Open Access

Identification between the bulk and boundary conserved quantities

Gerui Chen ^1,2,*, Zien Gao^2,3,†, Xin Lan^2,3,‡, Jieqiang Wu^4,5,§, and Hongbao Zhang ^2,3,∥

¹College of Electronic Information and Physics, Central South University of Forestry and Technology, Changsha 410004, China
²School of Physics and Astronomy, Beijing Normal University, Beijing 100875, China
³Key Laboratory of Multiscale Spin Physics, Ministry of Education, Beijing Normal University, Beijing 100875, China
⁴CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
⁵School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

^*Contact author: t20152277@csuft.edu.cn
^†Contact author: zegao@mail.bnu.edu.cn
^‡Contact author: xinlan@mail.bnu.edu.cn
^§Contact author: jieqiangwu@itp.ac.cn
^∥Contact author: hongbaozhang@bnu.edu.cn

Phys. Rev. D 113, 084024 – Published 13 April, 2026

DOI: https://doi.org/10.1103/ln51-5v1j

Abstract

By using Wald formalism, we show that the identification between the bulk and boundary conserved quantities induced by the perturbation of generic nonelectromagnetic matter field holds not only on top of the asymptotically flat stationary spacetimes but also on top of the asymptotically AdS stationary ones. We further show that such an identification reduces to the familiar form for the test point particle by viewing it as the limiting case of general matter.

Physics Subject Headings (PhySH)

General relativity

Article Text

References (11)

S. Gao and R. M. Wald, Phys. Rev. D 64, 084020 (2001).
J. V. Rocha and V. Cardoso, Phys. Rev. D 83, 104037 (2011).
J. V. Rocha and R. Santarelli, Phys. Rev. D 89, 064065 (2014).
J. V. Rocha, R. Santarelli, and T. Delsate, Phys. Rev. D 89, 104006 (2014).
R. M. Wald, General Relativity (University of Chicago Press, Chicago, 1984).
R. M. Wald, Phys. Rev. D 48, R3427 (1993).
V. Iyer and R. M. Wald, Phys. Rev. D 50, 846 (1994).
J. Sorce and R. M. Wald, Phys. Rev. D 96, 104014 (2017).
S. Hollands, A. Ishibashi, and D. Marolf, Classical Quantum Gravity 22, 2881 (2005).
R. M. Wald and A. Zoupas, Phys. Rev. D 61, 084027 (2000).
R. M. Wald, Ann. Phys. (N.Y.) 82, 548 (1974).

Phys. Rev. D 113, 084024– Published 13 April, 2026

Vol. 113, Iss. 8 — 15 April 2026

Received 20 December 2025
Accepted 25 March 2026

DOI: https://doi.org/10.1103/ln51-5v1j

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physical Review D

Reuse & Permissions

Export citation

Export citation

Identification between the bulk and boundary conserved quantities

Abstract

Physics Subject Headings (PhySH)

Article Text

References (11)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation