Exact black hole and cosmological solutions in a two-dimensional dilaton-spectator theory of gravity

Abstract

Exact black hole and cosmological solutions are obtained for a special two-dimensional dilaton--spectator () theory of gravity. We show how in this context any desired spacetime behaviour can be determined by an appropriate choice of a dilaton potential function and a `coupling function' in the action. We illustrate several black hole solutions as examples. In particular, asymptotically flat double- and multiple-horizon black hole solutions are obtained. One solution bears an interesting resemblance to the 2D string-theoretic black hole and contains the same thermodynamic properties; another resembles the 4D Reissner--Nordstrom solution. We find two characteristic features of all the black hole solutions. First the coupling constants in must be set equal to constants of integration (typically the mass). Second, the spectator field and its derivative both diverge at any event horizon. A test particle with `spectator charge' (i.e. one coupled either to or ) will therefore encounter an infinite tidal force at the horizon or an `infinite potential barrier' located outside the horizon, respectively. We also compute the Hawking temperature and entropy for our solutions. In 2D FRW cosmology, two non-singular solutions, which resemble two exact solutions in 4D string-motivated cosmology, are obtained. In addition, we construct a singular model which describes the 4D standard non-inflationary big bang cosmology (). Motivated by the similarities between 2D and 4D gravitational field equations in FRW cosmology, we briefly discuss a special 4D dilaton--spectator action constructed from the bosonic part of the low-energy heterotic string action and get an exact solution which contains dust and radiation behaviour.