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arXiv · 1704.05493

Lichnerowicz Modes and Black Hole Families in Ricci Quadratic Gravity

H. Lu·A. Perkins·C. N. Pope·K. S. Stelle
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Abstract

A new branch of black hole solutions occurs along with the standard Schwarzschild branch in $n$-dimensional extensions of general relativity including terms quadratic in the Ricci tensor. The standard and new branches cross at a point determined by a static negative-eigenvalue eigenfunction of the Lichnerowicz operator, analogous to the Gross-Perry-Yaffe eigenfunction for the Schwarzschild solution in standard $n=4$ dimensional general relativity. This static eigenfunction has two r\^oles: both as a perturbation away from Schwarzschild along the new black-hole branch and also as a threshold unstable mode lying at the edge of a domain of Gregory-Laflamme-type instability of the Schwarzschild solution for small-radius black holes. A thermodynamic analogy with the Gubser and Mitra conjecture on the relation between quantum thermodynamic and classical dynamical instabilities leads to a suggestion that there may be a switch of stability properties between the old and new black-hole branches for small black holes with radii below the branch crossing point.

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H. Lu, A. Perkins, C. N. Pope, K. S. Stelle. 2017-04-18. Lichnerowicz Modes and Black Hole Families in Ricci Quadratic Gravity. https://doi.org/10.1103/physrevd.96.046006

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