A deformed Calogero model accommodates unitary principal series states of sl(2,R) via operator domain changes, preserving unitarity and invariance while altering integrability, with solutions for N=2 and 3.
Scaling and Universality in Extremal Black Hole Perturbations
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abstract
We show that the emergent near-horizon conformal symmetry of extremal black holes gives rise to universal behavior in perturbing fields, both near and far from the black hole horizon. The scale-invariance of the near-horizon region entails power law time-dependence with three universal features: (1) the decay off the horizon is always precisely twice as fast as the decay on the horizon; (2) the special rates of $1/t$ off the horizon and $1/\sqrt{v}$ on the horizon commonly occur; and (3) sufficiently high-order transverse derivatives grow on the horizon (Aretakis instability). The results are simply understood in terms of near-horizon ($\mathrm{AdS}_2$) holography. We first show how the general features follow from symmetry alone and then go on to present the detailed universal behavior of scalar, electromagnetic, and gravitational perturbations of $d$-dimensional electrovacuum black holes.
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Couch-Torrence inversion matches Newman-Penrose charges at null infinity to Aretakis charges near horizons for D3-branes in D=10 and bound states in D=4,5, with supersymmetry mapping scalar charges to spinorial dilatino charges.
Black holes with infinitely degenerate horizons are proposed to be stable against Aretakis instability, potentially serving as end states.
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Medicine show: A Calogero model with principal series states
A deformed Calogero model accommodates unitary principal series states of sl(2,R) via operator domain changes, preserving unitarity and invariance while altering integrability, with solutions for N=2 and 3.
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Couch-Torrence conformal inversion, supersymmetry and conserved charges for D3-branes
Couch-Torrence inversion matches Newman-Penrose charges at null infinity to Aretakis charges near horizons for D3-branes in D=10 and bound states in D=4,5, with supersymmetry mapping scalar charges to spinorial dilatino charges.
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Taming the Aretakis instability: extremal black holes with multi-degenerate horizons
Black holes with infinitely degenerate horizons are proposed to be stable against Aretakis instability, potentially serving as end states.
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