EXACT BLACK-HOLE AND COSMOLOGICAL SOLUTIONS IN A 2-DIMENSIONAL DILATON-SPECTATOR THEORY OF GRAVITY

Exact black hole and cosmological solutions are obtained for a special two-dimensional dilaton-spectator (phi - psi) theory of gravity. We s how how in this context any desired spacetime behaviour can be determi ned by an appropriate choice of a dilaton potential function V(phi) an d a 'coupling function' l(phi) in the action. We illustrate several bl ack hole solutions as examples. In particular, asymptotically flat dou ble- and multiple-horizon black hole solutions are obtained. One solut ion 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 featur es of all the black hole solutions. First the coupling constants in l( phi) must be set equal to constants of integration (typically the mass ). Second, the spectator field psi and its derivative psi' both diverg e at any event horizon. A test particle with 'spectator charge' (i.e. one coupled either to psi or psi') will therefore encounter an infinit e tidal force at the horizon or an 'infinite potential barrier' locate d outside the horizon, respectively. We also compute the Hawking tempe rature and entropy for our solutions. In 2D, FRW cosmology, two non-si ngular solutions, which resemble two exact solutions in 4D string-moti vated cosmology, are obtained. In addition, we construct a singular mo del which describes the 4D standard non-inflationary big bang cosmolog y (big-bang --> radiation --> dust). Motivated by the similarities bet ween 2D and 4D gravitational field equations in FRW cosmology, we brie fly discuss a special 4D dilaton-spectator action constructed from the bosonic part of the low-energy heterotic string action and get an exa ct solution which contains dust and radiation behaviour.