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...

We construct a Weyl-invariant extension of topologically massive gravity which, remarkably, turns out to include topologically massive electrodynamics, with a Proca mass term, conformally coupled to a scalar field. The action has no dimensionful parameters, therefore, the masses are generated via symmetry breaking either radiatively in flat backgrounds or spontaneously in constant curvature backgrounds. The broken phase of the theory, generically, has a single massive spin-2 and a massive spin-1 excitation. Chiral gravity in asymptotically anti-de Sitter spacetimes does not arise as a low energy theory, while chiral gravity in de Sitter spacetime is not ruled out.

A form of infinite derivative gravity is free from ghost-like instabilities with improved small scale behavior. In this theory, we calculate the tree-level scattering amplitude and the corresponding weak field potential energy between two localized covariantly conserved spinning point-like sources that also have velocities and orbital motion. We show that the spin-spin and spin-orbit interactions take the same form as in Einstein's gravity at large separations, whereas at small separations, the results are different. We find that not only the usual Newtonian potential energy but also the spin-spin and spin-orbit interaction terms in the potential energy are non-singular as one approaches r → 0.PACS numbers: * Electronic address: ercan.kilicarslan@usak.edu.tr 1 For recent developments on IDG, see [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].

We study the constraints coming from local causality requirement in various 2 + 1 dimensional dynamical theories of gravity. In topologically massive gravity, with a single parity non-invariant massive degree of freedom, and in new massive gravity, with two massive spin-2 degrees of freedom, causality and unitarity are compatible with each other and both require the Newton's constant to be negative. In their extensions, such as the Born-Infeld gravity and the minimal massive gravity the situation is similar and quite different from their higher dimensional counterparts, such as quadratic (e.g., Einstein-Gauss-Bonnet) or cubic theories, where causality and unitarity are in conflict. We study the problem both in asymptotically flat and asymptotically anti-de Sitter spaces.

We revisit the problem of the bulk-boundary unitarity clash in 2 + 1 dimensional gravity theories, which has been an obstacle in providing a viable dual two-dimensional conformal field theory for bulk gravity in anti-de Sitter (AdS) spacetime. Chiral gravity, which is a particular limit of cosmological topologically massive gravity (TMG), suffers from perturbative log-modes with negative energies inducing a non-unitary logarithmic boundary field theory. We show here that any f (R) extension of TMG does not improve the situation. We also study the perturbative modes in the metric formulation of minimal massive gravityoriginally constructed in a first-order formulation-and find that the massive mode has again negative energy except in the chiral limit. We comment on this issue and also discuss a possible solution to the problem of negative energy modes. In any of these theories, the infinitesimal dangerous deformations might not be integrable to full solutions; this suggests a linearization instability of AdS spacetime in the direction of the perturbative log-modes.