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Singularities in Graviton-Dilaton System: Their Implications on the PPN Parameters and the Cosmological Constant
High Energy Physics - Theory · Submitted 10 Nov 1994
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Requiring their absence upto a distance $r_*$ implies a bound $| \Lambda | < 10^{- 102} (\frac{r_*}{{\rm pc}})^{- 2}$ in natural units.
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The abstract, sentence by sentence
Alternatives to Einstein's theory of general relativity can be distinguished by measuring the parametrised post Newtonian parameters. Two such parameters $\beta$ and $\gamma$, equal to one in Einstein theory, can be obtained from static spherically symmetric solutions. For the graviton-dilaton system, as in Brans-Dicke or low energy string theory, we find that if $\gamma \ne 1$ for a charge neutral point star, then there exist naked singularities. Thus, if $\gamma$ is measured to be different from one, then it cannot be explained by these theories, without implying naked singularities. We also couple a cosmological constant $\Lambda$ to the graviton-dilaton system, a la string theory. We find that static spherically symmetric solutions in low energy string theory, which describe the gravitational field of a point star in the real universe atleast upto a distance $r_* \simeq {\cal O} ({\rm pc})$, always lead to curvature singularities. These singularities are stable and much worse than the naked ones. Requiring their absence upto a distance $r_*$ implies a bound $| \Lambda | < 10^{- 102} (\frac{r_*}{{\rm pc}})^{- 2}$ in natural units. If $r_* \simeq 1 {\rm Mpc}$ then $| \Lambda | < 10^{- 114}$, and if $r_*$ extends all the way upto the edge of the universe ($10^{28} {\rm cm}$) then $| \Lambda | < 10^{- 122}$ in natural units.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Alternatives to Einstein's theory of general relativity can be distinguished by measuring the parametrised post Newtonian parameters. | background 1.00 | 0.06 | 0.03 | asserted 0.96 |
| s1 | Two such parameters $\beta$ and $\gamma$, equal to one in Einstein theory, can be obtained from static spherically symmetric solutions. | background 0.98 | 0.13 | 0.03 | asserted 0.99 |
| s2 | For the graviton-dilaton system, as in Brans-Dicke or low energy string theory, we find that if $\gamma \ne 1$ for a charge neutral point star, then there exist naked singularities. | result 1.00 | 0.93 | 0.26 | asserted 1.00 |
| s3 | Thus, if $\gamma$ is measured to be different from one, then it cannot be explained by these theories, without implying naked singularities. | interpretation 0.98 | 0.64 | 0.27 | asserted 0.98 |
| s4 | We also couple a cosmological constant $\Lambda$ to the graviton-dilaton system, a la string theory. | contribution 0.85 | 0.88 | 0.03 | asserted 0.96 |
| s5 | We find that static spherically symmetric solutions in low energy string theory, which describe the gravitational field of a point star in the real universe atleast upto a distance $r_* \simeq {\cal O} ({\rm pc})$, always lead to curvature singularities. | result 0.96 | 0.90 | 0.27 | asserted 1.00 |
| s6 | These singularities are stable and much worse than the naked ones. | result 0.80 | 0.87 | 0.10 | asserted 1.00 |
| s7 | Requiring their absence upto a distance $r_*$ implies a bound $| \Lambda | < 10^{- 102} (\frac{r_*}{{\rm pc}})^{- 2}$ in natural units. | result 0.99 | 0.92 | 0.33 | asserted 1.00 |
| s8 | If $r_* \simeq 1 {\rm Mpc}$ then $| \Lambda | < 10^{- 114}$, and if $r_*$ extends all the way upto the edge of the universe ($10^{28} {\rm cm}$) then $| \Lambda | < 10^{- 122}$ in natural units. | result 0.96 | 0.88 | 0.22 | asserted 0.99 |
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Original abstract
Alternatives to Einstein's theory of general relativity can be distinguished by measuring the parametrised post Newtonian parameters. Two such parameters $\beta$ and $\gamma$, equal to one in Einstein theory, can be obtained from static spherically symmetric solutions. For the graviton-dilaton system, as in Brans-Dicke or low energy string theory, we find that if $\gamma \ne 1$ for a charge neutral point star, then there exist naked singularities. Thus, if $\gamma$ is measured to be different from one, then it cannot be explained by these theories, without implying naked singularities. We also couple a cosmological constant $\Lambda$ to the graviton-dilaton system, a la string theory. We find that static spherically symmetric solutions in low energy string theory, which describe the gravitational field of a point star in the real universe atleast upto a distance $r_* \simeq {\cal O} ({\rm pc})$, always lead to curvature singularities. These singularities are stable and much worse than the naked ones. Requiring their absence upto a distance $r_*$ implies a bound $| \Lambda | < 10^{- 102} (\frac{r_*}{{\rm pc}})^{- 2}$ in natural units. If $r_* \simeq 1 {\rm Mpc}$ then $| \Lambda | < 10^{- 114}$, and if $r_*$ extends all the way upto the edge of the universe ($10^{28} {\rm cm}$) then $| \Lambda | < 10^{- 122}$ in natural units.
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The analysis for the PPN parameter for such gravity-dilaton system has been performed in [ref] .
Solar System Constraints on Scalar Tensor Theories with Non-Standard Action · Introduction · 0.93
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