1. Spontaneous Lorentz-Symmetry Breaking in Gravity
Erik Lentz
Embry-Riddle Aeronautical University

2. Lorentz-Symmetry
Invariance of reference frames under rotations and boosts
Rotations: rotate about one of three axis
A boost is giving a reference frame a constant velocity
Boosts and rotations of coordinate systems are observer Lorentz transformations

3. Lorentz-Symmetry Breaking
Implies a change in the properties of matter when matter is rotated relative to a fixed background
Background (red arrows)

4. Why Test It?
General Relativity and the Standard Model are based on it.
The two theories are not unified.

5. Testing Model: Standard-Model Extension (SME)
(Colladay and Kostelecký PRD 97, 98; Kostelecký PRD 04)
Gravity Sector:
Leading Lorentz-violating couplings

6. SME experiments testing Lorentz symmetry to date:
meson oscillations (BABAR, BELLE, DELPHI, FOCUS, KTeV, OPAL, …)
neutrino oscillations (MiniBooNE, LSND, Minos, Super K,… )
muon tests (Hughes, BNL g-2) Yale, …
spin-polarized torsion pendulum tests (Adelberger, Hou, …) U. of Washington
tests with resonant cavities (Lipa, Mueller, Peters, Schiller, Wolf, …)
Stanford, Institut fur Physik, Univ. West. Aust.
clock-comparison tests (Hunter, Walsworth, Wolf, …) Harvard-Smithsonian
Penning-trap tests (Dehmelt, Gabrielse, …) U. of Washington
Lunar laser ranging (Battat, Stubbs, Chandler) Harvard
Atom interferometric gravimeters (Chu, Mueller, …) Stanford
cosmological birefringence (Carroll, Jackiw, Mewes, Kostelecky) MIT, IU
pulsar timing (Altschul) South Carolina
synchrotron radiation (Altschul) South Carolina
Cosmic Microwave Background (Mewes, Kostelecky) Marquette U., IU

7. Spontaneous Breaking Two varieties Why study a specific model?
Explicit: conflicts with Riemann geometry
Spontaneous: Lorentz symmetry holds in the underlying theory but the solutions break it
OK with Riemann geometry√
Why study a specific model?
To investigate Lorentz-symmetry breaking in strong-field gravity
Want to find meaning of these terms
Note: This model already being tested in weak-field gravity with lunar laser ranging, atom interferometry, etc.

8. We consider a two-tensor model
Einstein Equation
Two-tensor field equation
Key feature: The potential V has a minimum for some constant bμν0 V B

9. Flat spacetime limit (Btz only)
Results
Flat spacetime limit (Btz only)
Functions seem to be independent of their inherent directions.
(x2 +y2) Btz = 4λ (-2B2tz+b2)Btz
Graph shows oscillations about two minimum values (+ or – b/√2) for dependence on one variable
Minkowski metric

10. Results (cont.) Complications:
Dependence on x and y
Complications:
Differential equations are nonlinear ellipticals which present difficulty in both analytical and numerical analysis

11. What’s next? Curved spacetime
Toy Metric: made to explore curved space-time
Future Metrics (generalized black hole solution?)
Figure:
Ultimate goal: understand Lorentz violation in strong-field gravity