A consistent theory of D → 4 Einstein-Gauss-Bonnet gravity
We investigate the D→4 limit of the D-dimensional Einstein-Gauss-Bonnet gravity, where the limit is taken with α˜=(D−4)α kept fixed and α is the original Gauss-Bonnet coupling. Using the ADM decomposition in D dimensions, we clarify that the limit is rather subtle and ambiguous (if not ill-defined)...
Main Authors: | , , |
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Format: | Article |
Language: | English |
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Elsevier
2020-11-01
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Series: | Physics Letters B |
Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269320306468 |
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author | Katsuki Aoki Mohammad Ali Gorji Shinji Mukohyama |
author_facet | Katsuki Aoki Mohammad Ali Gorji Shinji Mukohyama |
author_sort | Katsuki Aoki |
collection | DOAJ |
description | We investigate the D→4 limit of the D-dimensional Einstein-Gauss-Bonnet gravity, where the limit is taken with α˜=(D−4)α kept fixed and α is the original Gauss-Bonnet coupling. Using the ADM decomposition in D dimensions, we clarify that the limit is rather subtle and ambiguous (if not ill-defined) and depends on the way how to regularize the Hamiltonian or/and the equations of motion. To find a consistent theory in 4 dimensions that is different from general relativity, the regularization needs to either break (a part of) the diffeomorphism invariance or lead to an extra degree of freedom, in agreement with the Lovelock theorem. We then propose a consistent theory of D→4 Einstein-Gauss-Bonnet gravity with two dynamical degrees of freedom by breaking the temporal diffeomorphism invariance and argue that, under a number of reasonable assumptions, the theory is unique up to a choice of a constraint that stems from a temporal gauge condition. |
first_indexed | 2024-12-11T16:14:01Z |
format | Article |
id | doaj.art-eee59bdde3e944a89cddb002d65cc257 |
institution | Directory Open Access Journal |
issn | 0370-2693 |
language | English |
last_indexed | 2024-12-11T16:14:01Z |
publishDate | 2020-11-01 |
publisher | Elsevier |
record_format | Article |
series | Physics Letters B |
spelling | doaj.art-eee59bdde3e944a89cddb002d65cc2572022-12-22T00:59:00ZengElsevierPhysics Letters B0370-26932020-11-01810135843A consistent theory of D → 4 Einstein-Gauss-Bonnet gravityKatsuki Aoki0Mohammad Ali Gorji1Shinji Mukohyama2Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, 606-8502, Kyoto, Japan; Corresponding author.Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, 606-8502, Kyoto, JapanCenter for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, 606-8502, Kyoto, Japan; Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, 277-8583, Chiba, JapanWe investigate the D→4 limit of the D-dimensional Einstein-Gauss-Bonnet gravity, where the limit is taken with α˜=(D−4)α kept fixed and α is the original Gauss-Bonnet coupling. Using the ADM decomposition in D dimensions, we clarify that the limit is rather subtle and ambiguous (if not ill-defined) and depends on the way how to regularize the Hamiltonian or/and the equations of motion. To find a consistent theory in 4 dimensions that is different from general relativity, the regularization needs to either break (a part of) the diffeomorphism invariance or lead to an extra degree of freedom, in agreement with the Lovelock theorem. We then propose a consistent theory of D→4 Einstein-Gauss-Bonnet gravity with two dynamical degrees of freedom by breaking the temporal diffeomorphism invariance and argue that, under a number of reasonable assumptions, the theory is unique up to a choice of a constraint that stems from a temporal gauge condition.http://www.sciencedirect.com/science/article/pii/S0370269320306468 |
spellingShingle | Katsuki Aoki Mohammad Ali Gorji Shinji Mukohyama A consistent theory of D → 4 Einstein-Gauss-Bonnet gravity Physics Letters B |
title | A consistent theory of D → 4 Einstein-Gauss-Bonnet gravity |
title_full | A consistent theory of D → 4 Einstein-Gauss-Bonnet gravity |
title_fullStr | A consistent theory of D → 4 Einstein-Gauss-Bonnet gravity |
title_full_unstemmed | A consistent theory of D → 4 Einstein-Gauss-Bonnet gravity |
title_short | A consistent theory of D → 4 Einstein-Gauss-Bonnet gravity |
title_sort | consistent theory of d 4 einstein gauss bonnet gravity |
url | http://www.sciencedirect.com/science/article/pii/S0370269320306468 |
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