Metric fluctuations in higher-dimensional black holes

We investigated the impact of metric fluctuations on the higher-dimensional black hole geometry. We generalized the four-dimensional model to higher dimensions to treat quantum vacuum fluctuations by the classical approach. A fluctuating black hole is portrayed by a higher-dimensional Vaidya metric with a spherically oscillating mass. Assuming a small fluctuation amplitude, we employed a perturbation method to obtain a radially outgoing null geodesic equation up to the second order in the fluctuation. Furthermore, the fluctuation of the event horizon up to the second order depends on the number of spacetime dimensions. Therefore, the time-averaged values of the thermodynamic variables defined at the horizon also feature dimension-dependent correction terms. A general solution was obtained for rays propagating near the horizon within a fluctuating geometry. Upon examining this in a large D limit, we found that a complete solution can be obtained in a compact form.

Automated summary

We studied the effects of metric fluctuations on the geometry of higher-dimensional black holes and extended the four-dimensional model to higher dimensions to account for quantum vacuum fluctuations. Using a perturbation method for small fluctuation amplitudes, we obtained the null geodesic equation for radially outgoing rays up to second order in the fluctuations. The fluctuation of the event horizon and the thermodynamic variables defined at the horizon also have dimension-dependent correction terms up to second order. A general solution for rays propagating near the horizon in a fluctuating geometry was derived, and in the large D limit, a compact form solution was found.