Unruh effect of multiparticle states and black hole radiation

Abstract

In this study, we investigated the field under the Unruh effect. The energy and entanglement properties of the single-mode <inline-formula><tex-math id="M1">\begin{document}$q$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2022-0039_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2022-0039_M1.png"/></alternatives></inline-formula>-particle states were discussed. We found that in the non-inertial reference frame <inline-formula><tex-math id="M2">\begin{document}$|q, 0\rangle_\alpha$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2022-0039_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2022-0039_M2.png"/></alternatives></inline-formula> states exhibit a similar energy spectrum to vacuum <inline-formula><tex-math id="M3">\begin{document}$|0, 0\rangle_\alpha$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2022-0039_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2022-0039_M3.png"/></alternatives></inline-formula>, but with different entanglement properties. With respect to an application, we proposed a black hole radiation model, assuming that states near the horizon are constructed via <inline-formula><tex-math id="M4">\begin{document}$q$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2022-0039_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2022-0039_M4.png"/></alternatives></inline-formula>-particle states. We calculated the evolution of the entanglement entropy of radiation and proved that our model can reproduce the Page curve. Hence, this can be considered as an indication solution of the black hole information paradox.