Abstract
In this paper we discuss possible effects of non-locality in black hole spacetimes. We consider a two-dimensional theory in which the action describing matter is a ghost-free modification of the Polyakov action. For this purpose we write the Polyakov action in a local form by using an auxiliary scalar field and modify its kinetic term by including into it a non-local ghost-free form factor. We demonstrate that the effective stress-energy tensor is modified and we study its properties in a background of a two-dimensional black hole. We obtain the expression for the contribution of the ghost-free auxiliary field to the entropy of the black hole. We also demonstrate that if the back-reaction effects are not taken into account, such a ghost-free modification of the theory does not change the energy flux of the Hawking radiation measured at infinity. We illustrate the discussed properties for black hole solution of a 2D dilaton gravity model which admits a rather complete analytical study.
Highlights
Nonlocal field theories have a long history, especially in the context of attempts to manage the ultraviolet (UV) behavior of quantum scattering amplitudes
II we present the standard Polyakov action in a local form by introducing an auxiliary scalar field and the effective stress-energy tensor associated with this action
III we describe a ghost-free modification of the Polyakov action in the local form, obtain an expression for the effective stress-energy tensor of such a theory, and demonstrate that this tensor can be explicitly written as a sum of two terms
Summary
Nonlocal field theories have a long history, especially in the context of attempts to manage the ultraviolet (UV) behavior of quantum scattering amplitudes. The flux of Hawking radiation of an evaporating black hole is described by the retarded propagator of the corresponding scalar field [35] It might depend on the scale of nonlocality inherent to ghost-free theories. Suppose that gμν is a black hole solution of Sg1⁄2gμν In this given background, we may ask how the ghost-free deformation of the theory, described by Wmatter, affects the effective stress-energy tensor and the Hawking radiation of the black hole in particular.
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