  Locating the critical endpoint of QCD and the region of a first-order phase
transition at finite baryon chemical potential is an active research area for
QCD matter. We provide a gravitational dual description of QCD matter at finite
baryon chemical potential and finite temperature using the non-perturbative
approach from gauge/gravity duality. After fixing all model parameters using
state-of-the-art lattice QCD data at zero chemical potential, the predicted
equations of state and QCD trace anomaly relation are in quantitative agreement
with the latest lattice results. We then give the exact location of the
critical endpoint as well as the first-order transition line, which is within
the coverage of many upcoming experimental measurements. Moreover, using the
data from our model at finite baryon chemical potential, we calculate the
spectrum of the stochastic gravitational wave background associated with the
first-order QCD transition in the early universe, which could be observable via
pulsar timing in the future.
