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

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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?




  • 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 spacetimes

(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



Massless scalar field
Massless scalar field spacetimes

(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 spacetimes

(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.



Scalar field
Scalar field spacetimes


Are spikes really smoothed out use pamr to see
Are spikes really smoothed out? spacetimesUse PAMR to see.


Conclusions
Conclusions spacetimes

  • 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.


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