Back-Reaction of Classical Fields on Black Hole Area Law

(This is the unpublished manuscript while parts are corrected and included in version III of arXiv:1602.00964 which is submitted to the journal.) We study the back-reaction of classical Maxwell field and massive scalar field on the BTZ black hole entropy. The exact values of the modification which correct the black hole area law are found. We discuss the similar properties between the scalar and Maxwell fields which are investigated in both of Coulomb gauge and Lorentz gauge. The dependences of mass and mode number on the black hole entropy are illustrated. We also study the back-reaction by D branes, which are described by DBI action, and explicitly check that the classical solution which gives the black hole entropy precisely corrects the black hole area law. Our results extend the calculations of the generalized gravitational entropy proposed in recent by Lewkowycz and Maldacena [1].

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