Probing QCD critical point and induced gravitational wave by black hole physics

Locating the critical endpoint of QCD and the region of a first-order 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 $\mu_B$ 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 a zero chemical potential, the predicted equation of states and QCD trace anomaly relation are in quantitative agreement with the latest lattice results available. We then give the exact location of the critical endpoint and the first-order transition line that can actually be probed by experimental facilities in the near future. Moreover, using the data from our model at finite $\mu_B$, we calculate the spectrum of the stochastic gravitational wave background associated with the first-order QCD transition in the early universe, which is found to be detected by IPTA and SKA, while NANOGrav is less likely.