# f(Ricci) gravity

## TL;DR

f(Ricci) gravity is a higher curvature theory that admits Einstein manifolds as solutions, can be ghost free around Einstein vacua, and yields consistent black hole entropy calculations.

## Contribution

The paper demonstrates that f(Ricci) gravity admits Einstein solutions, can be ghost free, and provides consistent entropy calculations for black holes.

## Key findings

- Admits Einstein manifolds as vacuum solutions
- Can be ghost free around Einstein vacua
- Black hole entropy calculations agree across methods

## Abstract

f(Ricci) gravity is a special kind of higher curvature gravity whose bulk Lagrangian density is the trace of a matrix-valued function of the Ricci tensor. It is shown that, under some mild constraints, f(Ricci) gravity admits Einstein manifolds as exact vacuum solutions, and can be ghost free around maximally symmetric Einstein vacua. It is also shown that the entropy for spherically symmetric black holes in f(Ricci) gravity calculated via Wald's method and the boundary Noether charge approach proposed by Majhi and Padmanabhan are in good agreement.