REVIEW 2 cited by
On integrability of the Killing equation
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
Killing tensor fields have been thought of as describing hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Many problems in classical mechanics can be formulated as geodesic problems in curved spaces and spacetimes, and thus solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate the equations of motion. In this paper we attempt to formulate the integrability conditions of the Killing equation, which serve to put an upper bound on the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. To this end, we first show the prologation for the Killing equation in a manner that uses Young symmetrizers. Then, using the prolonged equations, we provide the integrability conditions explicitly.
Forward citations
Cited by 2 Pith papers
-
From (Hidden) Symmetries to Stealth Solutions
Killing-Yano tensors generate p-form stealth solutions in a bumblebee-type Proca theory with fine-tuned curvature terms on arbitrary backgrounds.
-
On symmetry operators for the Maxwell equation on the Kerr-NUT-(A)dS spacetime
Using the Eisenhart-Duval lift, the authors reproduce previously known commuting symmetry operators for the Maxwell (LFKK) equation on Kerr-NUT-(A)dS spacetimes in covariant form, and construct the analogous operator ...
Discussion (0). Continue with ORCID to comment.