arXiv subjects

Mahdi Godazgar

Publications and source records attributed to Mahdi Godazgar.

At least 37 records · Page 2Linked to original sources

arXiv2017

Aretakis Charges and Asymptotic Null Infinity

We construct a relation between the Aretakis charge of any extreme black hole and the Newman-Penrose charge. This is achieved by constructing a conformal correspondence between extreme black holes and what we call weakly asymptotically flat space-times. Under this correspondence the Newman-Penrose charge of the weakly asymptotically flat space-time maps on to the Aretakis charge of the extreme black hole. Furthermore, we generalise the conformal isometry displayed by the extreme Reissner-Nordström solution to a novel conformal symmetry that acts within a class of static STU supergravity black holes.

hep-th↗

arXiv2017

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.

hep-th↗

arXiv2017

Entanglement entropy, the Einstein equation and the Sparling construction

We relate the recent derivation of the linearised Einstein equation on an AdS background from holographic entanglement entropy arguments to the Sparling construction: we derive the differential form whose exterior derivative gives the Einstein equation from the Sparling formalism. We develop the study of perturbations within the context of the Sparling formalism and find that the Sparling form vanishes for linearised perturbations on flat space.

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arXiv2016

The 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.

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arXiv2015

Consistent 4-form fluxes for maximal supergravity

We derive new ansaetze for the 4-form field strength of D=11 supergravity corresponding to uplifts of four-dimensional maximal gauged supergravity. In particular, the ansaetze directly yield the components of the 4-form field strength in terms of the scalars and vectors of the four-dimensional maximal gauged supergravity---in this way they provide an explicit uplift of all four-dimensional consistent truncations of D=11 supergravity. The new ansaetze provide a substantially simpler method for uplifting d=4 flows compared to the previously available method using the 3-form and 6-form potential ansaetze. The ansatz for the Freund-Rubin term allows us to conjecture a `master formula' for the latter in terms of the scalar potential of d=4 gauged supergravity and its first derivative. We also resolve a long-standing puzzle concerning the antisymmetry of the flux obtained from uplift ansaetze.

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arXiv2015

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 $3 \times 3$ matrix encoding the expansion, shear and twist of the aligned null direction has rank 2. The dependence of the solution on 2 coordinates is determined explicitly, so the Einstein equation reduces to PDEs in the 3 remaining coordinates, just as for four-dimensional algebraically special solutions. The solutions fall into several families. One of these consists of warped products of four-dimensional algebraically special solutions. The others are new.

gr-qc↗

arXiv2015

Linear mode stability of Kerr-Newman and its quasinormal modes

We provide strong evidence that, up to $99.999\%$ of extremality, Kerr-Newman black holes (KN BHs) are linear mode stable within Einstein-Maxwell theory. We derive and solve, numerically, a coupled system of two PDEs for two gauge invariant fields that describe the most general linear perturbations of a KN BH (except for trivial modes that shift the parameters of the solution). We determine the quasinormal mode (QNM) spectrum of the KN BH as a function of its three parameters and find no unstable modes. In addition, we find that the QNMs that are connected continuously to the gravitational $\ell=m=2$ Schwarzschild QNM dominate the spectrum for all values of the parameter space ($m$ is the azimuthal number of the wave function and $\ell$ measures the number of nodes along the polar direction). Furthermore, all QNMs with $\ell=m$ approach Re$\,ω= m Ω_H^{ext}$ and Im$\,ω=0$ at extremality; this is a universal property for any field of arbitrary spin $|s|\leq 2$ propagating on a KN BH background ($ω$ is the wave frequency and $Ω_H^{ext}$ the BH angular velocity at extremality). We compare our results with available perturbative results in the small charge or small rotation regimes and find good agreement. We also present a simple proof that the Regge-Wheeler (odd) and Zerilli (even) sectors of Schwarzschild perturbations must be isospectral.

gr-qc↗

arXiv2015

An SO(3)$\times$SO(3) invariant solution of $D=11$ supergravity

We construct a new SO(3)$\times$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.

hep-th↗

arXiv2015

Uniqueness of the Kerr-de Sitter spacetime as an algebraically special solution in five dimensions

We determine the most general solution of the five-dimensional vacuum Einstein equation, allowing for a cosmological constant, with (i) a Weyl tensor that is type II or more special in the classification of Coley et al., (ii) a non-degenerate "optical matrix" encoding the expansion, rotation and shear of the aligned null direction. The solution is specified by three parameters. It is locally isometric to the 5d Kerr-de Sitter solution, or related to this solution by analytic continuation or taking a limit. This is in contrast with four dimensions, where there exist infinitely many solutions with properties (i) and (ii).

gr-qc↗

arXiv2014

Supersymmetric E$_{7(7)}$ Exceptional Field Theory

We give the supersymmetric extension of exceptional field theory for E$_{7(7)}$, which is based on a $(4+56)$-dimensional generalized spacetime subject to a covariant constraint. The fermions are tensors under the local Lorentz group ${\rm SO}(1,3)\times {\rm SU}(8)$ and transform as scalar densities under the E$_{7(7)}$ (internal) generalized diffeomorphisms. The supersymmetry transformations are manifestly covariant under these symmetries and close, in particular, into the generalized diffeomorphisms of the 56-dimensional space. We give the fermionic field equations and prove supersymmetric invariance. We establish the consistency of these results with the recently constructed generalized geometric formulation of $D=11$ supergravity.

hep-th↗

arXiv2014

Einstein-Cartan Calculus for Exceptional Geometry

In this paper we establish and clarify the link between the recently found E7 generalised geometric structures, which are based on the SU(8) invariant reformulation of D=11 supergravity proposed long ago, and newer results obtained in the framework of recent approaches to generalised geometry, where E7 duality is built in and manifest from the outset. In making this connection, the so-called generalised vielbein postulate plays a key role. We explicitly show how this postulate can be used to define an E7 valued affine connection and an associated covariant derivative, which yields a generalised curvature tensor for the E7 based exceptional geometry. The analysis of the generalised vielbein postulate also provides a natural explanation for the emergence of the embedding tensor from higher dimensions.

hep-th↗

arXiv2013

The embedding tensor of Scherk-Schwarz flux compactifications from eleven dimensions

We study the Scherk-Schwarz reduction of D=11 supergravity with background fluxes in the context of a recently developed framework pertaining to D=11 supergravity. We derive the embedding tensor of the associated four-dimensional maximal gauged theories directly from eleven dimensions by exploiting the generalised vielbein postulates, and by analysing the couplings of the full set of 56 electric and magnetic gauge fields to the generalised vielbeine. The treatment presented here will apply more generally to other reductions of $D=11$ supergravity to maximal gauged theories in four dimensions.

hep-th↗

arXiv2013

Non-linear Kaluza-Klein theory for dual fields

We present non-linear uplift ansaetze for all the bosonic degrees of freedom and dual fields in the 7-sphere reduction of D=11 supergravity to maximal SO(8) gauged supergravity and test them for the SO$(7)^{\pm}$ invariant solutions. In particular, we complete the known ansaetze for the internal components of the metric and 4-form flux by constructing a non-linear ansatz for the internal components of the dual 7-form flux. Furthermore, we provide ansaetze for the complete set of 56 vector fields, which are given by more general structures than those available from standard Kaluza-Klein theory. The novel features encountered here have no conventional geometric interpretation and provide a new perspective on Kaluza-Klein theory. We study the recently found set of generalised vielbein postulates and, for the 7-sphere compactification, we show that they reduce to the E7(7) Cartan equation of maximal SO(8) gauged supergravity in four dimensions. The significance of this framework for a higher-dimensional understanding of the embedding tensor and other gauged maximal supergravities is briefly discussed.

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arXiv2013

Generalised geometry from the ground up

Extending previous work on generalised geometry, we explicitly construct an E7-valued vielbein in eleven dimensions that encompasses the scalar bosonic degrees of freedom of D=11 supergravity, by identifying new "generalised vielbeine" in eleven dimensions associated with the dual 6-form potential and the dual graviton. By maintaining full on-shell equivalence with the original theory at every step, our construction altogether avoids the constraints usually encountered in other approaches to generalised geometry and, as a side product, also furnishes the non-linear ansatz for the dual (magnetic) 7-form flux for any non-trivial compactification of D=11 supergravity, complementing the known non-linear ansaetze for the metric and the 4-form flux. A preliminary analysis of the generalised vielbein postulate for the new vielbein components reveals tantalising hints of new structures beyond D=11 supergravity and ordinary space-time covariance, and also points to the possible D=11 origins of the embedding tensor. We discuss the extension of these results to E8.

hep-th↗

arXiv2013

Duality completion of higher derivative corrections

We present a new method for completing higher derivative corrections for theories that exhibit duality symmetries under reduction. This proposal is based on the observation that duality symmetry in the reduced theory highly constrains the form of the unreduced theory. We apply this idea to closed bosonic string theory and complete the Riemann squared term to simply derive the known full tree-level effective action to order alpha'.

hep-th↗

arXiv2013

E8 duality and dual gravity

We construct the non-linear realisation of the E8 motion group and compare this with the bosonic sector of eleven dimensional supergravity. The construction naturally leads to the introduction of a new potential field. We identify this new field with the dual gravity field by considering the reduction of the eleven-dimensional theory to three dimensions.

hep-th↗

arXiv2013

Testing the non-linear flux ansatz for maximal supergravity

We put to test the recently proposed non-linear flux ansatz for maximal supergravity in eleven dimensions, which gives the seven-dimensional flux in terms of the scalars and pseudoscalars of maximal N=8 supergravity, by considering a number of non-trivial solutions of gauged supergravity for which the higher dimensional solutions are known. These include the G$_2$ and SU(4)$^-$ invariant stationary points. The examples considered constitute a very non-trivial check of the ansatz, which it passes with remarkable success.

hep-th↗

arXiv2012

Peeling of the Weyl tensor and gravitational radiation in higher dimensions

The peeling behaviour of the Weyl tensor near null infinity is determined for an asymptotically flat higher dimensional spacetime. The result is qualitatively different from the peeling property in 4d. To leading order, the Weyl tensor is type N. The first subleading term is type II. The next term is algebraically general in 6 or more dimensions but in 5 dimensions another type N term appears before the algebraically general term. The Bondi energy flux is written in terms of "Newman-Penrose" Weyl components.

gr-qc↗