Consistency Problems of Conformal Killing Gravity

Abstract

We show that gravity field equations based on a tensor with rank greater than 2 have consistency problems in the sense that integration constants in the solutions, such as the parameter $m$ in the Schwarzschild metric, do not allow for an interpretation in terms of conserved quantities in the theory. The recently introduced Conformal Killing Gravity, an interesting extension of General Relativity that inherits all the solutions of the latter, and defined with a rank-3 tensor field equation that does not arise from a diffeomorphism-invariant action, is plagued with this problem. In this theory, it is not clear at all how one can define the energy and angular momentum for black hole solutions, or define the analogues of the formulas, such as the quadrupole formula, in the weak field limit for gravitational waves emitted by compact sources.

11 pages, v2 matches the published version

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Cited by in corpus (6)

• Black Hole Thermodynamics in Harada's inspired theory of gravity: Stability, Phase Structure and Geometrothermodynamics
• Note on conserved currents in static Conformal Killing Gravity
• Constraints on cosmological parameters and CMB first acoustic peak in conformal Killing gravity
• Black hole solutions in Cotton gravity coupled to nonlinear electrodynamics
• Thermodynamic formulation of Cotton gravity in the Codazzi parametrization
• Generalized Vaidya Spacetime in Cotton and Conformal Killing Theories