Braneworld localisation in hyperbolic spacetime

We present a construction employing a type IIA supergravity and 3-form flux background together with an NS5-brane that localises massless gravity near the 5-brane worldvolume. The nonsingular underlying type IIA solution is a lift to 10D of the vacuum solution of the 6D Salam-Sezgin model and has a hyperbolic ${\cal H}^{(2,2)}\times S^1$ structure in the lifting dimensions. A fully back-reacted solution including the NS5-brane is constructed by recognising the 10D Salam-Sezgin vacuum solution as a "brane resolved through transgression." The background hyperbolic structure plays a key r\^ole in generating a mass gap in the spectrum of the transverse-space wave operator, which gives rise to the localisation of gravity on the 6D NS5-brane worldvolume, or, equally, in a further compactification to 4D. Also key to the successful localisation of gravity is the specific form of the corresponding transverse wavefunction Schr\"odinger problem, which asymptotically involves a $V=-1/(4\rho^2)$ potential, where $\rho$ is the transverse-space radius, and for which the NS5-brane source gives rise to a specific choice of self-adjoint extension for the transverse wave operator. The corresponding boundary condition as $\rho\to0$ ensures the masslessness of gravity in the effective braneworld theory. Above the mass gap, there is a continuum of massive states which give rise to small corrections to Newton's law.Comment: 32 pages, 2 figures; misprints corrected & some clarification adde

Conservation laws for self-adjoint first order evolution equations

In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using the recent Ibragimov's Theorem on conservation laws, we establish the conservation laws of the equations admiting self-adjoint equations. We illustrate our results applying them to the inviscid Burgers' equation. In particular an infinite number of new symmetries of these equations are found and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of Nonlinear Mathematical Physic

Dual gravitational charges and soft theorems

Abstract We consider the consequences of the dual gravitational charges for the phase space of radiating modes, and find that they imply a new soft NUT theorem. In particular, we argue that the existence of these new charges removes the need for imposing boundary conditions at spacelike infinity that would otherwise preclude the existence of NUT charges.</jats:p

Tower of subleading dual BMS charges

We supplement the recently found dual gravitational charges with dual charges for the whole BMS symmetry algebra. Furthermore, we extend the dual charges away from null infinity, defining subleading dual charges. These subleading dual charges complement the subleading BMS charges in the literature and together account for all the NewmanPenrose charges

Consistent Warped-Space Kaluza-Klein Reductions, Half-Maximal Gauged Supergravities and CP^n Constructions

We obtain new consistent Kaluza-Klein embeddings of the gauged supergravities with half of maximal supersymmetry in dimensions D=7, 6, 5 and 4. They take the form of warped embeddings in type IIA, type IIB, M-theory and type IIB respectively, and are obtained by performing Kaluza-Klein circle reductions or T-duality transformations on Hopf fibres in S^3 submanifolds of the previously-known sphere reductions. The new internal spaces are in some sense ``mirror manifolds'' that are dual to the original internal spheres. The vacuum AdS solutions of the gauged supergravities then give rise to warped products with these internal spaces. As well as these embeddings, which have singularities, we also construct new non-singular warped Kaluza-Klein embeddings for the D=5 and D=4 gauged supergravities. The geometry of the internal spaces in these cases leads us to study Fubini-Study metrics on complex projective spaces in some detail.Comment: Latex, 29 pages, typos corrected and references adde

Conformal symmetries for extremal black holes with general asymptotic scalars in STU supergravity

Abstract We present a construction of the most general BPS black holes of STU supergravity ($$\mathcal{N}$$ N = 2 supersymmetric D = 4 supergravity coupled to three vector super-multiplets) with arbitrary asymptotic values of the scalar fields. These solutions are obtained by acting with a subset of the global symmetry generators on STU BPS black holes with zero values of the asymptotic scalars, both in the U-duality and the heterotic frame. The solutions are parameterized by fourteen parameters: four electric and four magnetic charges, and the asymptotic values of the six scalar fields. We also present BPS black hole solutions of a consistently truncated STU supergravity, which are parameterized by two electric and two magnetic charges and two scalar fields. These latter solutions are significantly simplified, and are very suitable for further explicit studies. We also explore a conformal inversion symmetry of the Couch-Torrence type, which maps any member of the fourteen-parameter family of BPS black holes to another member of the family. Furthermore, these solutions are expected to be valuable in the studies of various swampland conjectures in the moduli space of string compactifications.</jats:p

Subleading BMS charges and fake news near null infinity

In this paper we establish a relation between the non-linearly conserved Newman-Penrose charges and certain subleading terms in a large-$r$ expansion of the BMS charges in an asymptotically-flat spacetime. We define the subleading BMS charges by considering a $1/r$-expansion of the Barnich-Brandt prescription for defining asymptotic charges in an asymptotically-flat spacetime. At the leading order, i.e. $1/r^0$, one obtains the standard BMS charges, which would be integrable and conserved in the absence of a flux term at null infinity, corresponding to gravitational radiation, or Bondi news. At subleading orders, analogous terms in general provide obstructions to the integrability of the corresponding charges. Since the subleading terms are defined close to null infinity, but vanish actually at infinity, the analogous obstructions are not associated with genuine Bondi news. One may instead describe them as corresponding to "fake news." At order $r^{-3}$, we find that a set of integrable charges can be defined and that these are related to the ten non-linearly conserved Newman-Penrose charges.Comment: 34 pages;few minor typos correcte

Black holes in D=4 higher-derivative gravity

Extensions of Einstein gravity with higher-order derivative terms are natural generalizations of Einstein’s theory of gravity. They may arise in string theory and other effective theories, as well as being of interest in their own right. In this paper we study static black-hole solutions in the example of Einstein gravity with additional quadratic curvature terms in four dimensions. A Lichnerowicz-type theorem simplifies the analysis by establishing that they must have vanishing Ricci scalar curvature. By numerical methods we then demonstrate the existence of further black-hole solutions over and above the Schwarzschild solution. We discuss some of their thermodynamic properties, and show that they obey the first law of thermodynamics