A note on the definition of gravitational energy for quadratic curvature gravity via topological regularization

Within the framework of four-dimensional quadratic curvature gravities in the appearance of a negative cosmological constant,a definition for the gravitational energy of solutions with anti-de Sitter(AdS)asymptotics was put forward by Giribet et al.[Phys.Rev.D 98044046(2018)].This was achieved by adding proper topological invariant terms to the gravity action to render the variation problem well-posed.We prove that the definition via the procedure of topological regularization can be covered by our previous work[Int.J.Mod.Phys.A 352050102(2020)]in four dimensions.Motivated by this,we further generalize the results to generic diffeomorphism invariant theories of gravity in arbitrary even dimensions.

Improved Reall-Santos method for AdS black holes in general 4-derivative gravities

For asymptotically flat black holes,Reall-Santos method is a convenient tool to compute leading higher derivative corrections to the thermodynamic quantities without actually solving the modified field equations.However,there are subtleties in its generalization to asymptotically AdS black holes with general higher derivative corrections.First of all,it is necessary to know all the higher derivative holographic counterterms and the surface terms implementing the variational principle and subtracting the divergence.One then needs to solve for the modified AdS radius and rescale the time coordinate in an appropriate way such that the induced metric on the conformal boundary of AdS black hole is not modified.We observe that Reall-Santos method can be directly applied to a particular 4-derivative gravity model,known as the Einstein-Weyl gravity,which does not modify the AdS radius and requires only the Gibbons-Hawking-York term and holographic counterterms for the 2-derivative theory.We thus suggest that to compute the thermodynamic quantities of AdS black holes in general 4-derivative theories of gravity,one simply needs to transform it to a Einstein-Weyl gravity with identical thermodynamic variables by appropriate field redefinitions.We explicitly verify this proposal with spherically-symmetric and static charged black holes in Einstein-Maxwell theory extended with generic 4-derivative interactions.

Negative corrections to black hole entropy from string theory

We report for the first time that in heterotic string compactified on 4-torus or equivalently IIA string compactified on K3,the leading α′corrections to the rotating black string entropy at fixed conserved charges can be negative.This further implies that the correction to the mass of extremal rotating string is positive,opposite to the standard expectation from the weak gravity conjecture.Our result suggests that the validity of positivity of entropy shift due to higher order operators depends on other factors omitted previously in the effective field theory analysis.

Higher derivative scalar-tensor monomials and their classification

We make a full classification of scalar monomials built of the Riemann curvature tensor up to the quadratic order and of the covariant derivatives of the scalar field up to the third order.From the point of view of the effective field theory,the third or even higher order covariant derivatives of the scalar field are of the same importance as the higher curvature terms,and thus should be taken into account.Moreover,the higher curvature terms and the higher order derivatives of the scalar field are complementary to each other,of which novel ghostfree combinations may exist.We make a systematic classification of all the possible monomials,according to the numbers of the Riemann tensor and the higher derivatives of the scalar field in each monomial.A complete basis of monomials at each order is derived,of which the linear combinations may yield novel ghostfree Lagrangians.We also develop diagrammatic representations for the monomials,which may help to simplify the analysis.