On the Lagrangian Holographic Relation at $D\to 2$ and $4$ Limits of Gravity

Abstract

The gravitational Lagrangian can be written as a summation of a bulk and a total derivative term. For some theories of gravity such as Einstein gravity, or more general Lovelock gravities, there are Lagrangian holographic relations between the bulk and the total derivative term such that the latter is fully determined by the former. However at the $D\to 2\&4$ limit, the bulks of Einstein or Gauss-Bonnet theories become themselves total derivatives. Performing the Kaluza-Klein reduction on Einstein and Gauss-Bonnet gravities gives rise to some two-dimensional or four-dimensional scalar-tensor theories respectively. We obtain the holographic relations for the $D=2$ and $D=4$ cases, which have the same form as the holographic relations in pure gravity in the foliation independent formalism.

Latex, 11 pages

References in corpus (4)

• A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
• The 4D Einstein-Gauss-Bonnet Theory of Gravity: A Review
• Holography of Gravitational Action Functionals
• Classical Holographic Relations and Alternative Boundary Conditions for Lovelock Gravity

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• Observational Feasibility of 4D Einstein-Gauss-Bonnet Cosmology: Bouncing and Non-Bouncing Universes
• General Solutions of Einstein Gravity at $D\to 2$
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• Cosmology with Higher-Derivative Gravities
• AdS${}_3$ black holes with primary Proca hair from a regularized Gauss-Bonnet coupling
• Cosmological Time Crystals from Gauss-Bonnet Gravity in Four Dimensions
• Regular AdS${}_3$ black holes from regularized Gauss-Bonnet coupling