# (1+1)-dimensional gauge symmetric gravity model and related exact black hole and cosmological solutions in string theory

## TL;DR

This paper develops a (1+1)-dimensional gauge symmetric gravity model based on an extended Poincaré algebra, finds duality with AdS gravity, and derives exact black hole and cosmological solutions in string theory that match those from the gravity model.

## Contribution

It introduces a novel gauge symmetric gravity model in (1+1) dimensions using an extended algebra and connects it to string theory solutions.

## Key findings

- Derived black hole solutions in the gauge gravity model.
- Obtained cosmological solutions matching string theory metrics.
- Demonstrated duality with (1+1)-dimensional AdS gravity.

## Abstract

We introduce a four-dimensional extension of the Poincar\'{e} algebra $(\mathcal{N})$ in (1+1)-dimensional space-time and obtain a (1+1)-dimensional gauge symmetric gravity model using the algebra $\mathcal{N}$. We show that the obtained gravity model is dual (canonically transformed) to the (1+1)-dimensional anti de Sitter ($AdS$) gravity. We also obtain some black hole and Friedmann-Robertson-Walker (FRW) solutions by solving its classical equations of motion. Then, we study $\frac{\mathbf{A}_{\mathbf{4,8}}}{\mathbf{A}_{\mathbf{1}}\otimes \mathbf{A}_{\mathbf{1}}}$ gauged Wess-Zumino-Witten (WZW) model and obtain some exact black hole and cosmological solutions in string theory. We show that some obtained black hole and cosmological metrics in string theory are same as the metrics obtained in solutions of our gauge symmetric gravity model.