Lee–Wick black holes

Abstract

We derive and study an approximate static vacuum solution generated by a point-like source in a higher derivative gravitational theory with a pair of complex conjugate ghosts. The gravitational theory is local and characterized by a high derivative operator compatible with Lee-Wick unitarity. In particular, the tree-level two-point function only shows a pair of complex conjugate poles besides the massless spin two graviton. We show that singularity-free black holes exist when the mass of the source M exceeds a critical value Mcrit. For M > Mcrit the spacetime structure is characterized by an outer event horizon and an inner Cauchy horizon, while for M = Mcrit we have an extremal black hole with vanishing Hawking temperature. The evaporation process leads to a remnant that approaches the zero-temperature extremal black hole state in an infinite amount of time. *

Effective delta sources and regularity in higher-derivative and ghost-free gravity

“…We omit the result as the expression is not illuminating. Instead, it is more instructive to use the expansion (18) in association to (19) to show that, near the origin,…”

Weak-field limit and regular solutions in polynomial higher-derivative gravities

“…Then, a, b and c are also polynomials, but with different coefficients, and the equations for χ and ω are essentially the same. Therefore, we explicitly work out the solution for (14) and, mutatis mutandis, write down the solution for (15). The solution for χ can be easily found by means of the heat kernel approach, based on the Laplace transformation, as carried out in [51].…”

“…The last assumption is physically justified by the requirement that the potential decays to zero at large distances, as well as to avoid tachyons on the model. The former assumption, however, is related to the heat kernel method used to solve (14) and the premise that the operatorĤ −1 has the form of (21). Actually, the solution (31) also holds for the cases in which the polynomial a(−ξ) has roots with | Im m i | > Re m i > 0, as the Bessel functions provide the analytical continuation of each term in (28) viewed as function of an arbitrary m 2 i with Re m i > 0.…”

“…In this regard, two models have been the subject of interesting investigations in recent years. The first one we mention is the Lee-Wick gravity [11,12]-see, e.g., [10,[13][14][15][16] for further developments and applications. This theory is defined by the Einstein-Hilbert action enlarged by curvature-squared terms which contain polynomial functions of the d'Alembert operator, such as R µν F 1 (✷)R µν and RF 2 (✷)R. A general action of this type can be called polynomial higher-derivative gravity and was introduced in [5]; the Lee-Wick gravity assumes, furthermore, that the polynomials F i are such that all the massive poles of the propagator which correspond to ghost modes are complex.…”

Quantum radiation from a sandwich black hole

“…Similar theory appears naturally also in the context of noncommutative geometry deformation of the Einstein gravity [11,12] (see a review [13] and references therein). The application of the ghost free theory of gravity to the problem of singularities in cosmology and black holes can be found in [14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In spite of a number of promising results, we still do not have a final conclusive solution of this problem in the ghost-free gravity.…”