Quasi-topological Ricci polynomial gravities

A bstract Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ansätze. They therefore play no rôle in constructing these solutions, but can affect the general perturbations. We consider Einstein gravity exten...

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Published in:The journal of high energy physics Vol. 2018; no. 2; pp. 1 - 46
Main Authors: Li, Yue-Zhou, Liu, Hai-Shan, Lü, H.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2018
Springer Nature B.V
SpringerOpen
Subjects:
AdS-CFT Correspondence
Classical and Quantum Gravitation
Classical Theories of Gravity
Elementary Particles
Equations of motion
Gravitation
High energy physics
Holography
Holography and condensed matter physics (AdS/CMT)
Invariants
Linearization
Physics
Physics and Astronomy
Polynomials
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Set theory
Shear viscosity
String Theory
Classical Theories of Gravity
AdS-CFT Correspondence
Holography and condensed matter physics (AdS/CMT)
ISSN:1029-8479, 1029-8479
Online Access:Get full text
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Summary:A bstract Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ansätze. They therefore play no rôle in constructing these solutions, but can affect the general perturbations. We consider Einstein gravity extended with Ricci tensor polynomial invariants, which admits Einstein metrics with appropriate effective cosmological constants as its vacuum solutions. We construct three types of quasi-topological gravities. The first type is for the most general static metrics with spherical, toroidal or hyperbolic isometries. The second type is for the special static metrics where g tt g rr is constant. The third type is the linearized quasitopological gravities on the Einstein metrics. We construct and classify results that are either dependent on or independent of dimensions, up to the tenth order. We then consider a subset of these three types and obtain Lovelock-like quasi-topological gravities, that are independent of the dimensions. The linearized gravities on Einstein metrics on all dimensions are simply Einstein and hence ghost free. The theories become quasi-topological on static metrics in one specific dimension, but non-trivial in others. We also focus on the quasi-topological Ricci cubic invariant in four dimensions as a specific example to study its effect on holography, including shear viscosity, thermoelectric DC conductivities and butterfly velocity. In particular, we find that the holographic diffusivity bounds can be violated by the quasi-topological terms, which can induce an extra massive mode that yields a butterfly velocity unbound above.
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP02(2018)166