Exact Black Hole and Cosmological Solutions in a Two-Dimensional Dilaton-Spectator Theory of Gravity

Details Exact Black Hole and Cosmological Solutions in a Two-Dimensional Dilaton-Spectator Theory of Gravity Exact Black Hole and Cosmological Solutions in a Two-Dimensional Dilaton-Spectator Theory of Gravity

1995-01-24

arxiv.org/abs/gr-qc/9501028v2

Class.Quant.Grav.12:1609-1640,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

34 pgs. Plain Tex, revised version contains some clarifying comments concerning the relationship between the constants of inte

Scientific paper

10.1088/0264-9381/12/7/006

Exact black hole and cosmological solutions are obtained for a special two-dimensional dilaton-spectator ($\phi-\psi$) 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 $V(\phi)$ and a ``coupling function'' $l(\phi)$ 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 $l(\phi)$ must be set equal to constants of integration (typically the mass). Second, the spectator field $\psi$ and its derivative $\psi^{'}$ both diverge at any event horizon. A test particle with ``spectator charge" ({\it i.e.} one coupled either to $\psi$ or $\psi^{'}$), 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 ($big-bang\rightarrow radiation\rightarrow dust$). Motivated by the similaritiesbetween $2D$ 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

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