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Papers by David McNutt

Int J Geom Methods Mod Phys, 2009

We study the class of higher-dimensional Kundt metrics admitting a covariantly constant null vect... more We study the class of higher-dimensional Kundt metrics admitting a covariantly constant null vector, known as CCN V spacetimes. We pay particular attention to those CCN V spacetimes with constant (polynomial) curvature invariants (CSI). We investigate the existence of an additional isometry in CCN V spacetimes, by studying the Killing equations for the general form of the CCN V metric. In particular, we list all CCN V spacetimes allowing an additional nonspacelike isometry for all values of the lightcone coordinate v, which are of interest due to the invariance of the metric under a translation in v. As an application we use our results to find all CSI CCN V spacetimes with an additional isometry as well as the subset of these spacetimes in which the isometry is non-spacelike for all values v.

We present an improvement to the equivalence algorithm for three-dimensional gravity utilizing a ... more We present an improvement to the equivalence algorithm for three-dimensional gravity utilizing a three-dimensional analogue of the Newman- Penrose spinor formalism. To illustrate this algorithm we classify the entire class of Godel-like spacetimes. After introducing the key quantities required for the calculation of the curvature for the Godel-like spacetimes, we summarize the permitted Segre types for the Ricci tensor and list the constraints for the metric functions in each case. With this first step towards classification we continue the Cartan-Karlhede algorithm for each case. As an application, we express the polynomial scalar curvature invariants for Segre type [11,1] Godel-like spacetimes in terms of the Cartan invariants.

Classical and Quantum Gravity mathcalI\mathcal{I}mathcalI-non-degenerate spaces are spacetimes that can be characterized uniquely by their sc... more $\mathcal{I}$-non-degenerate spaces are spacetimes that can be characterized uniquely by their scalar curvature invariants. The ultimate goal of the current work is to construct a basis for the scalar polynomial curvature invariants in three dimensional Lorentzian spacetimes. In particular, we seek a minimal set of algebraically independent scalar curvature invariants formed by the contraction of the Riemann tensor and its covariant derivatives up to fifth order of differentiation. We use the computer software \emph{Invar} to calculate an overdetermined basis of scalar curvature invariants in three dimensions. We also discuss the equivalence method and the Karlhede algorithm for computing Cartan invariants in three dimensions.

It is of interest to study supergravity solutions preserving a non-minimal fraction of supersymme... more It is of interest to study supergravity solutions preserving a non-minimal fraction of supersymmetries. A necessary condition for supersymmetry to be preserved is that the spacetime admits a Killing spinor and hence a null or timelike Killing vector. Spacetimes admitting a covariantly constant null vector (CCNV), and hence a null Killing vector, belong to the Kundt class. We investigate the existence of additional isometries in the class of higher-dimensional CCNV Kundt metrics.

Journal of Geometry and Physics, 2015

While the Lorentzian and Riemannian metrics for which all polynomial scalar curvature invariants ... more While the Lorentzian and Riemannian metrics for which all polynomial scalar curvature invariants vanish (the VSI property) are well-studied, less is known about the fourdimensional neutral signature metrics with the VSI property. Recently it was shown that the neutral signature metrics belong to two distinct subclasses: the Walker and Kundt metrics. In this paper we have chosen an example from each of the two subcases of the Ricci-flat VSI Walker metrics respectively.

International Journal of Geometric Methods in Modern Physics, 2010

International Journal of Geometric Methods in Modern Physics, 2009

We study the class of higher-dimensional Kundt metrics admitting a covariantly constant null vect... more We study the class of higher-dimensional Kundt metrics admitting a covariantly constant null vector, known as CCN V spacetimes. We pay particular attention to those CCN V spacetimes with constant (polynomial) curvature invariants (CSI). We investigate the existence of an additional isometry in CCN V spacetimes, by studying the Killing equations for the general form of the CCN V metric. In particular, we list all CCN V spacetimes allowing an additional nonspacelike isometry for all values of the lightcone coordinate v, which are of interest due to the invariance of the metric under a translation in v. As an application we use our results to find all CSI CCN V spacetimes with an additional isometry as well as the subset of these spacetimes in which the isometry is non-spacelike for all values v.

Classical and Quantum Gravity, 2014

ABSTRACT We will construct explicit examples of four-dimensional neutral signature Walker (but no... more ABSTRACT We will construct explicit examples of four-dimensional neutral signature Walker (but not necessarily degenerate Kundt) spaces for which all of the polynomial scalar curvature invariants vanish. We then investigate the properties of some particular subclasses of Ricci flat spaces. We also briefly describe some four-dimensional neutral signature Einstein spaces for which all of the polynomial scalar curvature invariants are constant.

Int J Geom Methods Mod Phys, 2009

We study the class of higher-dimensional Kundt metrics admitting a covariantly constant null vect... more We study the class of higher-dimensional Kundt metrics admitting a covariantly constant null vector, known as CCN V spacetimes. We pay particular attention to those CCN V spacetimes with constant (polynomial) curvature invariants (CSI). We investigate the existence of an additional isometry in CCN V spacetimes, by studying the Killing equations for the general form of the CCN V metric. In particular, we list all CCN V spacetimes allowing an additional nonspacelike isometry for all values of the lightcone coordinate v, which are of interest due to the invariance of the metric under a translation in v. As an application we use our results to find all CSI CCN V spacetimes with an additional isometry as well as the subset of these spacetimes in which the isometry is non-spacelike for all values v.

We present an improvement to the equivalence algorithm for three-dimensional gravity utilizing a ... more We present an improvement to the equivalence algorithm for three-dimensional gravity utilizing a three-dimensional analogue of the Newman- Penrose spinor formalism. To illustrate this algorithm we classify the entire class of Godel-like spacetimes. After introducing the key quantities required for the calculation of the curvature for the Godel-like spacetimes, we summarize the permitted Segre types for the Ricci tensor and list the constraints for the metric functions in each case. With this first step towards classification we continue the Cartan-Karlhede algorithm for each case. As an application, we express the polynomial scalar curvature invariants for Segre type [11,1] Godel-like spacetimes in terms of the Cartan invariants.

Classical and Quantum Gravity mathcalI\mathcal{I}mathcalI-non-degenerate spaces are spacetimes that can be characterized uniquely by their sc... more $\mathcal{I}$-non-degenerate spaces are spacetimes that can be characterized uniquely by their scalar curvature invariants. The ultimate goal of the current work is to construct a basis for the scalar polynomial curvature invariants in three dimensional Lorentzian spacetimes. In particular, we seek a minimal set of algebraically independent scalar curvature invariants formed by the contraction of the Riemann tensor and its covariant derivatives up to fifth order of differentiation. We use the computer software \emph{Invar} to calculate an overdetermined basis of scalar curvature invariants in three dimensions. We also discuss the equivalence method and the Karlhede algorithm for computing Cartan invariants in three dimensions.

It is of interest to study supergravity solutions preserving a non-minimal fraction of supersymme... more It is of interest to study supergravity solutions preserving a non-minimal fraction of supersymmetries. A necessary condition for supersymmetry to be preserved is that the spacetime admits a Killing spinor and hence a null or timelike Killing vector. Spacetimes admitting a covariantly constant null vector (CCNV), and hence a null Killing vector, belong to the Kundt class. We investigate the existence of additional isometries in the class of higher-dimensional CCNV Kundt metrics.

Journal of Geometry and Physics, 2015

While the Lorentzian and Riemannian metrics for which all polynomial scalar curvature invariants ... more While the Lorentzian and Riemannian metrics for which all polynomial scalar curvature invariants vanish (the VSI property) are well-studied, less is known about the fourdimensional neutral signature metrics with the VSI property. Recently it was shown that the neutral signature metrics belong to two distinct subclasses: the Walker and Kundt metrics. In this paper we have chosen an example from each of the two subcases of the Ricci-flat VSI Walker metrics respectively.

International Journal of Geometric Methods in Modern Physics, 2010

International Journal of Geometric Methods in Modern Physics, 2009

We study the class of higher-dimensional Kundt metrics admitting a covariantly constant null vect... more We study the class of higher-dimensional Kundt metrics admitting a covariantly constant null vector, known as CCN V spacetimes. We pay particular attention to those CCN V spacetimes with constant (polynomial) curvature invariants (CSI). We investigate the existence of an additional isometry in CCN V spacetimes, by studying the Killing equations for the general form of the CCN V metric. In particular, we list all CCN V spacetimes allowing an additional nonspacelike isometry for all values of the lightcone coordinate v, which are of interest due to the invariance of the metric under a translation in v. As an application we use our results to find all CSI CCN V spacetimes with an additional isometry as well as the subset of these spacetimes in which the isometry is non-spacelike for all values v.

Classical and Quantum Gravity, 2014

ABSTRACT We will construct explicit examples of four-dimensional neutral signature Walker (but no... more ABSTRACT We will construct explicit examples of four-dimensional neutral signature Walker (but not necessarily degenerate Kundt) spaces for which all of the polynomial scalar curvature invariants vanish. We then investigate the properties of some particular subclasses of Ricci flat spaces. We also briefly describe some four-dimensional neutral signature Einstein spaces for which all of the polynomial scalar curvature invariants are constant.