Progress of Theoretical Physics
Vol. 100 No. 2 (1998) pp. 291-313
URL : http://ptp.ipap.jp/link?PTP/100/291/
DOI : 10.1143/PTP.100.291

A Maximum Mass-to-Size Ratio in Scalar-Tensor Theories of Gravity

Tooru Tsuchida,^*) Go Kawamura ^**) and Kazuya Watanabe ^***)

(Received February 23, 1998)

We derive a modified Buchdahl inequality for scalar-tensor theories of gravity. In general relativity, Buchdahl has shown that the maximum value of the mass-to-size ratio, 2M/R, is 8/9 for static and spherically symmetric stars under some physically reasonable assumptions. We formally apply Buchdahl's method to scalar-tensor theories and obtain theory-independent inequalities. After discussing the mass definition in scalar-tensor theories, these inequalities are related to a theory-dependent maximum mass-to-size ratio. We show that its value can exceed not only Buchdahl's limit, 8/9, but also unity, which we call the black hole limit, in contrast to general relativity. Next, we numerically examine the validity of the assumptions made in deriving the inequalities and the applicability of our analytic results. We find that the assumptions are mostly satisfied and that the mass-to-size ratio exceeds both Buchdahl's limit and the black hole limit. However, we also find that this ratio never exceeds Buchdahl's limit when we impose the further condition, ρ-3p≥0, on the density, ρ, and pressure, p, of the matter.

^*)E-mail:tsuchida@astro2.sc.niigata-u.ac.jp
^**)E-mail:kawamura@astro2.sc.niigata-u.ac.jp
^***)E-mail:kazuya@astro2.sc.niigata-u.ac.jp

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1. Progress of Theoretical Physics Vol. 101 No. 1 (1999) pp. 73-90 :

   Comment on the Exterior Solutions and Their Geometry in Scalar-Tensor Theories of Gravity

   Tooru Tsuchida and Kazuya Watanabe

2. Progress of Theoretical Physics Vol. 115 No. 3 (2006) pp. 487-522 :

   Light Propagation and Gravitational Lensing in Weyl-Like Spacetime in Scalar-Tensor Theories of Gravity

   Shin-ei Tsuneishi, Kazuya Watanabe and Tooru Tsuchida

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