Note About Hamiltonian Formalism of Modified $F(R)$ Ho\v{r}ava-Lifshitz Gravities and Their Healthy Extension

TL;DR

This paper explores the Hamiltonian formalism of modified F(R) Horava-Lifshitz gravity theories and their healthy extensions, revealing unique properties and contributing to the understanding of their theoretical structure.

Contribution

It provides a detailed Hamiltonian analysis of recent F(R) Horava-Lifshitz gravity models and their healthy extensions, highlighting their distinctive features.

Findings

Many unusual properties identified in the theories.

Hamiltonian formalism developed for modified F(R) models.

Insights into the structure of healthy extended Horava-Lifshitz gravities.

Abstract

This note is devoted to the study of Hamiltonian formalism of modified F(R) Horava-Lifshitz theories of gravity that were proposed recently in arXiv:1001.4102[hep-th]. We also study Hamiltonian formulation of the healthy extended Horava-Lifshitz gravities and show that these theories have many unusual and interesting properties.