Gravitational Waves and Degrees of Freedom in Higher Derivative Gravity

Patric H\"olscher

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Gravitational Waves and Degrees of Freedom in Higher Derivative Gravity

Patric Hölscher

General Relativity and Quantum Cosmology · Submitted 25 Jun 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For the special case of quadratic gravity in four-dimensional spacetime, we show that only the quadrupole moment contributes to the gravitational radiation from an idealized binary system.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,329 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.33 · compares with prior results 0.06 · mentions code or data availability 0.01.

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We study the degrees of freedom of the metric in a general class of higher derivative gravity models, which are interesting in the context of quantum gravity as they are (super)renormalizable. First, we linearize the theory for a flat background metric in Teyssandier gauge for an arbitrary number of spacetime dimensions $D$. The higher-order derivative field equations for the metric perturbation can be decomposed into tensorial and scalar field equations resembling massless and massive wave equations. For the massive tensor field in $D$-dimensions we demonstrate that the harmonic gauge condition is induced dynamically and only the transverse modes are excited in the presence of a matter source. For the special case of quadratic gravity in four-dimensional spacetime, we show that only the quadrupole moment contributes to the gravitational radiation from an idealized binary system.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the degrees of freedom of the metric in a general class of higher derivative gravity models, which are interesting in the context of quantum gravity as they are (super)renormalizable.	contribution 0.82	0.68	0.07	asserted 0.93
s1	First, we linearize the theory for a flat background metric in Teyssandier gauge for an arbitrary number of spacetime dimensions $D$.	method 0.99	0.94	0.03	asserted 0.89
s2	The higher-order derivative field equations for the metric perturbation can be decomposed into tensorial and scalar field equations resembling massless and massive wave equations.	result 0.65	0.84	0.13	asserted 1.00
s3	For the massive tensor field in $D$-dimensions we demonstrate that the harmonic gauge condition is induced dynamically and only the transverse modes are excited in the presence of a matter source.	result 0.99	0.93	0.18	asserted 1.00
s4	For the special case of quadratic gravity in four-dimensional spacetime, we show that only the quadrupole moment contributes to the gravitational radiation from an idealized binary system.	result 0.99	0.94	0.24	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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The paper

Original abstract

We study the degrees of freedom of the metric in a general class of higher derivative gravity models, which are interesting in the context of quantum gravity as they are (super)renormalizable. First, we linearize the theory for a flat background metric in Teyssandier gauge for an arbitrary number of spacetime dimensions $D$. The higher-order derivative field equations for the metric perturbation can be decomposed into tensorial and scalar field equations resembling massless and massive wave equations. For the massive tensor field in $D$-dimensions we demonstrate that the harmonic gauge condition is induced dynamically and only the transverse modes are excited in the presence of a matter source. For the special case of quadratic gravity in four-dimensional spacetime, we show that only the quadrupole moment contributes to the gravitational radiation from an idealized binary system.

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2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 1 paper

Unlike General Relativity, where the leading order gravitational radiation is produced by quadrupole moments, the additional degree of freedom predicts gravitational radiation of all multipoles, in particular monopoles and dipoles, as this is the case for the most alternative gravity theories known today.

On Gravitational Radiation in Quadratic $f(R)$ Gravity · 0.95

Papers citing it · 1 sentence without a confident label

Cites it as background 1 paper

There are also models that study the generation and properties of gravitational waves [ref] .

Second-order corrections to Starobinsky inflation · Introduction · 0.98

What it cites · 12 sentences without a confident label

Uses the method or tool of 1 paper

Inserting [ref] into [ref] and following the steps in [ref] one finds

Interesting features of a general class of higher derivative theories of quantum gravity · Linearized Wave Equations · 0.95

Cites as support 1 paper

This leads to an exponential suppression for the massive spin-0 mode and to a negligible contribution to the gravitational radiation (see [ref] for details).

Astrophysical Gravitational Waves in Conformal Gravity · The Massive Spin-0 Field · 0.96

Cites as background 3 papers

In this work, we want to analyze aspects of the gravitational wave solutions in generalized higher-derivative gravity [ref] (see also [ref] for studies of measurable effects in the low-energy regime).

Weak-field limit and regular solutions in polynomial higher-derivative gravities · Introduction · 0.96
Besides that, the small value of the cosmological constant (compared to the zero-point energy density from particle physics) is not understood [ref] .

TASI Lectures on the Cosmological Constant · Introduction · 0.87
Besides that, the small value of the cosmological constant (compared to the zero-point energy density from particle physics) is not understood [ref] .

The Cosmological Constant · Introduction · 0.87

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