1. Barak Kol Hebrew University - Jerusalem Bremen, Aug 2008 Outline Domain of applicability Brief review of results Example: 1 st Post-Newtonian order Discussion Based on hep-th’s 0712.2822 – caged w. Smolkin 0712.4116 – PN w. Smolkin 0804.0187 - BH deg of freedom

2. Domain of applicability General condition Consider a field theory with two widely separated scales r 0 <<L See solutions perturbatively in r 0 /L.

3. Two (equivalent) methods Matched Asymptotic Expansion (MAE) Two zones. Bdry cond. come from matching over overlap. Near: r 0 finite, L invisible. Far: L finite, r 0 point- like. Effective Field Theory (EFT) Replace the near zone by effective interactions of a point particle

4. Born-Oppenheimer Caged BHs Binary system Post Newtonian (PN) Extreme Mass Ratio (EMR) BHs in Higher dimensions Non-gravitational Applications Born-Oppenheimer approximation (1927) 0+1 Field theory Compute Ψ e w. static nuclei and derive the effective nuclear interactions. In this way the EFT replaces the near zone by effective interactions “Near” “Far”

5. Caged Black Holes r0r0 Near L Far Effective interaction: field quadrupole at hole’s location induces a deformation and mass quadrupole

6. The search for Gravitational waves is on: LIGO (US), VIRGO (Italy), GEO (Hannover), TAMA (Japan) Sources: binary system (steady), collapse, collision Dim’less parameters For periodic motion the latter two are comparable – virial theorem Binary system

7. Post-Newtonian Small parameter v2v2 Far zone Validity always initially, never at merger Extreme Mass Ratio m/M if initially, then throughout

8. Higher dimensional black objects Higher d ring Near zone Emparan, Harmark, Niarchos, Obers, Rodrigues

9. Non-gravitational Electro-statics of conducting spheres Scattering of long λ waves Boundary layers in fluid dynamics More…

10. Brief review of results Goldberger & Rothstein (9.2004) – Post- Newtonian (PN) including 1PN=Einstein- Infeld-Hoffmann (EIH) Goldberger & Rothstein (11.2005) BH absorption incorporated through effective BH degrees of freedom Chu, Goldberger & Rothstein (2.2006) caged black holes – asymptotic charges

11. Caged BH’s and CLEFT CLEFT = CLassical Effective Field Theory, no i’s, no ‘s NRG decompostion (=Non Relativistic Gravitation, which is the same as temporal KK reduction) BK & Smolkin 12.07

12. Definition of ADM mass in terms of a 0-pt function, rather than 1-pt function as in CGR Rotating black holes CGR US

13. Post-Newtonian approx. NRG decompostion terms Reconstructed EIH and following Cardoso-Dias- Figueras generalized to higher dimensions Damour, Blanchet, Schafer BK & Smolkin 12.07b

14. BH degrees of freedom Physical origin of eff. deg. of freedom? Near horizon fields (notably the metric) delocalized through decomposition to spherical harmonics

15. EIH in CLEFT Newtonian two-body action Add corrections in v/c Expect contributions from –Kinetic energy –Potential energy –Retardation

16. EIH in CLEFT Feynman rules Action x φ AiAi

17. Feynman diagrams

18. Detailed calculation of retardation

19. Summary Exciting new theoretical tool wide applicability Efficient Insight into divergences, regularization and renormalization in Quantum Field Theory

20. Challenges Renormalization and counter-terms within CLEFT. 1/ε→? Black hole effective action Open questions 2PN extend the 1PN (EIH) to reproduce the2PN result. Post-Minkowski separation much larger that Schw radii, but velocities are not assumed small (see Schafer) More…