Singularities: does matter matter?

• Gravitational collapse and singularities

• Homogeneous anisotropic spacetimes

• Vacuum

• Stiff fluid

• Scalar field with exponential potential

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?

• 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

)1(3

2

222222

)3/8()/(

)(

wa

wP

aa

dzdydxadtds

Homogeneous, anisotropic spacetime

3

22222222

a

wP

dzdydxdtds

)1(3

23

22

21

2

622

321

33

32

31

))(6/1(

)3/8()/(

0

//

//

//

waP

ccck

akaa

ccc

acaa

acaa

acaa

• 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

• Use CMC slicing• Use scale invariant

variables like H/

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

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

(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.

ceVV 0

Scale invariant shear

Scalar field

Are spikes really smoothed out?Use PAMR to see.

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.