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

Source: [Exact Black Hole and Cosmological Solutions in a Two-Dimensional Dilaton-Spectator Theory of Gravity](<https://www.sota2.com/research/paper/68fa292e1e209131ce831d95>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T12:44:03.897Z

Authors: K.C.K. Chan, R.B. Mann

Published: 1995-01-24T14:11:36.000Z

## Abstract

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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/gr-qc/9501028>)

[PDF](<https://arxiv.org/pdf/gr-qc/9501028.pdf>)