Barak Kol Hebrew University Jerusalem Jun 2011 Milos

Barak Kol Hebrew University - Jerusalem Jun 2011, Milos Outline • set-up • puzzles and previous work Based on ar. Xiv: 1103. 5741 BK • The new effective theory W. Goldberger – early collaboration • Results w/ M. Smolkin - related work

Set-up Ultra relativistic (massless) weak scattering The parameters Generalizations: Possible interactions, dimensions, masses

Planckian scattering • Intuitive condition for black hole creation • Quantum black holes

The perturbative regime • The small parameter • Objective: – trajectories and especially – scattering angle

Background puzzles • ‘t Hooft – natural probe for quantum gravity - 4 d Gravity simplifies for lightlike - reminiscent of 3 d branch cuts • w. Dray (1985) jump at shock wave • (1987) Classical dominance including sub-planckian b! • Relation with Veneziano amplitude

Background puzzles • Amati, Ciafaloni, Veneziano (1987, …, 2008) string theory as quant. Grav. Eikonal approx, effective theory “H” correction diagram, dealing with IR div • Verlinde 2 (1992) – “topological field theory” • Giddings • Computer simulations Choptuik-Pretorius 2009 Sperhake et al (2010)

Post-Newtonian approximation • Definition: relativistic correction to slow motion in Damour, Blanchet, Schäfer flat space-time i. e. Mercury around the sun, binary system in adiabatic inspiral • Small parameter v 2/c 2 ~GM/R <<1 Goldberger, Rothstein • The EFT approach r 0=2 GM<<R (2004) • The instantaneous spatial propagator

Grav Field Re-definition Stationary (t-independent) problem • Technically – KK reduction over time • “Non-Relativistic Gravitation” - NRG fields Non-linear definition Physical interpretation of fields • Φ – Newtonian potential • A – Gravito-magnetic vector potential, similar poles attract 0712. 4116 BK, Smolkin

Recovering time dependence 1009. 4116 BK, Smolkin Non-orthonormal frame 1 PN: 0712 Kol Smolkin 2 PN: 0809 Gilmore Ross 3 PN: 1104 Sturani-Foffa

Difficulty in importing PN ideas Each particle unperturbed motion is invariant under a different light-cone coordinate z+, z-.

Relation to other work presented at this meeting • Holographic renormalization (Papadimitriou) • Hydrodynamics and gravity (Y. Oz, A. Strominger, K. Skenderis)

Related concepts Vought_V-173 “flying pancake” experimental aircraft tested 1942 -7

Related concepts Beat 1 Beat 2 Mahler symphony no. 2, 3 rd movement Conducted by L. Bernstein “St. Anthony Preaches to the Fishes” Beat 3

The effective theory Recall the set-up. . The action

Field lines • Imagine the field lines emanating from a point charge • At rest – spherical • When ultra relativistic – Lorentz contracted longitudinally – pancake-shaped transversely – Aichelburg-Sexl • “The particle carries a pancake on its nose” “flying pancake”

Sudden interaction • The moment of passing – when the pancakes coincide • Interaction localized in z, t • Eq of motion are sudden, algebraic recursion rather than differential Mahler’s 2 nd

The propagator 2 k+ k- is a quadratic perturbation The momentum transfer

Field decomposition • Dimensional reduction onto transverse space à la Kaluza-Klein • Gab are (transverse) scalars. Analogous to the Newtonian potential. G++ couples to R, G-- couples to L. • Aai are two (transverse) vectors. couple to mass current in the transverse plane. • Spin is dipole charge for vectors. BK 2010

Whole action BK (2011) Yoon (1996, 99) Extrinsic curvature de. Witt metric

Results 1 st order and momentum transfer

Ultra-relativistic dynamics • “Light-cone”/ “infinite momentum frame” • A particle has a total of 3 degrees of Dirac Weinberg Susskind freedom • 2 transverse (ordinary) degrees of freedom • p+ plays the role of mass, z+ is time • z- is a 1 st order ODE – constraint – half dof • e the world-line metric, or equiv z+ is the other half

2 -body effective action Scalar interaction For scalar→gravitational change e factors, add non-linear blik vertices

2 nd order Mass shall Energy unchanged in CM frame

Improved “renormalization” • “Ordinary” initial conditions for scattering at t=-∞ • Specify initial conditions at nearest approach “t=0” pretending to know them. Higher symmetry: parity in the pert theory Evolve both forward and backward in time to eliminate the t=0 conditions

Interaction duration – 3 rd order • Obtain a term of type • ε 2 c 3/c 1 estimates τ2, where τ is the (finite) duration At d=4 there is a pole in dim. Reg. • We find τ≈ε b BK 2011 • This is consistent with the arc’s radius of curvature being b, namely the center of force being at the other particle

Discussion • We defined a classical effective field theory (CLEFT) - different from PN. • Result: interaction duration resolved • Relation with eikonal approximation Late 1960 s, QFT context, concept borrowed from optics – an approximation of wave optics calculated on the basis of rays Eikon=image in greek

Open questions Non-conservation due to radiation: Energy, momentum, angular momentum Cylon raider from Battlestar Galactica

ΕΦΧΑΡΙΣΤΟ! Thank you! Darkness and Light in our region