# Entropy Formula and Conserved Charges of Spin-3 Chern-Simons-Like Theories of Gravity

## TL;DR

This paper extends Chern-Simons-like theories of gravity to include spin-3 fields, deriving conserved charges and black hole entropy formulas, and analyzes a specific spin-3 gravity model with physical mode conditions.

## Contribution

It generalizes CSLTG to spin-3, provides a formalism for conserved charges and entropy, and applies it to a specific model with detailed mode analysis.

## Key findings

- The model propagates two massive spin-2 and two massive spin-3 modes.
- No-ghost and no-tachyon conditions are identified in the parameter space.
- Energy, angular momentum, and entropy of a black hole solution are computed.

## Abstract

In this paper we present the generalization of Chern-Simons-like theories of gravity (CSLTG) to spin-3. We propose a Lagrangian describing the spin-3 fields coupled to Chern-Simons-like theories of gravity. Then we obtain conserved charges of these theories by using a quasi-local formalism. We find a general formula for entropy of black holes solutions of Spin-3 CSLTG. As an example, we apply our formalism to the spin-3 Generalized minimal massive gravity (GMMG) model. We analysis this model at linearized level and show that this model propagate two massive spin-2 modes and two massive spin-3 modes. We find no-ghost and no-tachyon conditions, which can be satisfy in the parameter space of the model. Then we find energy, angular momentum and entropy of a special black hole solution of this model.