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Cited by 25Cosmology and Gravitation TheoriesBlack Holes and Theoretical PhysicsRelativity and Gravitational Theory

The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index; none of the 16 sources its claims cite is checked for support yet.

Gravitation and cosmology in generalized (1 + 1)-dimensional dilaton gravity

Open access
Chan, J S F, Mann, R B·1995·Classical and Quantum Gravity
DOI 10.1088/0264-9381/12/2/006
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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 a 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.

Overview

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TL;DR

The paper generalizes (1+1)-dimensional dilaton gravity actions, including “R = T” and string-inspired theories, into a single action characterized by two functions \(H(\Phi)\) and \(D(\Phi)\). It studies two possible interpretations of the matter stress-energy tensor, yielding type-I and type-II field equations, and analyzes weak-field, post-Newtonian, stellar-structure, and cosmological consequences.

Key findings

  • The generalized action \(S=S_g-S_s\) with \(H(\Phi)\), \(D(\Phi)\), and potential \(V\) yields two sets of field equations: type-I from defining \(T_{\mu\nu}\) as the metric variation of the matter action, and type-II under \(H(\Phi)=kD'(\Phi)\), which incorporates the dilaton variation. Type-II includes both the “R = T” and string-inspired theories; type-I and type-II have the same dynamical properties only if condition (10) holds and the dilaton source vanishes.
  • In weak-field calculations, the roles of dilaton and matter sources are interchanged: for type-I, the dilaton perturbation depends only on the matter source while the trace of the metric perturbation depends on both dilaton and matter sources; the reverse occurs for type-II.
  • Post-Newtonian expansions can be carried to arbitrary high order for both equation types. Stellar equilibrium reduces to Newton’s equation in the Newtonian limit: for type-I when \([D'(0)]^2/H(0)=2\), and for type-II when \(D'(0)=2k\). The case \(H=0\) is not appropriate for modeling one-dimensional stellar structure.
  • Cosmological solutions are given for dust (\(\gamma=1\)) and radiation (\(\gamma=2\)) universes, with radiation-filled solutions generally more complicated. For inflationary exponential expansion, type-I requires \(H(\Phi)\) strictly negative; type-II yields \(D(\Phi)\) functions so complicated that the relevant differential equations appear analytically intractable, leaving numerical solutions as the only practical option.

Methods

  • Theoretical analysis of a generalized (1+1)-dimensional dilaton gravity action, varying with respect to the metric and dilaton field, and deriving type-I and type-II field equations under different interpretations of the matter stress-energy tensor.
  • Weak-field expansion about a background with conformal transformations and harmonic gauge; post-Newtonian expansion in powers of velocity \(v\); static metric and perfect-fluid stress tensor for stellar structure; Robertson-Walker metric with equation of state \(p=(\gamma-1)\rho\) for cosmology, considering \(\gamma=1,2,0\).
  • Computations are carried out without restricting \(D\), \(H\), and \(V\) except for the constraint \(D'(\Phi)\neq 0\); Maple V was used for expansions.

Limitations

  • The paper states that ambiguity in interpreting the matter action arises from lack of knowledge of the potential density \(V\), and can only be clarified once \(V\) is explicitly specified; many other interpretations are possible, but only type-I and type-II are considered.
  • Type-II equations require \(H\neq 0\); if \(H=0\), only type-I equations are available. The paper also notes that \(H=0\) is not appropriate for modeling one-dimensional stellar structure.
  • For inflationary type-II solutions, the derived \(D(\Phi)\) functions make the differential equations analytically intractable, so numerical solutions are the only practical option.
  • Evident from the text: the analysis is confined to (1+1)-dimensional models, and many results depend on unspecified characteristic functions \(D\) and \(H\), so no direct (3+1)-dimensional observational predictions are established.

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Integrity signals

Registry

Crossref · 10.1088/0264-9381/12/2/006

Cites

15 of 15 references verified0 citation errors · 0 not checkable

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Claims the paper makes

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Citations

Cites

Show all 15 references

Research works printed but not linked: 5

  1. Gegenberg J, 1988, Phys. Rev., 37
  2. Torre C G, 1989, Phys. Rev., 40
  3. Mann R B, 1991, Phys. Rev., 43
  4. Callan C G, 1992, Phys. Rev., 45
  5. Gegenberg J, 1993, Phys. Rev., 47, 4192

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Metadata

Authors
Chan, J. S. F., & Mann, R. B.
Affiliations
University of Waterloo (CA)
Venue
Classical and Quantum Gravity
Publisher
IOP Publishing
Published
1995-02-01
Volume
12
Issue
2
Pages
351-371
ISSN
  • 0264-9381 (ISSN-L)
  • 1361-6382
DOI
10.1088/0264-9381/12/2/006
OpenAlex
W2132163639
Cited by
25
References
15
Citations by year
2025: 1 · 2019: 2 · 2018: 1
FWCI
2.76
Type
journal article
Language
en
Open access
Locations
  • Classical and Quantum Gravity (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Funders
Natural Sciences and Engineering Research Council of Canada
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
Keywords
dilaton gravity, 1+1 dimensional gravity, string-inspired gravity, field equations, weak field approximation, post-Newtonian approximation, hydrostatic equilibrium

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