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.

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