Higher order gravities and the Strong Equivalence Principle

We show that, in all metric theories of gravity with a general covariant action, gravity couples to the gravitational energy-momentum tensor in the same way it couples to the matter energy-momentum tensor order by order in the weak field approximation around flat spacetime. We discuss the relation of this property to the Strong Equivalence Principle. We also study the gauge transformation properties of the gravitational energy-momentum tensor.Comment: Additional resulting the gauge transformation of the gravitational energy-momentum tensor and references added. 18 pages, no figure

Supersymmetric solutions of 4-dimensional supergravities

We review some general and recent results on the characterization and construction of timelike supersymmetric solutions of 4-dimensional supergravity theories.Comment: Latex2e, 14 pages. Contribution to the Proceedings of the IV Mexican Meeting in Mathematical and Experimental Physics held at El Colegio Nacional, M\'exico DF. July 19th to 23rd, 201

A Note on Supersymmetric Godel Black Holes, Strings and Rings of Minimal d=5 Supergravity

We show how any asymptotically flat supersymmetric solution of minimal d=5 supergravity with flat base space can be deformed into another supersymmetric asymptotically-Godel solution and apply this procedure to the recently found supersymmetric black-ring and black-string solutions.Comment: 9 pages, Latex2e. Additional references include

Extremality Versus Supersymmetry in Stringy Black Holes

We study general black-hole solutions of the low-energy string effective action in arbitrary dimensions using a general metric that can describe them all in a unified way both in the extreme and non-extreme cases. We calculate the mass, temperature and entropy and study which relations amongst the charges and the mass lead to extremality. We find that the temperature always vanishes in the extreme limit and we find that, for a set of n charges (no further reducible by duality) there are 2^{(n-1)} combinations of the charges that imply extremality. Not all of these combinations can be central charge eigenvalues and, thus, there are in general extreme black holes which are not supersymmetric (or ``BPS-saturated''). In the N=8 supergravity case we argue that the existence of roughly as many supersymmetric and non-supersymmetric extreme black holes suggests the existence of an underlying twelve-dimensional structure.Comment: Latex2e file with optional macros for small versions. References to Kutasov and Martinec's work adde

O(n,n) invariance and Wald entropy formula in the Heterotic Superstring effective action at first order in alpha'

We perform the toroidal compactification of the full Bergshoeff-de Roo version of the Heterotic Superstring effective action to first orderin $\alpha'$. The dimensionally-reduced action is given in a manifestly-O(n,n)-invariant form which we use to derive a manifestly-O(n,n)-invariant Wald entropy formula which we then use to compute the entropy of $\alpha'$-corrected, 4-dimensional, 4-charge, static, extremal, supersymmetric black holes.Comment: References and comments added. Version to be published in Journal of High Energy Physic

Non-Supersymmetric (but) Extreme Black Holes, Scalar Hair and Other Open Problems

We give a brief overview of black-hole solutions in four-dimensional supergravity theories and their extremal and supersymmetric limits. We also address problems like cosmic censorship and no-hair theorems in supergravity theories. While supergravity by itself seems not to be enough to enforce cosmic censorship and absence of primary scalar hair, superstring theory may be.Comment: Latex file, 18 pages (or less with optional macros included) Enhanced Version of the Contribution to the Proceedings of the XXXIII Karpacz Winter School of Theoretical Physics Duality, Strings and Fields, 13-22 February, Karpacz, Polan

On timelike supersymmetric solutions of gauged minimal 5-dimensional supergravity

We analyze the timelike supersymmetric solutions of minimal gauged 5-dimensional supergravity for the case in which the K\"ahler base manifold admits a holomorphic isometry and depends on two real functions satisfying a simple second-order differential equation. Using this general form of the base space, the equations satisfied by the building blocks of the solutions become of, at most, fourth degree and can be solved by simple polynomic ansatzs. In this way we construct two 3-parameter families of solutions that contain almost all the timelike supersymmetric solutions of this theory with one angular momentum known so far and a few more: the (singular) supersymmetric Reissner-Nordstr\"om-AdS solutions, the three exact supersymmetric solutions describing the three near-horizon geometries found by Gutowski and Reall, three 1-parameter asymptotically-AdS$_{5}$ black-hole solutions with those three near-horizon geometries (Gutowski and Reall's black hole being one of them), three generalizations of the G\"odel universe and a few potentially homogenous solutions. A key r\^ole in finding these solutions is played by our ability to write AdS$_{5}$'s K\"ahler base space ($\overline{\mathbb{CP}}^{2}$ or SU$(1,2)/$U$(2)$) is three different, yet simple, forms associated to three different isometries. Furthermore, our ansatz for the K\"ahler metric also allows us to study the dimensional compactification of the theory and its solutions in a systematic way.Comment: 57 pages. References and comments adde

T duality and Wald entropy formula in the Heterotic Superstring effective action at first order in α′\alpha'

We consider the compactification on a circle of the Heterotic Superstring effective action to first order in the Regge slope parameter $\alpha'$ and re-derive the $\alpha'$-corrected Buscher rules first found in arXiv:hep-th/9506156 , proving the T duality invariance of the dimensionally-reduced action to that order in $\alpha'$. We use Iyer and Wald's prescription to derive an entropy formula that can be applied to black-hole solutions which can be obtained by a single non-trivial compactification on a circle and discuss its invariance under the $\alpha'$-corrected T duality transformations. This formula has been successfully applied to $\alpha'$-corrected 4-dimensional non-extremal Reissner-Nordstr\"om black holes in arXiv:1910.14324 and we apply it here to a heterotic version of the Strominger-Vafa 5-dimensional extremal black hole.Comment: Version published in the journa