  We consider solutions of (super) gravities associated to non-critical (super)
string theories in arbitrary space-time dimension D=p+3, that describe
generically non extremal black p-branes charged under NSNS or RR gauge fields,
embedded in some non critical vacuum. In the case of vacuum (uncharged)
backgrounds, we solve completely the problem obtaining all the possible
solutions, that consist of the (p+1)-dimensional Minkowski space times a linear
dilaton times a S^1, and a three parameter family of solutions that include
(p+1)-dimensional Minkowski space times the cigar, and its T-dual
(p+1)-dimensional Minkowski space times the trumpet. For NSNS charged
solutions, we also solve in closed form the problem, obtaining several families
of solutions, that include in particular the fundamental non-critical string
solution embedded in the cigar vacuum, recently found in hep-th/0604202, a
solution that we interpret as a fundamental non-critical string embedded in the
linear dilaton vacuum, and a two-parameter family of regular curvature
solutions asymptotic to AdS_{1,2}\times S^1. In the case of RR charged
Dp-branes solutions, an ansatz allows us to find a non conformal, constant
curvature, asymptotically AdS_{1,p+1} space, T-dual to AdS_{1,p+2}, together
with a two-parameter family of solutions that includes the non conformal, AdS
black hole like solution associated with the earlier space. The solutions
obtained by T-duality are Einstein spaces consisting of a two-parameter family
of conformal, constant dilaton solutions, that include, in particular, the AdS
black hole of hep-th/0403254. We speculate about the possible applications of
some of them in the framework of the gauge-gravity correspondence.
