Null infinity as an open Hamiltonian system
Abstract When a system emits gravitational radiation, the Bondi mass decreases. If the Bondi energy is Hamiltonian, it can thus only be a time-dependent Hamiltonian. In this paper, we show that the Bondi energy can be understood as a time-dependent Hamiltonian on the covariant phase space. Our deriv...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-04-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP04(2021)095 |
| _version_ | 1819199997865885696 |
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| author | Wolfgang Wieland |
| author_facet | Wolfgang Wieland |
| author_sort | Wolfgang Wieland |
| collection | DOAJ |
| description | Abstract When a system emits gravitational radiation, the Bondi mass decreases. If the Bondi energy is Hamiltonian, it can thus only be a time-dependent Hamiltonian. In this paper, we show that the Bondi energy can be understood as a time-dependent Hamiltonian on the covariant phase space. Our derivation starts from the Hamiltonian formulation in domains with boundaries that are null. We introduce the most general boundary conditions on a generic such null boundary, and compute quasi-local charges for boosts, energy and angular momentum. Initially, these domains are at finite distance, such that there is a natural IR regulator. To remove the IR regulator, we introduce a double null foliation together with an adapted Newman-Penrose null tetrad. Both null directions are surface orthogonal. We study the falloff conditions for such specific null foliations and take the limit to null infinity. At null infinity, we recover the Bondi mass and the usual covariant phase space for the two radiative modes at the full non-perturbative level. Apart from technical results, the framework gives two important physical insights. First of all, it explains the physical significance of the corner term that is added in the Wald-Zoupas framework to render the quasi-conserved charges integrable. The term to be added is simply the derivative of the Hamiltonian with respect to the background fields that drive the time-dependence of the Hamiltonian. Secondly, we propose a new interpretation of the Bondi mass as the thermodynamical free energy of gravitational edge modes at future null infinity. The Bondi mass law is then simply the statement that the free energy always decreases on its way towards thermal equilibrium. |
| first_indexed | 2024-12-23T03:25:14Z |
| format | Article |
| id | doaj.art-87451ec622f24ef49efcce5d5cb0bb67 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-23T03:25:14Z |
| publishDate | 2021-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-87451ec622f24ef49efcce5d5cb0bb672022-12-21T18:01:52ZengSpringerOpenJournal of High Energy Physics1029-84792021-04-012021415310.1007/JHEP04(2021)095Null infinity as an open Hamiltonian systemWolfgang Wieland0Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of SciencesAbstract When a system emits gravitational radiation, the Bondi mass decreases. If the Bondi energy is Hamiltonian, it can thus only be a time-dependent Hamiltonian. In this paper, we show that the Bondi energy can be understood as a time-dependent Hamiltonian on the covariant phase space. Our derivation starts from the Hamiltonian formulation in domains with boundaries that are null. We introduce the most general boundary conditions on a generic such null boundary, and compute quasi-local charges for boosts, energy and angular momentum. Initially, these domains are at finite distance, such that there is a natural IR regulator. To remove the IR regulator, we introduce a double null foliation together with an adapted Newman-Penrose null tetrad. Both null directions are surface orthogonal. We study the falloff conditions for such specific null foliations and take the limit to null infinity. At null infinity, we recover the Bondi mass and the usual covariant phase space for the two radiative modes at the full non-perturbative level. Apart from technical results, the framework gives two important physical insights. First of all, it explains the physical significance of the corner term that is added in the Wald-Zoupas framework to render the quasi-conserved charges integrable. The term to be added is simply the derivative of the Hamiltonian with respect to the background fields that drive the time-dependence of the Hamiltonian. Secondly, we propose a new interpretation of the Bondi mass as the thermodynamical free energy of gravitational edge modes at future null infinity. The Bondi mass law is then simply the statement that the free energy always decreases on its way towards thermal equilibrium.https://doi.org/10.1007/JHEP04(2021)095Classical Theories of GravityModels of Quantum Gravity |
| spellingShingle | Wolfgang Wieland Null infinity as an open Hamiltonian system Journal of High Energy Physics Classical Theories of Gravity Models of Quantum Gravity |
| title | Null infinity as an open Hamiltonian system |
| title_full | Null infinity as an open Hamiltonian system |
| title_fullStr | Null infinity as an open Hamiltonian system |
| title_full_unstemmed | Null infinity as an open Hamiltonian system |
| title_short | Null infinity as an open Hamiltonian system |
| title_sort | null infinity as an open hamiltonian system |
| topic | Classical Theories of Gravity Models of Quantum Gravity |
| url | https://doi.org/10.1007/JHEP04(2021)095 |
| work_keys_str_mv | AT wolfgangwieland nullinfinityasanopenhamiltoniansystem |