I think I somewhat understood now finally theargument, how the speed of convergence in a simple Solow model is increased by access to world capital markets, if we are in a small, open-economy setup. Capital markets can be considered to be the “grease” for economies. They link savers to investors and create in a setup with risk-aversion a value-added due to their risk pooling abilities. In a simple Solow model, we can see how capital markets increase the speed of convergence.
Essentially, a fundamental result of Solow is that “history does not matter“; furthermore, it also suggests that “inequality does not matter“. The Solow model predicts convergence in levels of capital stock per capita and also in GDP per capita with no long-run growth (all growth is exogeneous, e.g. due to technological progress etc.).