How to tell a gravastar from a black hole (also when it is rotating...)

Axial-Perturbations analysisWe use a “triangular grid”,i.e a purely outgoing nullslicing, and evolve theperturbation equation afterintroducing an initialGaussian pulse. Thesolutionψis extracted at alarge distance and after theinitial transient has died off.

Rotating gravastarsIn a recent work (Cardoso et al, 2007), a generalization of the originalstatic, spherically symmetric gravastar model was considered, in orderto describe rotating gravastars.A slow rotation approximation was used to describe the axiallysymmetric spacetime of a rotating gravastar. It was argued thatgravastars might be unstable due to the ergoregion instability.The preliminary results obtained by Cardoso et al indicate that thetime scale of the instability could be very short when compared tothe Hubble time. Further investigation is still needed...

Rotating gravastarsds 2 = −e ν(r) dt 2 + e λ(r) dr 2 + r 2 dθ 2 + r 2 sin 2 θ (dφ − ω(r)dt) 2ω(r) gives the dragging of the inertial frameAnisotropic energy momentum tensorT µν = (ρ + p t )u µ u ν + p t g µν + (p r − p t )s µ s νΩSlow rotation approximation (to first order in )u µ u µ = −1 , s µ s µ = 1 , u µ s µ = 0 ,u r = u θ = 0 , u φ = Ωu t ,u t = [ −(g tt + 2Ωg tφ + Ω 2 g φφ ) ] −1/2Ω is the angular velocityof the gravastar

Ergoregion instability: effective potentialsfor a scalar field in thebackground metric, thereare the two rotationallysplit “effective potentials”V + and V − .ψ ,rr + m 2 T (r, Σ)ψ = 0 ,T = e λ−ν (Σ − V + )(Σ − V − ) ,V ± = −ω ± e ν 2rΣ = σ m

Size of the ergoregionThe size of the ergoregion increases with both the compactness andthe thickness of the shell. But there are constrains...

Where is an ergoregion possible?We have already discussed the spaceof possible solutions in the (µ, δ) planefor spherical g*’sThis spaceis furtherdivided ifrotation istaken intoaccountno ergoregion

Where is an ergoregion possible?For a given pointin the (µ, δ)plane it ispossible todetermine thecritical angularvelocity abovewhich anergoregion ispresent.G*’s with angular velocities smaller than the critical one do nothave an ergoregion and are therefore expected to be stable.WKB analysis or calculation of eigenfrequencies will then establishwhether unstable g*’s are so in a Hubble time...

Conclusionso g*’s are an ingenious solution of the Einstein eqs: can be arbitrarily compact, withouter surface just outside the horizon of BH of same masso Still unclear processes leading to formation of g*’s and if they exist at all. If exist,heat capacity of the surface high enough to avoid heating and black-body emissiono We have constructed a simple but general class of g*’s with the basic features ofthe thin-shell model but allows for a stability analysis.o Two basic questions have two basic answers: g*’s are stable (axial perturbations):can be discerned from a BH through the emission of GWs via QNM oscillationso Rotating g*’s could be subject to an “ergoregion instability” (Cardoso et al. 2007). Sofar, found the space of parameters that allows the existence of an ergoregion.o Interesting new result: an ergoregion is not present for all g*’s and hence somerotating g*’s could be ergoregion-stable.o Future work: compute eigenfrequencies of unstable g*’s and assess if instabilityoccurs on timescales shorter than Hubble time.

Where is an ergoregion possible?We have already discussed the spaceof possible solutions in the (µ, δ) planefor spherical g*’sThis spaceis furtherdivided ifrotation istaken intoaccountno ergoregion