Sigbjorn Hervik - Profile on Academia.edu (original) (raw)

Papers by Sigbjorn Hervik

arXiv (Cornell University), Apr 6, 2015

We show that a metric of arbitrary dimension and signature which allows for a standard Wick-rotat... more We show that a metric of arbitrary dimension and signature which allows for a standard Wick-rotation to a Riemannian metric necessarily has a purely electric Riemann and Weyl tensor. 1 This is a not really a proper inner product since it is not positive definite, but rather a C-bilinear non-degenerate form defining a holomorphic inner product. 2 Let W and W be real slices of a holomorphic inner product space: (E, g). Assume they

We study Lorentzian spacetimes for which all scalar invariants constructed from the Riemann tenso... more We study Lorentzian spacetimes for which all scalar invariants constructed from the Riemann tensor and its covariant derivatives are constant (CSI spacetimes). We obtain a number of general results in arbitrary dimensions. We study and construct warped product CSI spacetimes and higher-dimensional Kundt CSI spacetimes. We show how these spacetimes can be constructed from locally homogeneous spaces and V SI spacetimes. The results suggest a number of conjectures. In particular, it is plausible that for CSI spacetimes that are not locally homogeneous the Weyl type is II, III, N or O, with any boost weight zero components being constant. We then consider the four-dimensional CSI spacetimes in more detail. We show that there are severe constraints on these spacetimes, and we argue that it is plausible that they are either locally homogeneous or that the spacetime necessarily belongs to the Kundt class of CSI spacetimes, all of which are constructed. The four-dimensional results lend support to the conjectures in higher dimensions.

arXiv (Cornell University), Jul 6, 2007

We study a class of constant scalar invariant (CSI) spacetimes, which belong to the higher-dimens... more We study a class of constant scalar invariant (CSI) spacetimes, which belong to the higher-dimensional Kundt class, that are solutions of supergravity. We review the known CSI supergravity solutions in this class and we explicitly present a number of new exact CSI supergravity solutions, some of which are Einstein.

Classical and Quantum Gravity, Oct 6, 2009

The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provide... more The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provides examples of future geodesically complete spacetimes that admit a 'kinematic singularity' at which the fluid congruence is inextendible but all frame components of the Weyl and Ricci tensors remain bounded. We show that for any positive integer n there are examples of Bianchi type V spacetimes admitting a kinematic singularity such that the covariant derivatives of the Weyl and Ricci tensors up to the nth order also stay bounded. We briefly discuss singularities in classical spacetimes.

Classical and Quantum Gravity, Jul 1, 2011

There are a number of algebraic classifications of spacetimes in higher dimensions utilizing alig... more 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.

It is well known that certain pp-wave metrics, belonging to a more general class of Ricci-flat ty... more It is well known that certain pp-wave metrics, belonging to a more general class of Ricci-flat type N, τi = 0, Kundt spacetimes, are universal and thus they solve vacuum equations of all gravitational theories with Lagrangian constructed from the metric, the Riemann tensor and its derivatives of arbitrary order. In this paper, we show (in an arbitrary number of dimensions) that in fact all Ricciflat type N, τi = 0, Kundt spacetimes are universal and we also generalize this result in a number of ways by relaxing τi = 0, Λ = 0 and type N conditions. First, we show that a universal spacetime is necessarily a CSI spacetime, i.e. all curvature invariants constructed from the Riemann tensor and its derivatives are constant. Then we focus on type N where we arrive at a simple necessary and sufficient condition: a type N spacetime is universal if and only if it is an Einstein Kundt spacetime. Similar statement does not hold for type III Kundt spacetimes, however, we prove that a subclass of...

Journal of High Energy Physics, 2020

We prove that a generalized Schwarzschild-like ansatz can be consistently employed to construct d... more We prove that a generalized Schwarzschild-like ansatz can be consistently employed to construct d-dimensional static vacuum black hole solutions in any metric theory of gravity for which the Lagrangian is a scalar invariant constructed from the Riemann tensor and its covariant derivatives of arbitrary order. Namely, we show that, apart from containing two arbitrary functions a(r) and f (r) (essentially, the gtt and grr components), in any such theory the line-element may admit as a base space any isotropy-irreducible homogeneous space. Technically, this ensures that the field equations generically reduce to two ODEs for a(r) and f (r), and dramatically enlarges the space of black hole solutions and permitted horizon geometries for the considered theories. We then exemplify our results in concrete contexts by constructing solutions in particular theories such as Gauss-Bonnet, quadratic, F(R) and F(Lovelock) gravity, and certain conformal gravities.

Physica Scripta, 2018

We consider four-dimensional spaces of neutral signature and give examples of universal spaces of... more We consider four-dimensional spaces of neutral signature and give examples of universal spaces of Walker type. These spaces have no analogue in other signatures in four dimensions and provide with a new class of spaces being universal.

Journal of Geometry and Physics, 2018

We show that a metric of arbitrary dimension and signature which allows for a standard Wick-rotat... more We show that a metric of arbitrary dimension and signature which allows for a standard Wick-rotation to a Riemannian metric necessarily has a purely electric Riemann and Weyl tensor. 1 This is a not really a proper inner product since it is not positive definite, but rather a C-bilinear non-degenerate form defining a holomorphic inner product. 2 Let W and W be real slices of a holomorphic inner product space: (E, g). Assume they

Classical and Quantum Gravity, 2018

We study universal electromagnetic (test) fields, i.e., p-forms fields F that solve simultaneousl... more We study universal electromagnetic (test) fields, i.e., p-forms fields F that solve simultaneously (virtually) any generalized electrodynamics (containing arbitrary powers and derivatives of F in the field equations) in n spacetime dimensions. One of the main results is a sufficient condition: any null F that solves Maxwell's equations in a Kundt spacetime of aligned Weyl and traceless-Ricci type III is universal (in particular thus providing examples of p-form Galileons on curved Kundt backgrounds). In addition, a few examples in Kundt spacetimes of Weyl type II are presented. Some necessary conditions are also obtained, which are particularly strong in the case n = 4 = 2p: all the scalar invariants of a universal 2-form in four dimensions must be constant, and vanish in the special case of a null F .

Journal of High Energy Physics, 2017

Universal spacetimes are exact solutions to all higher-order theories of gravity. We study these ... more Universal spacetimes are exact solutions to all higher-order theories of gravity. We study these spacetimes in four dimensions and provide necessary and sufficient conditions for universality for all Petrov types except of type II. We show that all universal spacetimes in four dimensions are algebraically special and Kundt. Petrov type D universal spacetimes are necessarily direct products of two 2-spaces of constant and equal curvature. Furthermore, type II universal spacetimes necessarily possess a null recurrent direction and they admit the above type D direct product metrics as a limit. Such spacetimes represent gravitational waves propagating on these backgrounds. Type III universal spacetimes are also investigated. We determine necessary and sufficient conditions for universality and present an explicit example of a type III universal Kundt non-recurrent metric.

Classical and Quantum Gravity, 2015

We study type II universal metrics of the Lorentzian signature. These metrics simultaneously solv... more We study type II universal metrics of the Lorentzian signature. These metrics simultaneously solve vacuum field equations of all theories of gravitation with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of an arbitrary order. We provide examples of type II universal metrics for all composite number dimensions. On the other hand, we have no examples for prime number dimensions and we prove the non-existence of type II universal spacetimes in five dimensions. We also present type II vacuum solutions of selected classes of gravitational theories, such as Lovelock, quadratic and L(Riemann) gravities.

ISRN Geometry, 2011

A classical solution is called universal if the quantum correction is a multiple of the metric. T... more A classical solution is called universal if the quantum correction is a multiple of the metric. Therefore, universal solutions play an important role in the quantum theory. We show that in a spacetime which is universal all scalar curvature invariants are constant (i.e., the spacetime is CSI).

Journal of Physics: Conference Series, 2015

We briefly summarize our recent results on universal spacetimes. We show that universal spacetime... more We briefly summarize our recent results on universal spacetimes. We show that universal spacetimes are necessarily CSI, i.e. for these spacetimes, all curvature invariants constructed from the Riemann tensor and its derivatives are constant. Then, we focus on type III universal spacetimes and discuss a proof of universality for a class of type III Kundt spacetimes. We also mention explicit examples of type III and II universal spacetimes.

Journal of Physics: Conference Series, 2015

Universal spacetimes are vacuum solutions to all theories of gravity with the Lagrangian L = L(g ... more Universal spacetimes are vacuum solutions to all theories of gravity with the Lagrangian L = L(g ab , R abcd , ∇a 1 R bcde , . . . , ∇a 1 ...ap R bcde ). Well known examples of universal spacetimes are plane waves which are of the Weyl type N. Here, we discuss recent results on necessary and sufficient conditions for all Weyl type N spacetimes in arbitrary dimension and we conclude that a type N spacetime is universal if and only if it is an Einstein Kundt spacetime. We also summarize the main points of the proof of this result.

Classical and Quantum Gravity, 2014

Universal spacetimes are spacetimes for which all conserved symmetric rank-2 tensors, constructed... more Universal spacetimes are spacetimes for which all conserved symmetric rank-2 tensors, constructed as contractions of polynomials from the metric, the Riemann tensor and its covariant derivatives of arbitrary order, are multiples of the metric. Consequently, metrics of universal spacetimes solve vacuum equations of all gravitational theories with Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its derivatives of arbitrary order. In the literature, universal metrics are also discussed as metrics with vanishing quantum corrections and as classical solutions to string theory. Widely known examples of universal metrics are certain Ricci-flat pp waves. In this paper, we start a general study of geometric properties of universal metrics in arbitrary dimension and we arrive at a broader class of such metrics. In contrast with pp waves, these universal metrics also admit non-vanishing cosmological constant and in general do not have to possess a covariantly constant or recurrent null vector field. First, we show that a universal spacetime is necessarily a CSI spacetime, i.e. all curvature invariants constructed from the Riemann tensor and its derivatives are constant. Then we focus on type N spacetimes, where we arrive at a simple necessary and sufficient condition: a type N spacetime is universal if and only if it is an Einstein Kundt spacetime. A class of type III Kundt universal metrics is also found. Several explicit examples of universal metrics are presented.

Physical Review Letters, 2013

We show that the recently found AdS-plane and AdS-spherical wave solutions of quadratic curvature... more We show that the recently found AdS-plane and AdS-spherical wave solutions of quadratic curvature gravity also solve the most general higher derivative theory in D-dimensions. More generally, we show that the field equations of such theories reduce to an equation linear in the Ricci tensor for Kerr-Schild spacetimes having type-N Weyl and traceless Ricci tensors.

Journal of Geometry and Physics, 2012

In this paper we present a number of four-dimensional neutral signature exact solutions for which... more In this paper we present a number of four-dimensional neutral signature exact solutions for which all of the polynomial scalar curvature invariants vanish (VSI spaces) or are all constant (CSI spaces), which are of relevence in current theoretical physics.

Classical and Quantum Gravity, 2013

We consider time reversal transformations to obtain twofold orthogonal splittings of any tensor o... more We consider time reversal transformations to obtain twofold orthogonal splittings of any tensor on a Lorentzian space of arbitrary dimension n. Applied to the Weyl tensor of a spacetime, this leads to a definition of its electric and magnetic parts relative to an observer (defined by a unit timelike vector field u), in any dimension. We study the cases where one of these parts vanishes in detail, i.e., purely electric (PE) or magnetic (PM) spacetimes. We generalize several results from four to higher dimensions and discuss new features of higher dimensions. For instance, we prove that the only permitted Weyl types are G, I i and D, and discuss the possible relation of u with the Weyl aligned null directions (WANDs); we provide invariant conditions that characterize PE/PM spacetimes, such as Bel-Debever-like criteria, or constraints on scalar invariants, and connect the PE/PM parts to the kinematic quantities of u; we present conditions under which direct product spacetimes (and certain warps) are PE/PM, which enables us to construct explicit examples. In particular, it is also shown that all static spacetimes are necessarily PE, while stationary spacetimes (such as spinning black holes) are in general neither PE nor PM. Whereas ample classes of PE spacetimes exist, PM solutions are elusive; specifically, we prove that PM Einstein spacetimes of type D do not exist, in any dimension. Finally, we derive corresponding results for the electric/magnetic parts of the Riemann tensor, which is useful when considering spacetimes with matter fields, and moreover leads to first examples of PM spacetimes in higher dimensions. We also note in passing that PE/PM Weyl (or Riemann) tensors provide examples of minimal tensors, and we make the connection hereof with the recently proved alignment theorem (Hervik 2011 Class. Quantum Grav. 28 215009). This in turn sheds new light on the classification of the Weyl tensors based on null alignment, providing a further invariant characterization

Classical and Quantum Gravity, 2004

In this paper we construct negatively curved Einstein spaces describing gravitational waves havin... more In this paper we construct negatively curved Einstein spaces describing gravitational waves having a solvegeometry wave-front (i.e., the wavefronts are solvable Lie groups equipped with a left-invariant metric). Using the Einstein solvmanifolds (i.e., solvable Lie groups considered as manifolds) constructed in a previous paper as a starting point, we show that there also exist solvegeometry gravitational waves. Some geometric aspects are discussed and examples of spacetimes having additional symmetries are given, for example, spacetimes generalising the Kaigorodov solution. The solvegeometry gravitational waves are also examples of spacetimes which are indistinguishable by considering the scalar curvature invariants alone.

arXiv (Cornell University), Apr 6, 2015

We show that a metric of arbitrary dimension and signature which allows for a standard Wick-rotat... more We show that a metric of arbitrary dimension and signature which allows for a standard Wick-rotation to a Riemannian metric necessarily has a purely electric Riemann and Weyl tensor. 1 This is a not really a proper inner product since it is not positive definite, but rather a C-bilinear non-degenerate form defining a holomorphic inner product. 2 Let W and W be real slices of a holomorphic inner product space: (E, g). Assume they

We study Lorentzian spacetimes for which all scalar invariants constructed from the Riemann tenso... more We study Lorentzian spacetimes for which all scalar invariants constructed from the Riemann tensor and its covariant derivatives are constant (CSI spacetimes). We obtain a number of general results in arbitrary dimensions. We study and construct warped product CSI spacetimes and higher-dimensional Kundt CSI spacetimes. We show how these spacetimes can be constructed from locally homogeneous spaces and V SI spacetimes. The results suggest a number of conjectures. In particular, it is plausible that for CSI spacetimes that are not locally homogeneous the Weyl type is II, III, N or O, with any boost weight zero components being constant. We then consider the four-dimensional CSI spacetimes in more detail. We show that there are severe constraints on these spacetimes, and we argue that it is plausible that they are either locally homogeneous or that the spacetime necessarily belongs to the Kundt class of CSI spacetimes, all of which are constructed. The four-dimensional results lend support to the conjectures in higher dimensions.

arXiv (Cornell University), Jul 6, 2007

We study a class of constant scalar invariant (CSI) spacetimes, which belong to the higher-dimens... more We study a class of constant scalar invariant (CSI) spacetimes, which belong to the higher-dimensional Kundt class, that are solutions of supergravity. We review the known CSI supergravity solutions in this class and we explicitly present a number of new exact CSI supergravity solutions, some of which are Einstein.

Classical and Quantum Gravity, Oct 6, 2009

The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provide... more The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provides examples of future geodesically complete spacetimes that admit a 'kinematic singularity' at which the fluid congruence is inextendible but all frame components of the Weyl and Ricci tensors remain bounded. We show that for any positive integer n there are examples of Bianchi type V spacetimes admitting a kinematic singularity such that the covariant derivatives of the Weyl and Ricci tensors up to the nth order also stay bounded. We briefly discuss singularities in classical spacetimes.

Classical and Quantum Gravity, Jul 1, 2011

There are a number of algebraic classifications of spacetimes in higher dimensions utilizing alig... more 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.

It is well known that certain pp-wave metrics, belonging to a more general class of Ricci-flat ty... more It is well known that certain pp-wave metrics, belonging to a more general class of Ricci-flat type N, τi = 0, Kundt spacetimes, are universal and thus they solve vacuum equations of all gravitational theories with Lagrangian constructed from the metric, the Riemann tensor and its derivatives of arbitrary order. In this paper, we show (in an arbitrary number of dimensions) that in fact all Ricciflat type N, τi = 0, Kundt spacetimes are universal and we also generalize this result in a number of ways by relaxing τi = 0, Λ = 0 and type N conditions. First, we show that a universal spacetime is necessarily a CSI spacetime, i.e. all curvature invariants constructed from the Riemann tensor and its derivatives are constant. Then we focus on type N where we arrive at a simple necessary and sufficient condition: a type N spacetime is universal if and only if it is an Einstein Kundt spacetime. Similar statement does not hold for type III Kundt spacetimes, however, we prove that a subclass of...

Journal of High Energy Physics, 2020

We prove that a generalized Schwarzschild-like ansatz can be consistently employed to construct d... more We prove that a generalized Schwarzschild-like ansatz can be consistently employed to construct d-dimensional static vacuum black hole solutions in any metric theory of gravity for which the Lagrangian is a scalar invariant constructed from the Riemann tensor and its covariant derivatives of arbitrary order. Namely, we show that, apart from containing two arbitrary functions a(r) and f (r) (essentially, the gtt and grr components), in any such theory the line-element may admit as a base space any isotropy-irreducible homogeneous space. Technically, this ensures that the field equations generically reduce to two ODEs for a(r) and f (r), and dramatically enlarges the space of black hole solutions and permitted horizon geometries for the considered theories. We then exemplify our results in concrete contexts by constructing solutions in particular theories such as Gauss-Bonnet, quadratic, F(R) and F(Lovelock) gravity, and certain conformal gravities.

Physica Scripta, 2018

We consider four-dimensional spaces of neutral signature and give examples of universal spaces of... more We consider four-dimensional spaces of neutral signature and give examples of universal spaces of Walker type. These spaces have no analogue in other signatures in four dimensions and provide with a new class of spaces being universal.

Journal of Geometry and Physics, 2018

We show that a metric of arbitrary dimension and signature which allows for a standard Wick-rotat... more We show that a metric of arbitrary dimension and signature which allows for a standard Wick-rotation to a Riemannian metric necessarily has a purely electric Riemann and Weyl tensor. 1 This is a not really a proper inner product since it is not positive definite, but rather a C-bilinear non-degenerate form defining a holomorphic inner product. 2 Let W and W be real slices of a holomorphic inner product space: (E, g). Assume they

Classical and Quantum Gravity, 2018

We study universal electromagnetic (test) fields, i.e., p-forms fields F that solve simultaneousl... more We study universal electromagnetic (test) fields, i.e., p-forms fields F that solve simultaneously (virtually) any generalized electrodynamics (containing arbitrary powers and derivatives of F in the field equations) in n spacetime dimensions. One of the main results is a sufficient condition: any null F that solves Maxwell's equations in a Kundt spacetime of aligned Weyl and traceless-Ricci type III is universal (in particular thus providing examples of p-form Galileons on curved Kundt backgrounds). In addition, a few examples in Kundt spacetimes of Weyl type II are presented. Some necessary conditions are also obtained, which are particularly strong in the case n = 4 = 2p: all the scalar invariants of a universal 2-form in four dimensions must be constant, and vanish in the special case of a null F .

Journal of High Energy Physics, 2017

Universal spacetimes are exact solutions to all higher-order theories of gravity. We study these ... more Universal spacetimes are exact solutions to all higher-order theories of gravity. We study these spacetimes in four dimensions and provide necessary and sufficient conditions for universality for all Petrov types except of type II. We show that all universal spacetimes in four dimensions are algebraically special and Kundt. Petrov type D universal spacetimes are necessarily direct products of two 2-spaces of constant and equal curvature. Furthermore, type II universal spacetimes necessarily possess a null recurrent direction and they admit the above type D direct product metrics as a limit. Such spacetimes represent gravitational waves propagating on these backgrounds. Type III universal spacetimes are also investigated. We determine necessary and sufficient conditions for universality and present an explicit example of a type III universal Kundt non-recurrent metric.

Classical and Quantum Gravity, 2015

We study type II universal metrics of the Lorentzian signature. These metrics simultaneously solv... more We study type II universal metrics of the Lorentzian signature. These metrics simultaneously solve vacuum field equations of all theories of gravitation with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of an arbitrary order. We provide examples of type II universal metrics for all composite number dimensions. On the other hand, we have no examples for prime number dimensions and we prove the non-existence of type II universal spacetimes in five dimensions. We also present type II vacuum solutions of selected classes of gravitational theories, such as Lovelock, quadratic and L(Riemann) gravities.

ISRN Geometry, 2011

A classical solution is called universal if the quantum correction is a multiple of the metric. T... more A classical solution is called universal if the quantum correction is a multiple of the metric. Therefore, universal solutions play an important role in the quantum theory. We show that in a spacetime which is universal all scalar curvature invariants are constant (i.e., the spacetime is CSI).

Journal of Physics: Conference Series, 2015

We briefly summarize our recent results on universal spacetimes. We show that universal spacetime... more We briefly summarize our recent results on universal spacetimes. We show that universal spacetimes are necessarily CSI, i.e. for these spacetimes, all curvature invariants constructed from the Riemann tensor and its derivatives are constant. Then, we focus on type III universal spacetimes and discuss a proof of universality for a class of type III Kundt spacetimes. We also mention explicit examples of type III and II universal spacetimes.

Journal of Physics: Conference Series, 2015

Universal spacetimes are vacuum solutions to all theories of gravity with the Lagrangian L = L(g ... more Universal spacetimes are vacuum solutions to all theories of gravity with the Lagrangian L = L(g ab , R abcd , ∇a 1 R bcde , . . . , ∇a 1 ...ap R bcde ). Well known examples of universal spacetimes are plane waves which are of the Weyl type N. Here, we discuss recent results on necessary and sufficient conditions for all Weyl type N spacetimes in arbitrary dimension and we conclude that a type N spacetime is universal if and only if it is an Einstein Kundt spacetime. We also summarize the main points of the proof of this result.

Classical and Quantum Gravity, 2014

Universal spacetimes are spacetimes for which all conserved symmetric rank-2 tensors, constructed... more Universal spacetimes are spacetimes for which all conserved symmetric rank-2 tensors, constructed as contractions of polynomials from the metric, the Riemann tensor and its covariant derivatives of arbitrary order, are multiples of the metric. Consequently, metrics of universal spacetimes solve vacuum equations of all gravitational theories with Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its derivatives of arbitrary order. In the literature, universal metrics are also discussed as metrics with vanishing quantum corrections and as classical solutions to string theory. Widely known examples of universal metrics are certain Ricci-flat pp waves. In this paper, we start a general study of geometric properties of universal metrics in arbitrary dimension and we arrive at a broader class of such metrics. In contrast with pp waves, these universal metrics also admit non-vanishing cosmological constant and in general do not have to possess a covariantly constant or recurrent null vector field. First, we show that a universal spacetime is necessarily a CSI spacetime, i.e. all curvature invariants constructed from the Riemann tensor and its derivatives are constant. Then we focus on type N spacetimes, where we arrive at a simple necessary and sufficient condition: a type N spacetime is universal if and only if it is an Einstein Kundt spacetime. A class of type III Kundt universal metrics is also found. Several explicit examples of universal metrics are presented.

Physical Review Letters, 2013

We show that the recently found AdS-plane and AdS-spherical wave solutions of quadratic curvature... more We show that the recently found AdS-plane and AdS-spherical wave solutions of quadratic curvature gravity also solve the most general higher derivative theory in D-dimensions. More generally, we show that the field equations of such theories reduce to an equation linear in the Ricci tensor for Kerr-Schild spacetimes having type-N Weyl and traceless Ricci tensors.

Journal of Geometry and Physics, 2012

In this paper we present a number of four-dimensional neutral signature exact solutions for which... more In this paper we present a number of four-dimensional neutral signature exact solutions for which all of the polynomial scalar curvature invariants vanish (VSI spaces) or are all constant (CSI spaces), which are of relevence in current theoretical physics.

Classical and Quantum Gravity, 2013

We consider time reversal transformations to obtain twofold orthogonal splittings of any tensor o... more We consider time reversal transformations to obtain twofold orthogonal splittings of any tensor on a Lorentzian space of arbitrary dimension n. Applied to the Weyl tensor of a spacetime, this leads to a definition of its electric and magnetic parts relative to an observer (defined by a unit timelike vector field u), in any dimension. We study the cases where one of these parts vanishes in detail, i.e., purely electric (PE) or magnetic (PM) spacetimes. We generalize several results from four to higher dimensions and discuss new features of higher dimensions. For instance, we prove that the only permitted Weyl types are G, I i and D, and discuss the possible relation of u with the Weyl aligned null directions (WANDs); we provide invariant conditions that characterize PE/PM spacetimes, such as Bel-Debever-like criteria, or constraints on scalar invariants, and connect the PE/PM parts to the kinematic quantities of u; we present conditions under which direct product spacetimes (and certain warps) are PE/PM, which enables us to construct explicit examples. In particular, it is also shown that all static spacetimes are necessarily PE, while stationary spacetimes (such as spinning black holes) are in general neither PE nor PM. Whereas ample classes of PE spacetimes exist, PM solutions are elusive; specifically, we prove that PM Einstein spacetimes of type D do not exist, in any dimension. Finally, we derive corresponding results for the electric/magnetic parts of the Riemann tensor, which is useful when considering spacetimes with matter fields, and moreover leads to first examples of PM spacetimes in higher dimensions. We also note in passing that PE/PM Weyl (or Riemann) tensors provide examples of minimal tensors, and we make the connection hereof with the recently proved alignment theorem (Hervik 2011 Class. Quantum Grav. 28 215009). This in turn sheds new light on the classification of the Weyl tensors based on null alignment, providing a further invariant characterization

Classical and Quantum Gravity, 2004

In this paper we construct negatively curved Einstein spaces describing gravitational waves havin... more In this paper we construct negatively curved Einstein spaces describing gravitational waves having a solvegeometry wave-front (i.e., the wavefronts are solvable Lie groups equipped with a left-invariant metric). Using the Einstein solvmanifolds (i.e., solvable Lie groups considered as manifolds) constructed in a previous paper as a starting point, we show that there also exist solvegeometry gravitational waves. Some geometric aspects are discussed and examples of spacetimes having additional symmetries are given, for example, spacetimes generalising the Kaigorodov solution. The solvegeometry gravitational waves are also examples of spacetimes which are indistinguishable by considering the scalar curvature invariants alone.