Surface terms in higher derivative gravity

Bunch, T S

doi:10.1088/0305-4470/14/5/008

Cited by 27 publications

(49 citation statements)

References 7 publications

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“…In fact, the exact form of the boundary term for the action (I.2) of this paper is not yet known and according to the claim of Ref. [21] it does not exist. According to Ref.…”

Section: Problem Formulating Israel Junction Conditions In a Fourmentioning

confidence: 85%

“…However, in the fourth-order theory given by the action (I.2), the application of the continuity conditions (II.15)-(II.16) does not work. In order to discuss this let us first write down the field equations for the action (I.2) [15]: 21) where f X = ∂f /∂X etc. The reason for not being the same continuity conditions (II.15)-(II.16) valid here is that the Riemann tensor…”

Section: Problem Formulating Israel Junction Conditions In a Fourmentioning

confidence: 99%

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Generalized Israel junction conditions for a fourth-order brane world

Balcerzak

Dąbrowski

2008

Phys. Rev. D

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We discuss a general fourth-order theory of gravity on the brane. In general, the formulation of the junction conditions (except for Euler characteristics such as Gauss-Bonnet term) leads to the higher powers of the delta function and requires regularization. We suggest the way to avoid such a problem by imposing the metric and its first derivative to be regular at the brane, while the second derivative to have a kink, the third derivative of the metric to have a step function discontinuity, and no sooner as the fourth derivative of the metric to give the delta function contribution to the field equations. Alternatively, we discuss the reduction of the fourth-order gravity to the second-order theory by introducing an extra tensor field. We formulate the appropriate junction conditions on the brane. We prove the equivalence of both theories. In particular, we prove the equivalence of the junction conditions with different assumptions related to the continuity of the metric along the brane.

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“…In fact, the exact form of the boundary term for the action (I.2) of this paper is not yet known and according to the claim of Ref. [21] it does not exist. According to Ref.…”

Section: Problem Formulating Israel Junction Conditions In a Fourmentioning

confidence: 85%

Section: Problem Formulating Israel Junction Conditions In a Fourmentioning

confidence: 99%

Generalized Israel junction conditions for a fourth-order brane world

Balcerzak

Dąbrowski

2008

Phys. Rev. D

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“…In the physical theories which enter the dense quantum phase of the evolution of the universe one often applies quantum corrections to general relativity [15] which are composed of the curvature invariants R 2 , R ab R ab , R abcd R abcd and the Gauss-Bonnet invariant R GB [16] as well as their functions such as f (R) [17], f (R GB ) [18] as well as f (R 2 , R ab R ab , R abcd R abcd ) [19,20]. In fact, the additional terms which come from the inclusion of these curvature invariants play the role of the corrections to the standard gravity action [21].…”

Section: Conformal Transformations In Higher-order Gravitationmentioning

confidence: 99%

Conformal transformations and conformal invariance in gravitation

Dąbrowski¹,

Garecki²,

Blaschke³

2009

Ann. Phys.

105

115

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Conformal transformations are frequently used tools in order to study relations between various theories of gravity and the Einstein relativity. In this paper we discuss the rules of these transformations for geometric quantities as well as for the matter energy-momentum tensor. We show the subtlety of the matter energy-momentum conservation law which refers to the fact that the conformal transformation "creates" an extra matter term composed of the conformal factor which enters the conservation law. In an extreme case of the flat original spacetime the matter is "created" due to work done by the conformal transformation to bend the spacetime which was originally flat. We discuss how to construct the conformally invariant gravity theories and also find the conformal transformation rules for the curvature invariants R 2 , R ab R ab , R abcd R abcd and the Gauss-Bonnet invariant in a spacetime of an arbitrary dimension. Finally, we present the conformal transformation rules in the fashion of the duality transformations of the superstring theory.In such a case the transitions between conformal frames reduce to a simple change of the sign of a redefined conformal factor.

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“…Then, for the action being the combination of the square of the Weyl tensor and an arbitrary function of the scalar curvature they were found by Hawking and Lutrell [17] and Barrow and Madsen [18]. For the Gauss-Bonnet and other Lovelock densities they were found by Bunch [19], Mueller-Hoissen and Myers [20], Davis [21] and Gravanis and Willinson [22]. The boundary terms for the action being an arbitrary function of the curvature invariants were found by Barvinsky and Solodukhin [23].…”

Section: B Reduction To An Equivalent 2nd Order Theorymentioning

confidence: 85%

Higher-order brane gravity models

Dąbrowski¹,

Balcerzak²

2010

AIP Conference Proceedings

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Abstract. We discuss a very general theory of gravity, of which Lagrangian is an arbitrary function of the curvature invariants, on the brane. In general, the formulation of the junction conditions (except for Euler characteristics such as Gauss-Bonnet term) leads to the powers of the delta function and requires regularization. We suggest the way to avoid such a problem by imposing the metric and its first derivative to be regular at the brane, the second derivative to have a kink, the third derivative of the metric to have a step function discontinuity, and no sooner as the fourth derivative of the metric to give the delta function contribution to the field equations. Alternatively, we discuss the reduction of the fourth-order gravity to the second order theory by introducing extra scalar and tensor fields: the scalaron and the tensoron. In order to obtain junction conditions we apply two methods: the application of the Gauss-Codazzi formalism and the application of the generalized Gibbons-Hawking boundary terms which are appended to the appropriate actions. In the most general case we derive junction conditions without assuming the continuity of the scalaron and the tensoron on the brane. The derived junction conditions can serve studying the cosmological implications of the higher-order brane gravity models.

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Surface terms in higher derivative gravity

Cited by 27 publications

References 7 publications

Generalized Israel junction conditions for a fourth-order brane world

Generalized Israel junction conditions for a fourth-order brane world

Conformal transformations and conformal invariance in gravitation

Higher-order brane gravity models

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