Mahdi Godazgar

The Local symmetries of M-theory and their formulation in generalised geometry

A bstractIn the doubled field theory approach to string theory the T-duality group is promoted to a manifest symmetry at the expense of replacing ordinary Riemannian geometry with generalised geometry on a doubled space. The local symmetries are then given by a generalised Lie derivative and its associated algebra. This paper constructs an analogous structure for the extended geometry of M-theory. A crucial by-product of this construction is the derivation of the physical section condition for M-theory formulated in an extended space.

NR/HEP: roadmap for the future

Physic in curved spacetime describes a multitude of phenomena, ranging from astrophysics to high-energy physics (HEP). The last few years have witnessed further progress on several fronts, including the accurate numerical evolution of the gravitational field equations, which now allows highly nonlinear phenomena to be tamed. Numerical relativity simulations, originally developed to understand strong-field astrophysical processes, could prove extremely useful to understand HEP processes such as trans-Planckian scattering and gauge–gravity dualities. We present a concise and comprehensive overview of the state-of-the-art and important open problems in the field(s), along with a roadmap for the next years.

Spinor classification of the Weyl tensor in five dimensions

We investigate the spinor classification of the Weyl tensor in five dimensions due to De Smet. We show that a previously overlooked reality condition reduces the number of possible types in the classification. We classify all vacuum solutions belonging to the most special algebraic type. The connection between this spinor and the tensor classification due to Coley, Milson, Pravda and Pravdova is investigated and the relation between most of the types in each of the classifications is given. We show that the black ring is algebraically general in the spinor classification.

Linear Mode Stability of the Kerr-Newman Black Hole and Its Quasinormal Modes

We provide strong evidence that, up to 99.999% of extremality, Kerr-Newman black holes (KNBHs) are linear mode stable within Einstein-Maxwell theory. We derive and solve, numerically, a coupled system of two partial differential equations for two gauge invariant fields that describe the most general linear perturbations of a KNBH. We determine the quasinormal mode (QNM) spectrum of the KNBH as a function of its three parameters and find no unstable modes. In addition, we find that the lowest radial overtone QNMs that are connected continuously to the gravitational ℓ=m=2 Schwarzschild QNM dominate the spectrum for all values of the parameter space (m is the azimuthal number of the wave function and ℓ measures the number of nodes along the polar direction). Furthermore, the (lowest radial overtone) QNMs with ℓ=m approach Reω=mΩH(ext) and Imω=0 at extremality; this is a universal property for any field of arbitrary spin |s|≤2 propagating on a KNBH background (ω is the wave frequency and ΩH(ext) the black hole angular velocity at extremality). We compare our results with available perturbative results in the small charge or small rotation regimes and find good agreement.

The perturbation theory of higher-dimensional spacetimes in the manner of Teukolsky

We consider the possibility of deriving a decoupled equation in terms of Weyl tensor components for gravitational perturbations of the Schwarzschild?Tangherlini solution. We find that a particular gauge invariant component of the Weyl tensor does decouple and argue that this corresponds to the vector modes of Ishibashi and Kodama. Also, we construct a Hertz potential map for solutions of the electromagnetic and gravitational perturbation equations of a higher-dimensional Kundt background using the decoupled equation of Durkee and Reall. Motivated by the recent work of Guica and Strominger, we use this to construct the asymptotic behaviour of metric perturbations of the NHG of the 5D cohomogeneity-1 Myers?Perry black hole.

An SO(3)×SO(3) invariant solution of D = 11 supergravity

A bstractWe construct a new SO(3)×SO(3) invariant non-supersymmetric solution of the bosonic field equations of D = 11 supergravity from the corresponding stationary point of maximal gauged N = 8 supergravity by making use of the non-linear uplift formulae for the metric and the 3-form potential. The latter are crucial as this solution appears to be inaccessible to traditional techniques of solving Einstein’s field equations, and is arguably the most complicated closed form solution of this type ever found. The solution is also a promising candidate for a stable non-supersymmetric solution of M-theory uplifted from gauged supergravity. The technique that we present here may be applied more generally to uplift other solutions of gauged supergravity.

Embedding of gauged STU supergravity in eleven dimensions

The consistency of the embedding of four-dimensional SO(8) gauged N=8 supergravity into eleven-dimensional supergravity, where the internal directions are compactified on a seven-sphere, was established by de Wit and Nicolai in the 1980s. The reduction ansatz for the eleven-dimensional metric, and for some of the components of the 4-form field strength, were found at that time, and recently the complete expression for the 4-form reduction has been obtained. The expressions are quite complicated, and in many practical applications it would be sufficient to know the ansatz for a subset of the four-dimensional fields. In this paper, we obtain explicit expressions for the embedding of the truncation of the full N=8 gauged theory to the N=2 gauged STU supergravity. This corresponds, in the bosonic sector, to a consistent truncation of the N=8 supergravity fields to those that are singlets under the U(1)^4 Cartan subalgebra of SO(8). This truncation to STU supergravity, which comprises N=2 supergravity coupled to three vector multiplets, suffices, for example, for lifting the general 8-charge asymptotically-AdS rotating black holes to eleven dimensions. We also give two distinct further truncations to N=2 supergravities coupled to single vector multiplets.

Algebraic classification of five-dimensional spacetimes using scalar invariants

There are a number of algebraic classifications of spacetimes in higher dimensions utilizing alignment theory, bivectors and discriminants. Previous work gave a set of necessary conditions in terms of discriminants for a spacetime to be of a particular algebraic type. We demonstrate the discriminant approach by applying the techniques to the Sorkin–Gross–Perry soliton, the supersymmetric and doubly spinning black rings and some other higher dimensional spacetimes. We show that even in the case of some very complicated metrics, it is possible to compute the relevant discriminants and extract useful information from them.

Symmetries at the black hole horizon

We determine the asymptotic symmetry group of Killing horizons by choosing Gaussian null coordinates in the neighbourhood of the horizon and boundary conditions that respect the leading order terms in the metric. The analysis divides naturally into the two cases of subextremal and extremal horizons. In general, we find rather involved asymptotic symmetry generators that nevertheless involve supertranslations and Killing vectors on the compact horizon. The most striking observation is the difference in the dependence on the coordinate along the horizon; we relate this to the redshift effect for subextremal horizons. We consider the spherically symmetric case as a special and illuminating example.

Twisting algebraically special solutions in five dimensions

We determine the general form of the solutions of the five-dimensional vacuum Einstein equations with cosmological constant for which (i) the Weyl tensor is everywhere type II or more special in the null alignment classification of Coley et al, and (ii) the 3 × 3 matrix encoding the expansion, shear and twist of the aligned null direction has rank 2. The dependence of the solution on two coordinates is determined explicitly, so the Einstein equation reduces to PDEs in the three remaining coordinates, just as for four-dimensional (4d) algebraically special solutions. The solutions fall into several families. One of these consists of warped products of 4d algebraically special solutions. The others are new.