1 / 15

Parameterized Newtonian Theory

Parameterized Newtonian Theory. Tomoyuki Nakayama December 11, 2008. Outline. Introduction Why is it useful?/How is it used? Theory General formulation of PPN formalism Application to GR and Brans-Dicke theory Experimental tests Time delay/Light deflection. What is PPN formalism?.

gautam
Download Presentation

Parameterized Newtonian Theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Parameterized Newtonian Theory Tomoyuki Nakayama December 11, 2008

  2. Outline • Introduction • Why is it useful?/How is it used? • Theory • General formulation of PPN formalism • Application to GR and Brans-Dicke theory • Experimental tests • Time delay/Light deflection

  3. What is PPN formalism? • Parameterized Post-Newtonian formalism express Einstein's’ equation in terms of deviation from Newtonian theory. • Well describes weak field. Bring us further comprehension on Solar-system. • Theoretical foundation for experimental tests for alternative (metric) gravitational theory.

  4. Alternative Gravitational Theories • Metric theories • Have symmetric metric • Test bodies follow geodesics of the metric • In local Lorentz frames, non-gravitational laws are those of SR.

  5. Historical Background • A. S. Eddington (1922) – Analysis of vacuum gravitational field outside the Sun. • K. Nordtvedt (1968) developed the first full PPN formalism. • C. M. Will introduced hydrodynamical description.

  6. PPN Formalism by Will • γ - How much space curvature gij is produced by unit rest mass ? • β - How much nonlinearity is there in the superposition law for gravity g00 ? • β1 - How much gravity is produced by unit kinetic energy  ? • β2 - How much gravity is produced by unit gravitational potential energy ρ0 / U ? • β3 - How much gravity is produced by unit internal energy ρ0Π ? • β4 - How much gravity is produced by unit pressure p ? • ζ - Difference between radial and transverse kinetic energy on gravity • η - Difference between radial and transverse stress on gravity • Δ1 - How much dragging of inertial frames g0j is produced by unit momentum ρ0v ? • Δ2 - Difference between radial and transverse momentum on dragging of inertial frames

  7. Metric & Stress Tensors in PPN Formalism

  8. GR Solution in PPN approximation Brans-Dicke Application of PPN formalism to GR & Brans-Dicke theory

  9. PPN parameters in GR and Bran-Dicke Theory

  10. New Version of PPN parameterization

  11. Deflection/Time Delay of Light • One of the PPN parameter (γ) is related to the deflection of light. • It also describes the time delay of light.

  12. Experimental Results • VLBI light deflection 0.02 % from unity (1995). • Cassini spacecraft agrees with GR to 10-3 %. γ-1 = (2.1±2.3)×10-5 (2003)

  13. Current limits on PPN parameters

  14. Summary • PPN formalism, with sophistication of experimental technique, enabled to test the validity of metric theories. • GR has survived through all the experimental testing so far, while myriads of alternative gravitational theories disappeared.

  15. Thank you! • Reference • Misner, Thorne, Wheeler, (1973) Gravitation • Nordvedt (1976) Phys. Rev. 169, 1017-1025 • Will. Living Rev. Relativity 9 (2006), 3 • Chandrasekhar, Phys. Rev. Lett. vol 14, 1965 • Nutku, Astro. Journal, vol 155, March 1969 • Blanchet, Living Rev. Relativity 9 (2006), 4

More Related