2014/01/21 by Chethan N. Gowdigere, Gowdigere, Chethan N., Abhass Kumar +5 · 1 citation
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.1401.5189
openalex publication_date 2014/01/21 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We study the differentiability of the metric and other fields at any of the\nhorizons of multi center Reissner-Nordstrom black hole solutions in d \≥ 5\nand of multi center M2 brane solutions. The centers are distributed in a\nplane in transverse space, hence termed coplanar. We construct the Gaussian\nnull co-ordinate system for the neighborhood of a horizon by solving the\ngeodesic equations in expansions of (appropriate powers of) the affine\nparameter. Organizing the harmonic functions that appear in the solution in\nterms of what can be called generalized Gegenbauer polynomials is key to\nobtaining the solution to the geodesic equations in a compact and manageable\nform. We then compute the metric and other fields in the Gaussian null\nco-ordinate system and find that the differentiability of the coplanar solution\nis \identical to the differentiability of the collinear solution (centers\ndistributed on a line in transverse space). The results of this paper thus run\ncounter to a suggestion in the literature that posits reduction in the degree\nof smoothness to accompany reduction in symmetries. We end the paper with a\nconjecture on the degree of smoothness of the most general multi center\nsolution, the one with centers distributed arbitrarily and hence possessing no\ntransverse spatial isometries.\n