1. 三维黑洞和引力波 张宏升 上海师范大学 合作者：刘道军 李新洲

2. 3d Einstein gravity Vacuum: locally Mink ( no black hole, nor gravity wave) 4d : Riemann=Weyl+Ricci (20) (10) (10) 3d: Riemann=Weyl+Ricci (Vac or non-vac) (6) (0) (6) Riemann=Ricci Vacuum Ricci=0 Riemann=0, Mink

3. Quantum theory No graviton, thus no quantum theory However,

4. Chern-Simons theory Hilbert-Einstein action equals to A: SO(2,2) gauge field

5. Differences 1. sum over history 2. diffeomorphisms group It may be not surprised that 3d gravity has no quantum theory, However……

6. BTZ black hole Locally ADS Globally horizon, mass, entropy, and angular momentum Where can we find so many freedoms? Maybe we need more freedoms in the theory itself.

7. f(R) gravity Ostrogradski instability Renormalizability Once the higher derivative terms are introduced, they will dominate the behaviour of the space-time dynamics at high energy region.

8. Action

9. ansatz

10. Black hole

11. Dynamical solution

12. Source It is not an electromagnetic field. k=0 implies a pure gravitational wave.

13. Relation to the black hole solution

14. Physical significance Say something about quantum theory of 3d gravity Say something about the freedoms of 3d black holes

15. Higher dimensional case

16. Thank you for attention.