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)...

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Main Authors: Katsuki Aoki, Mohammad Ali Gorji, Shinji Mukohyama
Format: Article
Language:English
Published: Elsevier 2020-11-01
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.
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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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