Gravitation and Cosmology in Generalized (1+1)-dimensional dilaton gravity

TL;DR

This paper generalizes (1+1)-dimensional gravity theories, explores different interpretations of matter stress-energy, and analyzes their implications through weak-field, post-Newtonian, stellar, and cosmological models.

Contribution

It introduces a unified action for generalized (1+1)-dimensional gravity theories and examines the effects of different matter interpretations on resulting field equations.

Findings

Different interpretations lead to distinct field equations.

Some properties are common across the generalized theories.

Theories exhibit consistent behavior in weak-field and cosmological regimes.

Abstract

The actions of the ``$R=T$'' and string-inspired theories of gravity in (1+1) dimensions are generalized into one single action which is characterized by two functions. We discuss differing interpretations of the matter stress-energy tensor, and show how two such different interpretations can yield two different sets of field equations from this action. The weak-field approximation, post-Newtonian expansion, hydrostatic equilibrium state of star and two-dimensional cosmology are studied separately by using the two sets of field equations. Some properties in the ``$R=T$'' and string-inspired theories are shown to be generic in the theory induced by the generalized action.