An action for and hydrodynamics from the improved Large D membrane
Abstract It has recently been demonstrated that black hole dynamics at large D is dual to the motion of a probe membrane propagating in the background of a spacetime that solves Einstein’s equations. The equation of motion of this membrane is determined by the membrane stress tensor. In this paper w...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP09(2018)137 |
| _version_ | 1811342649516359680 |
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| author | Yogesh Dandekar Suman Kundu Subhajit Mazumdar Shiraz Minwalla Amiya Mishra Arunabha Saha |
| author_facet | Yogesh Dandekar Suman Kundu Subhajit Mazumdar Shiraz Minwalla Amiya Mishra Arunabha Saha |
| author_sort | Yogesh Dandekar |
| collection | DOAJ |
| description | Abstract It has recently been demonstrated that black hole dynamics at large D is dual to the motion of a probe membrane propagating in the background of a spacetime that solves Einstein’s equations. The equation of motion of this membrane is determined by the membrane stress tensor. In this paper we ‘improve’ the membrane stress tensor derived in earlier work to ensure that it defines consistent probe membrane dynamics even at finite D while reducing to previous results at large D. Our improved stress tensor is the sum of a Brown York term and a fluid energy momentum tensor. The fluid has an unusual equation of state; its pressure is nontrivial but its energy density vanishes. We demonstrate that all stationary solutions of our membrane equations are produced by the extremization of an action functional of the membrane shape. Our action is an offshell generalization of the membrane’s thermodynamical partition function. We demonstrate that the thermodynamics of static spherical membranes in flat space and global AdS space exactly reproduces the thermodynamics of the dual Schwarzschild black holes even at finite D. We study the long wavelength dynamics of membranes in AdS space that are everywhere approximately ‘parallel’ to the boundary, and demonstrate that the boundary ‘shadow’ of this membrane dynamics is boundary hydrodynamics with a definite constitutive relation. We determine the explicit form of shadow dual boundary stress tensor upto second order in derivatives of the boundary temperature and velocity, and verify that this stress tensor agrees exactly with the fluid gravity stress tensor to first order in derivatives, but deviates from the later at second order and finite D. |
| first_indexed | 2024-04-13T19:14:31Z |
| format | Article |
| id | doaj.art-50a645d098f64106a2008cc0063b71b7 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-13T19:14:31Z |
| publishDate | 2018-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-50a645d098f64106a2008cc0063b71b72022-12-22T02:33:43ZengSpringerOpenJournal of High Energy Physics1029-84792018-09-012018915910.1007/JHEP09(2018)137An action for and hydrodynamics from the improved Large D membraneYogesh Dandekar0Suman Kundu1Subhajit Mazumdar2Shiraz Minwalla3Amiya Mishra4Arunabha Saha5Department of Theoretical Physics, Tata Institute of Fundamental ResearchDepartment of Theoretical Physics, Tata Institute of Fundamental ResearchDepartment of Theoretical Physics, Tata Institute of Fundamental ResearchDepartment of Theoretical Physics, Tata Institute of Fundamental ResearchDepartment of Theoretical Physics, Tata Institute of Fundamental ResearchDepartment of Theoretical Physics, Tata Institute of Fundamental ResearchAbstract It has recently been demonstrated that black hole dynamics at large D is dual to the motion of a probe membrane propagating in the background of a spacetime that solves Einstein’s equations. The equation of motion of this membrane is determined by the membrane stress tensor. In this paper we ‘improve’ the membrane stress tensor derived in earlier work to ensure that it defines consistent probe membrane dynamics even at finite D while reducing to previous results at large D. Our improved stress tensor is the sum of a Brown York term and a fluid energy momentum tensor. The fluid has an unusual equation of state; its pressure is nontrivial but its energy density vanishes. We demonstrate that all stationary solutions of our membrane equations are produced by the extremization of an action functional of the membrane shape. Our action is an offshell generalization of the membrane’s thermodynamical partition function. We demonstrate that the thermodynamics of static spherical membranes in flat space and global AdS space exactly reproduces the thermodynamics of the dual Schwarzschild black holes even at finite D. We study the long wavelength dynamics of membranes in AdS space that are everywhere approximately ‘parallel’ to the boundary, and demonstrate that the boundary ‘shadow’ of this membrane dynamics is boundary hydrodynamics with a definite constitutive relation. We determine the explicit form of shadow dual boundary stress tensor upto second order in derivatives of the boundary temperature and velocity, and verify that this stress tensor agrees exactly with the fluid gravity stress tensor to first order in derivatives, but deviates from the later at second order and finite D.http://link.springer.com/article/10.1007/JHEP09(2018)137Black HolesClassical Theories of Gravity |
| spellingShingle | Yogesh Dandekar Suman Kundu Subhajit Mazumdar Shiraz Minwalla Amiya Mishra Arunabha Saha An action for and hydrodynamics from the improved Large D membrane Journal of High Energy Physics Black Holes Classical Theories of Gravity |
| title | An action for and hydrodynamics from the improved Large D membrane |
| title_full | An action for and hydrodynamics from the improved Large D membrane |
| title_fullStr | An action for and hydrodynamics from the improved Large D membrane |
| title_full_unstemmed | An action for and hydrodynamics from the improved Large D membrane |
| title_short | An action for and hydrodynamics from the improved Large D membrane |
| title_sort | action for and hydrodynamics from the improved large d membrane |
| topic | Black Holes Classical Theories of Gravity |
| url | http://link.springer.com/article/10.1007/JHEP09(2018)137 |
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