Cosmological and black hole brane-world Universes in higher derivative gravity

TL;DR

This paper explores higher derivative $R^2$-gravity in multidimensional brane-world models, analyzing black hole thermodynamics, brane dynamics, and holographic properties, revealing deviations from conformality and Lorentz invariance violations.

Contribution

It introduces a comprehensive model of $R^2$-gravity with Riemann tensor terms, constructs brane-world solutions, and examines their thermodynamics and holographic duals, highlighting non-conformal behavior.

Findings

Entropy and energy deviate from area and mass proportionality for non-zero $c$

Dual CFT becomes non-conformal when $c$ is non-zero

Asymmetrically warped backgrounds exhibit Lorentz invariance violation

Abstract

General model of multidimensional $R^2$-gravity including Riemann tensor square term (non-zero $c$ case) is considered. The number of brane-worlds in such model is constructed (mainly in five dimensions) and their properties are discussed. Thermodynamics of S-AdS BH (with boundary) is presented when perturbation on $c$ is used. The entropy, free energy and energy are calculated. For non-zero $c$ the entropy (energy) is not proportional to the area (mass). The equation of motion of brane in BH background is presented as FRW equation. Using dual CFT description it is shown that dual field theory is not conformal one when $c$ is not zero. In this case the holographic entropy does not coincide with BH entropy (they coincide for Einstein gravity or $c=0$ HD gravity where AdS/CFT description is well applied). Asymmetrically warped background (analog of charged AdS BH) where Lorentz invariance violation occurs is found. The cosmological 4d dS brane connecting two dS bulk spaces is formulated in terms of parameters of $R^2$-gravity. Within proposed dS/CFT correspondence the holographic conformal anomaly from five-dimensional higher derivative gravity in de Sitter background is evaluated.