Abstract
We investigate the stability of the inner horizon of a rotating BTZ black hole. We show that linear perturbations arising from smooth initial data are arbitrarily differentiable at the inner horizon if the black hole is sufficiently close to extremality. This is demonstrated for scalar fields, for massive Chern-Simons fields, for Proca fields, and for massive spin-2 fields. Thus the strong cosmic censorship conjecture is violated by a near-extremal BTZ black hole in a large class of theories. However, we show that a weaker \\rough" version of the conjecture is respected. We calculate the renormalized energymomentum tensor of a scalar field in the Hartle-Hawking state in the BTZ geometry. We show that the result is finite at the inner horizon of a near-extremal black hole. Hence the backreaction of vacuum polarization does not enforce strong cosmic censorship.
Highlights
We will consider the behaviour of linear scalar field perturbations of the BTZ spacetime
We investigate the stability of the inner horizon of a rotating BTZ black hole
For λγ ≥ 1 we are forced to choose H±∓λγ = 0. Either of these conditions lead to standard boundary conditions for ΦM γ and its first radial derivative (ΦM γ) of the form we discussed in section 2.1, provided we identify the dimensions of our two scalar fields as ∆ = {λγ, 2+λγ}
Summary
Non-zero matter fields will affect the geometry beyond the Cauchy horizon so that it differs from the metric obtained via analytic continuation of BTZ. U+ = −e−κ+u , V+ = eκ+v , φ+ = φ − Ω+t These coordinates allow the metric to be analytically extended into region II In these coordinates the metric is ds2 = −f dv2 + 2dvdr + r2 dφ − Ωdv 2 This metric can be analytically extended across the future event horizon HR+ (at r = r+) into region II so these coordinates cover regions I and II of figure 1. These coordinates are smooth at CH+L (i.e. at r = r−). We will use (2.22) to present our results in terms ∆ (instead of μ) because ∆ uniquely determines both the mass and the boundary conditions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
