Singularities does matter matter
This presentation is the property of its rightful owner.
Sponsored Links
1 / 18

Singularities: does matter matter? PowerPoint PPT Presentation


  • 81 Views
  • Uploaded on
  • Presentation posted in: General

Singularities: does matter matter?. Gravitational collapse and singularities Homogeneous anisotropic spacetimes Vacuum Stiff fluid Scalar field with exponential potential. Gravitational collapse and singularities.

Download Presentation

Singularities: does matter matter?

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


Singularities does matter matter

Singularities: does matter matter?


Singularities does matter matter

  • Gravitational collapse and singularities

  • Homogeneous anisotropic spacetimes

  • Vacuum

  • Stiff fluid

  • Scalar field with exponential potential


Gravitational collapse and singularities

Gravitational collapse and singularities

  • A massive star collapses to form a black hole: a singularity hidden by an event horizon

  • Exact solutions (Schwarzschild, FRW) with singularities are known

  • Singularity theorems tell us singularities form in the general case

  • What are the properties of general singularities?


Does matter matter

Does matter matter?

  • As a star collapses, the matter becomes more compressed and therefore more strongly gravitating.

  • As gravity gets strong, the nonlinearities of Einstein’s equation become important.

  • Which of these two effects is more important?


Frw spacetimes

FRW spacetimes


Homogeneous anisotropic spacetime

Homogeneous, anisotropic spacetime


Singularities does matter matter

  • If w<1 then matter doesn’t matter

  • More general homogeneous anisotropic spacetimes also behave like this,except there are “bounces” where the coefficients c1, c2, c3 change rapidly.


Numerical simulations of inhomogeneous anisotropic spacetimes

Numerical simulations of inhomogeneous, anisotropic spacetimes

  • Use CMC slicing

  • Use scale invariant variables like


Vacuum

Vacuum

(DG PRL 93, 161101 (2004))

  • Spatial derivatives become negligible

  • But spacetime does not become homogeneous

  • In fact spikes form at isolated points

  • However, at each point the dynamics is of a homogeneous spacetime with “bounces” in the anisotropy


Scale invariant shear in vacuum

Scale invariant shear in vacuum


Massless scalar field

Massless scalar field

(DG and Josh Curtis

PRD 72, 064003 (2005))

Similar behavior, except that there is a last bounce.


Scalar field with exponential potential

Scalar field with exponential potential

(DG, F. Pretorius, W. Lim, P. Steinhardt, in progress)

Such potentials are used in the cyclic universe scenario of Steinhardt and Turok.

Does the universe become homogeneous as the singularity is approached?

Yes, the spacetime becomes homogeneous and isotropic.


Scale invariant shear

Scale invariant shear


Scalar field

Scalar field


Are spikes really smoothed out use pamr to see

Are spikes really smoothed out?Use PAMR to see.


Conclusions

Conclusions

  • Extreme forms of matter can homogenize and isotropize the singularity.

  • We need to know what matter is like at extreme conditions to know what singularities are like.

  • Quantum resolution of FRW may not be just a toy problem.


  • Login