Public debt sustainability when the real interest rate is permanently lower than growth

When the real interest rate is higher than the real growth rate, the condition for public debt sustainability is well known: the primary fiscal surplus (excluding interest on the debt) must be higher than the product of the public debt ratio and the gap between the real interest rate and the real growth rate. But when the real interest rate is lower than the real growth rate, what happens to this sustainability condition? Whether the country has a primary fiscal deficit or a surplus, its public debt ratio converges towards a limit value, which is negative if there is a primary fiscal surplus and positive if there is a primary fiscal deficit. The only case where public debt sustainability is not ensured, when the real interest rate is lower than real growth, is that where the positive limit value of the public debt ratio is unacceptable (this level of public debt cannot be held by investors/savers). This is probably the case currently in the United States, Japan and France.