Abstract
Strong cosmic censorship conjecture has been one of the most important leap of faith in the context of general relativity, providing assurance in the deterministic nature of the associated field equations. Though it holds well for asymptotically flat spacetimes, a potential failure of the strong cosmic censorship conjecture might arise for spacetimes inheriting Cauchy horizon along with a positive cosmological constant. We have explicitly demonstrated that violation of the censorship conjecture holds true in the presence of a Maxwell field even when higher spacetime dimensions are invoked. In particular, for a higher dimensional Reissner-Nordström-de Sitter black hole the violation of cosmic censorship conjecture is at a larger scale compared to the four dimensional one, for certain choices of the cosmological constant. On the other hand, for a brane world black hole, the effect of extra dimension is to make the violation of cosmic censorship conjecture weaker. For rotating black holes, intriguingly, the cosmic censorship conjecture is always respected even in presence of higher dimensions. A similar scenario is also observed for a rotating black hole on the brane.
Highlights
A generic initial data, it is not possible to extend the spacetime across the Cauchy horizon, such that the spacetime metric is still twice differentiable [5]
Strong cosmic censorship conjecture asserts that the dynamics of gravity can be formulated in a deterministic manner
In presence of a positive cosmological constant, it turns out, the metric can be safely extended beyond the Cauchy horizon with locally square integrable connections, if the decay rate of any perturbing scalar field living in the spacetime becomes comparable to the blueshift at the Cauchy horizon
Summary
In this paper we will be working with spacetimes inheriting extra spatial dimensions and it is legitimate to ask whether the above condition on β, namely eq (1.2), still results into violation of strong cosmic censorship conjecture, even for higher dimensional black holes. Following the same analogy as the spherically symmetric spacetime, for rotating higher dimensional black hole spacetime as well, the scalar field can be decomposed into individual parts depending on time and the angular coordinates, while the radial part satisfies a Schrodinger-like second order differential equation with certain potential [67, 68]. In this case as well the differential equation for the radial part can be solved in the near Cauchy horizon limit, yielding two independent solutions as in eq (2.1). Based on the above discussion, we provide an estimation of the parameter β in the eikonal approximation, using the Lyapunov exponent associated with circular null geodesics
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