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

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.

13 pages, references added, end of the Section IV-A is revised, version published in Phys. Rev. D

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• Quantum entanglement of masses with non-local gravitational interaction
• Impulsive waves in ghost free infinite derivative gravity in anti-de Sitter spacetime
• Nonlocal gravity with worldline inversion symmetry
• Ghost-free modification of the Polyakov action and Hawking radiation
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• Perturbations in higher derivative gravity beyond maximally symmetric spacetimes
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• An anisotropic bouncing universe in non-local gravity
• Retarded field of a uniformly accelerated source in non-local scalar field theory
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• Non-local scalar fields in static spacetimes via heat kernels
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• Non-locality and gravitoelectromagnetic duality
• Infinite derivative gravity resolves nonscalar curvature singularities
• Nondiffracting gravitational waves
• Nonlocal modification of the Kerr metric
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• Gravitational field of scalar lumps in higher-derivative gravity
• Exact gyratons in higher and infinite derivative gravity
• Ghost-free infinite-derivative dilaton gravity in two dimensions
• Smearing out contact terms in ghost-free infinite derivative quantum gravity
• Nonlocal scalar field in an external potential: WKB approximation
• Kerr-Schild perturbations in higher derivative gravity theories in $D$ dimensions