The DOI matches its Crossref record.
Critical Gravity in Four Dimensions
Open accessAbstract
We study four-dimensional gravity theories that are rendered renormalizable by the inclusion of curvature-squared terms to the usual Einstein action with a cosmological constant. By choosing the parameters appropriately, the massive scalar mode can be eliminated and the massive spin-2 mode can become massless. This "critical" theory may be viewed as a four-dimensional analogue of chiral topologically massive gravity, or of critical "new massive gravity" with a cosmological constant, in three dimensions. We find that the on-shell energy for the remaining massless gravitons vanishes. There are also logarithmic spin-2 modes, which have positive energy. The mass and entropy of standard Schwarzschild-type black holes vanish. The critical theory might provide a consistent toy model for quantum gravity in four dimensions.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
de Rham, C. (2014) · Living Reviews in Relativity · doi:10.12942/lrr-2014-7 · Cited by 1,120
Nordstrom's scalar theory of gravity and the equivalence principle
Deruelle, N. (2011) · General Relativity and Gravitation · doi:10.1007/s10714-011-1247-x · Cited by 59
Types III andNsolutions to quadratic gravity
Málek, T., & Pravda, V. (2011) · Physical Review D · doi:10.1103/physrevd.84.024047 · Cited by 33
Metadata
- Authors
- Lü, H., & Pope, C. N.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2011-05-06
- Volume
- 106
- Issue
- 18
- Pages
- 181302-181302
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2027548982
- Cited by
- 254
- References
- 0
- FWCI
- 20.27
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Critical Gravity in Four Dimensions. https://app.cochat.ai/papers/10.1103/physrevlett.106.181302
- The paper
- Lü, H., & Pope, C. N. (2011). Critical Gravity in Four Dimensions. Physical Review Letters. https://doi.org/10.1103/physrevlett.106.181302
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
