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

Abstract

We introduce a four-dimensional extension of the Poincaré 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 $\frac{{\mathbf{A}}_{4,8}}{{\mathbf{A}}_1\otimes {\mathbf{A}}_1}$ 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.

15 pages. Section 4 is rewritten and 2 refs. are added

References in corpus (8)

• Generalized cosmological term from Maxwell symmetries
• Topological gravity and transgression holography
• 2 + 1 dimensional gravity from Maxwell and semi-simple extension of the Poincare gauge symmetric models
• Generating infinite-dimensional algebras from loop algebras by expanding Maurer Cartan forms
• A generalized action for $\left(2+1\right)$-dimensional Chern--Simons gravity
• Maxwell-affine gauge theory of gravity
• Gauge Theory of Maxwell-Weyl Group
• Exact three dimensional black hole with gauge fields in string theory