Krylov complexity grows quadratically in pure Lifshitz backgrounds and its late-time exponent is controlled by the hyperscaling violation parameter, with a special oscillatory regime.
Lifshitz Singularities
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abstract
Lifshitz spacetimes are possible gravitational duals to strongly coupled field theories with an anisotropic scaling symmetry. These spacetimes however, have a null curvature singularity. We find that higher dimensional embeddings of Lifshitz also have a similar singularity. We study the propagation of test strings in this background and find that they become infinitely excited if they try to propagate through the singularity. This means that the Lifshitz geometry is unstable and will receive large corrections in string theory.
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Treating the cosmological constant as pressure in black hole thermodynamics yields an extended dictionary with enthalpy, thermodynamic volume, and chemical-like phase transitions including Van der Waals behavior, reentrant transitions, and triple points.
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Black hole chemistry: thermodynamics with Lambda
Treating the cosmological constant as pressure in black hole thermodynamics yields an extended dictionary with enthalpy, thermodynamic volume, and chemical-like phase transitions including Van der Waals behavior, reentrant transitions, and triple points.