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

Giacchini, Breno L.; Netto, Tibério de Paula

doi:10.1140/epjc/s10052-019-6727-2

Cited by 35 publications

(58 citation statements)

References 117 publications

(408 reference statements)

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“…For regularity properties of higher derivative gravity theories which contain at least six derivatives, see[56,57] 11. We would like to thank the referee to bring this point to our attention.…”

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confidence: 99%

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

Kilicarslan

2019

Phys. Rev. D

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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...

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confidence: 99%

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

Kilicarslan

2019

Phys. Rev. D

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“…Now considerφ(s) defined bỹ where we again assume that the contour could be closed to encircle all of poles. Then using the Cauchy residue theorem 13 we havẽ…”

Section: Calculation Of the Tracementioning

confidence: 99%

“…By the inverse Mellin transform (C.4), we can write for small t Once again being sloppy about the contour and not pretending to be rigorous we can read of poles of Γ(s)ζ P (s): Res(Γ(s)ζ P (s))| s= d−n m = a n (P ) . (C.19) 13 Here by χ (k) we denote in a standard way the k-th derivative of the cut-off function with respect to its argument p: χ (k) = d k χ(p) dp k .…”

Section: Calculation Of the Tracementioning

confidence: 99%

Spectral action approach to higher derivative gravity

2020

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We study the spectral action approach to higher derivative gravity. The work focuses on the classical aspects. We derive the complete and simplified form of the purely gravitational action up to the 6-derivative terms. We also derive the equivalent forms of the action, which might prove useful in different applications, namely Riemann-and Weyl-dominated representations. The spectral action provides a rather rigid structure of the higher derivative part of the theory. We discuss the possible consequences of this rigidness. As one of the applications, we check whether the conformal backgrounds are preferred in some way on the classical level, with the conclusion that at this level, there is no obvious reason for such a preference, the space S 1 × S 3 studied in earlier works being a special case. Some other possible properties of the higher derivative gravity given by the spectral action are briefly discussed.1 The presence of this function χ(p) and the scale Λ is the reason why the spectral triple almost fixes the spectral action. As we will discuss, they should be considered as independent inputs of the theory, presumably fixed by some fundamental theory of QG.2 Another nice feature of the spectral action is that Higgs field finds its natural place on the geometry side of the picture (rather than on the matter side which is completely encoded in the Hilbert space H). 3 The cut-off function is a non-local object so, strictly speaking it introduces the infinite number of parameters, but in a very controlled way, see below.

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“…Just as in general relativity [27], Schwarzschild spacetime is a stable solution in NLG at the linear level. Whether this solution also represents an actual, astrophysical black hole remains to be seen, since approximated solutions of the linearized equations of motion (EOM) look regular [28][29][30][31][32][33]. More recently, in [34] it was found that the NLG dynamics of small perturbations of Minkowski metric is the same as in Einstein gravity.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear stability in nonlocal gravity

2019

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We address the stability issue of Ricci-flat and maximally symmetric spacetimes in nonlocal gravity to all perturbative orders in the gravitational perturbation. Assuming a potential at least cubic in curvature tensors but quadratic in the Ricci tensor, our proof consists on a mapping of the stability analysis in nonlocal gravity to the same problem in Einstein-Hilbert theory. One of the consequences is that only the graviton field can propagate and the theory is ghost-free at all perturbative orders. All the results known in Einstein gravity in vacuum with or without a cosmological constant can be exported to the case of nonlocal gravity: if a spacetime is stable at all perturbative orders in Einstein gravity, it is stable also in nonlocal gravity. Minkowski and de Sitter spacetimes are particular examples. We also study how the theory affects the propagation of gravitational waves in a cosmological background.

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

Cited by 35 publications

References 117 publications

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

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

Spectral action approach to higher derivative gravity

Nonlinear stability in nonlocal gravity

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