parameterized newtonian theory
Download
Skip this Video
Download Presentation
Parameterized Newtonian Theory

Loading in 2 Seconds...

play fullscreen
1 / 15

Parameterized Newtonian Theory - PowerPoint PPT Presentation


  • 123 Views
  • Uploaded on

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?.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Parameterized Newtonian Theory' - gautam


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
parameterized newtonian theory

Parameterized Newtonian Theory

Tomoyuki Nakayama

December 11, 2008

outline
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
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.
alternative gravitational theories
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.
historical background
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.
ppn formalism by will
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
application of ppn formalism to gr brans dicke theory
GR

Solution in PPN approximation

Brans-Dicke

Application of PPN formalism to GR & Brans-Dicke theory
deflection time delay of light
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.
experimental results
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)
summary
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.
thank you
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
ad