pp -waves as exact solutions to ghost-free infinite derivative gravity

Abstract

We construct exact pp-wave solutions of ghost-free infinite derivative 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. I. INTRODUCTIONAmong the small scale modifications of Einstein's theory of General Relativity (GR), infinite derivative gravity (IDG) [1-3] seems to be a viable candidate to have a complete theory in the UV scale (short distances). A particular form of IDG is free from the Ostragradsky type instabilities and black hole or cosmological type singularities. The theory is described by a Lagrangian density built from analytic form factors which lead to non-local interactions. The propagator of ghost and singularity free IDG in flat background is obtained by the modification of a pure GR propagator via an exponential of an entire function that has no roots in the finite domain [2,4]. This modification provides that the theory does not have ghost-like instabilities and extra degree of freedom (DOF) other than the massless graviton. On the other hand, an infinite derivative extension of GR describes non-singular Newtonian potential for a point-like source at small distances [2,5]. This result is extended to the case where point-like sources also have velocities, spins, and orbital motion which leads to spin-spin and spin-orbit interactions in addition to mass-mass interactions [6]. It was shown that not only mass-mass interaction but also spin-spin and spin orbit interactions are non-singular in the UV regime of non-locality. Hence, the theory is well-behaved in the small scale unlike GR. Furthermore, power counting arguments have been recently studied for renormalizability discussion and it is shown that loop-diagrams beyond one-loop may give finite result with dressed propagators [3,[7][8][9][10][11]. Moreover, IDG may be devoid of black hole and cosmological Big Bang type singularities at a linear and non-linear level [1,2,9,[12][13][14][15][16][17][18][19][20]. These encouraging developments led us to study exact solutions of the theory.There are many works and some books on finding and classifying the exact solutions of Einstein's gravity [21]. Furthermore, some exact solutions are studied in detail in some specific modified gravity theories, such as the quadratic gravity [22][23][24][25][26][27], higher order theories of gravity [28], f (Riemann) theories [29], f (R µν ) theories [30] and f (R) theories [31]. On the other hand, although IDG received attention in the recent literature, exact solutions of the theory have not been studied at a non-linear level 1 since the field equations are very lengthy and complicated. At the linearized level around a flat background, some specific solutions have been found: a non-singular rotating solution without ring singularity was studied in [33], a solution for an electric point char...

Impulsive waves in ghost-free infinite derivative gravity in anti–de Sitter spacetime

“…It was shown that IDG may avoid not only black-hole type singularities [26][27][28][29][30][31][32][33], but also topological defects such as p branes [34], cosmic strings [35], and NUT-like singularities [36]. The exact pp-wave solutions have been studied in [37].…”

Nondiffracting gravitational waves

“…( 8), to put the metric (7) in the Kerr-Schild form ds 2 = d X 2 + dY 2 − du dV + du 2 (X 2 − Y 2 )d 2 u L/L. For these classes of metrics linear and non-linear theories coincide under certain conditions [48].…”

Generalized ghost-free propagators in nonlocal field theories

“…[20] for a more general treatment including some non-maximally symmetric spacetime. It was also noticed that the presence of nonlocality can regularize infinities and many efforts have been made towards the resolution of black hole [17,18,[21][22][23][24][25][26][27][28][29][30][31][32][33] and cosmological [16,[34][35][36][37] singularities. At the quantum level, the high energy behavior of loop integrals has been investigated in [38][39][40][41] and properties of causality and unitarity in [42,43] and [44][45][46][47], respectively.…”