  We discuss static spherically symmetric metrics which represent non-singular
black holes in four- and higher-dimensional spacetime. We impose a set of
restrictions, such as a regularity of the metric at the center $r=0$ and
Schwarzschild asymptotic behavior at large $r$. We assume that the metric
besides mass $M$ contains an additional parameter $\ell$, which determines the
scale where modification of the solution of the Einstein equations becomes
significant. We require that the modified metric obeys the limiting curvature
condition, that is its curvature is uniformly restricted by the value $\sim
\ell^{-2}$. We also make a "more technical" assumption that the metric
coefficients are rational functions of $r$. In particular, the invariant
$(\nabla r)^2$ has the form $P_n(r)/\tilde{P}_n(r)$, where $P_n$ and
$\tilde{P}_n$ are polynomials of the order of $n$. We discuss first the case of
four dimensions. We show that when $n\le 2$ such a metric cannot describe a
non-singular black hole. For $n=3$ we find a suitable metric, which besides $M$
and $\ell$ contains a dimensionless numerical parameter. When this parameter
vanishes the obtained metric coincides with Hayward's one. The characteristic
property of such spacetimes is $-\xi^2=(\nabla r)^2$, where $\xi^2$ is a
time-like at infinity Killing vector. We describe a possible generalization of
a non-singular black-hole metric to the case when this equality is violated. We
also obtain a metric for a charged non-singular black hole obeying similar
restrictions as the neutral one, and construct higher dimensional models of
neutral and charged black holes.
