For a ghost-free modification of the Polyakov action on a fixed 2D black hole background, the Hawking flux at infinity is unchanged; only diagonal stress-energy components and entropy get non-local corrections.
$pp$-waves as exact solutions to ghost-free infinite derivative gravity
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abstract
We construct exact pp-wave solutions of ghost-free infinite derivative gravity and demonstrate that the sourceless theory does not bring any pp-wave solutions save for that of Einstein's gravity. These waves described in the Kerr-Schild form also solve the linearized field equations of the theory. We also find an exact gravitational shock wave with non-singular curvature invariants and with a finite limit in the ultraviolet regime of non-locality which is in contrast to the divergent limit in Einstein's theory.
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Ghost-free modification of the Polyakov action and Hawking radiation
For a ghost-free modification of the Polyakov action on a fixed 2D black hole background, the Hawking flux at infinity is unchanged; only diagonal stress-energy components and entropy get non-local corrections.