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 – caged w. Smolkin – PN w. Smolkin BH deg of freedom

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

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

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”

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

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

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

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

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

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

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

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

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

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

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

EIH in CLEFT Feynman rules Action x φ AiAi

Feynman diagrams

Detailed calculation of retardation

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

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…