李光杰_量子场论导论课程ppt_Mimick Black Hole.pptx

1、Mimick Black Hole,中山大学物理学院14级物理学 李光杰,Gravitational Lens,Maxwell equations in gravitational field and in dielectric share the similar shape.,L. D. Landau, E. M. Lifshitz, “The Classical Theory of Fields”, Butterworth Heinemann(1995).,Maxwell Equations,In gravitational field,In dielectric, = , = 0, =

2、g 00 0, = g 00 , = g g ,=4,=0,= 1 ( ),= 1 + 4 ,=4,=0,= 1 ,= 1 + 4 ,= 1 g 00,Centrally-symmetric isotropic spacetime,d 2 = 2 2 d 2 2 (d 2 + 2 d 2 ),Static spacetime in homogeneous coordinates, = 1 2 g = = ( g ),Einstein field equation,Where,If we take = 2,d 2 = csc 2 2 2 d 2 2 () d 2 + 2 d 2 ,Traject

3、ory of light,d 2 = csc 2 2 2 d 2 2 () d 2 + 2 d 2 ,= 1 2 d d 2 = 1 2 g 00 () 2 + 2 ()( 2 + 2 2 ) , = g 00 2 2, = g 00 (),Total energy,Angular momentum, 2 = 2 4 2 2, 2 = 2 1+ 4 2,= ,= ,Lens equation,1 1 + 1 2 = 1 ,= 4 3 5,More general case: transformation optics,Schwarzschild metric,= + = + ,Chen, H.

4、, Miao, R.-X. & Li, M. Transformation optics that mimics the system outside a Schwarzschild black hole. Opt. Express 18, 1518315188 (2010),Unruh acoustic black hole,Unruh, William George. Experimental black-hole evaporation?. Physical Review Letters46.21 (1981): 1351.,The equations of motion for an irrotational fluid,Unruh, William George. Experimental black-hole evaporation?. Physical Review Letters46.21 (1