, Jerzy Kowalski-Glikman, and Aron Wall for discussions and feedback. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. LC is grateful to University of Milano Statale (and in particular Antonio Amariti) and University of Trento (and in particular Valter Moretti) for hospitality during the completion of this work. The work of RGL is partially supported by the U.S. Department of Energy under contract DE-SC0015655, and RGL thanks the Perimeter Institute for supporting collaborative visits.
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Ciambelli, L., Freidel, L. & Leigh, R.G. Null Raychaudhuri: canonical structure and the dressing time. J. High Energ. Phys. 2024, 166 (2024). https://doi.org/10.1007/JHEP01(2024)166
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DOI: https://doi.org/10.1007/JHEP01(2024)166