Energy in generic higher curvature gravity theories

By S. Deser, B. Tekin. 2002

444 citations recorded by the source corpus.

We define and compute the energy of higher curvature gravity theories in arbitrary dimensions. Generically, these theories admit constant curvature vacua (even in the absence of an explicit cosmological constant), and asymptotically constant curvature solutions with nontrivial energy properties. For concreteness, we study quadratic curvature models in detail. Among them, the one whose action is the square of the traceless Ricci tensor always has zero energy, unlike conformal (Weyl) gravity. We also study the string-inspired Einstein-Gauss-Bonnet model and show that both its flat and anti–de Sitter vacua are stable.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d480c706271399d6bcb0aa665f9d25714e7938ea

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Citations in the corpus

Warped AdS3 black holes (2008, methodology): “Closely related black objects were first discussed in [13, 14] and further studied in [39, 15] where their conserved ADT charges [40, 41, 42, 43] and some of their thermodynamic properties were computed.”
Kerr-CFT and gravitational perturbations (2009, methodology): “63) Now, assuming that ξ is a Killing field of the background, a standard manipulation [28, 29, 30] based on the second-order Einstein equation (3.”
Higher Order Gravity Theories and Their Black Hole Solutions (2008, background): “Discussions on issues of energy, stability and the hamiltonian formalism have been carried out in [21], [26] [27].”
f(R) Theories Of Gravity (2008, background): “…f(R)gµν = κGTµν , (18) ∇̄λ (√−gf ′(R)gµν ) = 0, (19) 6 Energy supertensors and pseudotensors in Palatini f(R) gravity were studied in (Barraco et al., 1999; Borowiec et al., 1994, 1998; Ferraris et al., 1992) and alternative energy definitions were given in (Deser and Tekin, 2002, 2003a,b, 2007).”
AdS and Lifshitz black holes in conformal and Einstein-Weyl gravities (2012, methodology): “The energy density can be calculated using the Deser-Tekin or AMD methods, giving E = M/(6π).”
Boundary charges in gauge theories: using Stokes theorem in the bulk (2003, methodology): “In future work, we plan to study general conditions under which the n 2 forms are path independent and apply the formalism to more complicated theories, for instance the higher curvature gravity theories considered in [38, 8, 39, 40 ], or more exotic black hole solutions involving scalar fields lik”
Comparison between various notions of conserved charges in asymptotically AdS spacetimes (2005, methodology): “hat our deﬁnition is equivalent to the spinor method in ddimensions, thereby generalizing a result of Davis [28] in d= 4. However, comparison with the Abbott-Deser approach [8]and its generalizations [29,30,31], as well as with the KBL approach [9, 10], is postponed for future investigation. In sect”
Modified Gravity and Cosmology (2011, unknown): “(851) is +M on both branches [415, 416, 1010].”
Surface charge algebra in gauge theories and thermodynamic integrability (2007, methodology): “In the Lagrangian framework, a variety of approaches have been proposed: pseudotensors [9], Komar integrals [10], Noether’s method applied to linearized field equations [11, 12, 13], a quasi-local approach [14, 15] and covariant phase space methods [16, 17, 18, 19, 20, 21, 22, 23].”
The Lovelock Black Holes (2008, methodology): “In five-dimensions this is given by the Boulware-Deser solution [34], whose most important properties we review.”
Advanced Lectures on General Relativity (2018, methodology): “The definition of surface charges using the equations of motion was developed for Einstein gravity and higher curvature theories in [9, 10, 11].”