# Lemaitre-Tolman-Bondi Static Universe in Rastall-like Gravity

## TL;DR

This paper introduces a new Rastall-like gravity theory that allows for stable Lemaitre-Tolman-Bondi static universes, overcoming limitations of general relativity and other modified gravity theories.

## Contribution

It proposes a novel Rastall-like gravity model that enables stable LTB static solutions, which are not possible in GR or original Rastall gravity.

## Key findings

- Stable LTB static universe solutions found in Rastall-like gravity
- Demonstrated stability against scalar perturbations
- Shows potential for alternative cosmological models

## Abstract

In this work, we try to obtain a stable Lemaitre-Tolman-Bondi (LTB) static universe, which is spherically symmetric and radially inhomogeneous. However, this is not an easy task, and fails in general relativity (GR) and various modified gravity theories, because the corresponding LTB static universes must reduce to the Friedmann-Robertson-Walker (FRW) static universes. We find a way out in a new type of modified gravity theory, in which the conservation of energy and momentum is broken. In this work, we have proposed a novel modification to the original Rastall gravity. In some sense, our Rastall-like gravity is essentially different from GR and the original Rastall gravity. In this Rastall-like gravity, LTB static solutions have been found. The stability of LTB static universe against both the homogeneous and the inhomogeneous scalar perturbations is also discussed in details. We show that a LTB static universe can be stable in this Rastall-like gravity.