arXiv subjects

David McNutt

Publications and source records attributed to David McNutt.

15 recordsLinked to original sources

arXiv2026

Potential Carroll Structures and Special Carrollian Manifolds

It is well-known that unlike space-like and time-like hypersurfaces, null hypersurfaces in Lorentzian manifolds do not naturally inherit an affine connection from the spacetime in which they are embedded. On the other hand, recent developments in flat-space holography motivate the study of the intrinsic geometry of null hypersurfaces such as null infinity and black hole event horizons. Here we initiate the study of potential Carroll structures, a candidate for an intrinsic description of null hypersurfaces which may be particularly useful in settings where conformal isometries are of interest, and we explore their relationship to another such candidate intrinsic geometry, the special Carrollian manifolds.

math.DG↗

arXiv2026

Gauge-Invariant Gravitational Wave Polarization in Metric f(R) Gravity with Cosmological Implications

We develop a fully gauge invariant analysis of gravitational wave polarizations in metric f(R) gravity with a particular focus on the modified Starobinsky model, whose constant curvature solution provides a natural deSitter background for both early and late time cosmology. Linearizing the field equations around this background, we derive the Klein Gordon equation for the curvature perturbation and show that the scalar propagating mode acquires a mass, highlighting how the same scalar degree of freedom governs inflationary dynamics at high curvature and the propagation of gravitational waves in the current accelerating Universe. Using the scalar vector tensor (SVT) decomposition and a decomposition of the perturbed Ricci tensor, we obtain a set of fully gauge invariant propagation equations that isolate the contributions of the scalar, vector, and tensor modes in the presence of matter. We find that the tensor sector retains the two transverse traceless polarizations of General Relativity, while the scalar sector supports a massive breathing-longitudinal mode determined by the massive scalar propagating mode. Through the geodesic deviation equation, computed both in a local Minkowski patch and in fully covariant de Sitter form, we independently recover the same polarization content and identify its tidal signatures. The resulting framework connects the extra scalar polarization to cosmological observables, providing a unified, gauge invariant link between gravitational wave phenomenology and the cosmological implications of metric f(R) gravity.

gr-qc↗

arXiv2024

IDEAL characterization of vacuum pp-waves

An IDEAL characterization of a particular spacetime metric, $g_0$, consists of a set of tensorial equations $T[g] = 0$ arising from expressions constructed from the metric, $g$, its curvature tensor and its covariant derivatives and which are satisfied if and only if $g$ is locally isometric to the original metric $g_0$. Earlier applications of the IDEAL classification of spacetimes relied on the construction of particular scalar polynomial curvature invariants as an important step in the procedure. In this paper we investigate the well-known class of vacuum pp-wave spacetimes, where all scalar polynomial curvature invariants vanish, and determine the applicability of an IDEAL classification for these spacetimes. We consider a modification of the IDEAL approach which permits a corresponding extension of the Stewart-Walker lemma. With this change, we are able to construct invariants and IDEAL-ly classify all of the vacuum pp-wave solutions which admit a two- or higher-dimensional isometry group, with the exception of one case.

gr-qc↗

arXiv2024

Detecting horizons of symmetric black holes using relative differential invariants

Let $\mathfrak{k}$ be a nontrivial finite-dimensional Lie algebra of vector fields on a manifold M, and consider the family of Lorentzian metrics on M whose Killing algebra contains $\mathfrak{k}$. We show that scalar relative differential invariants, with respect to a Lie algebra of vector fields on M preserving $\mathfrak{k}$, can be used to detect the horizons of several well-known black holes. In particular, using the Lie algebra structure of $\mathfrak{k}$, we construct a general relative differential invariant of order 0 that always vanishes on $\mathfrak{k}$-invariant Killing horizons.

gr-qc↗

arXiv2024

Taub-NUT Instanton as the Self-dual Analog of Kerr

It was recently conjectured that a certain vacuum Kerr-Schild spacetime, which may be regarded as a self-dual analog of the Kerr metric, is equivalent to the self-dual Taub-NUT instanton. We confirm this conjecture by applying the Cartan-Karlhede algorithm to each metric and showing that for suitable choices of null tetrad, the algorithm leads to the same invariants and linear isotropy groups for both, establishing their equivalence. While it is well-known that the Taub-NUT solution and its self-dual version admit a double Kerr-Schild form, the observation that the self-dual Taub-NUT instanton admits a single Kerr-Schild form has only been made very recently. The two metrics we compare may be regarded as either complex metrics with Lorentzian (1,3) signature or real metrics with Kleinian (2,2) signature; here we take the latter view. Significant simplifications occur when the null tetrads are chosen to consist of two pairs of complex conjugate null vectors rather than four real independent ones. As a bonus, our work provides the first example of applying the Cartan-Karlhede algorithm using a null tetrad of this type.

hep-th↗

arXiv2024

Horizons that Gyre and Gimble: A Differential Characterization of Null Hypersurfaces

Motivated by the thermodynamics of black hole solutions conformal to stationary solutions, we study the geometric invariant theory of null hypersurfaces. It is well-known that a null hypersurface in a Lorentzian manifold can be treated as a Carrollian geometry. Additional structure can be added to this geometry by choosing a connection which yields a Carrollian manifold. In the literature various authors have introduced Koszul connections to study the study the physics on these hypersurfaces. In this paper we examine the various Carrollian geometries and their relationship to null hypersurface embeddings. We specify the geometric data required to construct a rigid Carrollian geometry, and we argue that a connection with torsion is the most natural object to study Carrollian manifolds. We then use this connection to develop a hypersurface calculus suitable for a study of intrinsic and extrinsic differential invariants on embedded null hypersurfaces; motivating examples are given, including geometric invariants preserved under conformal transformations.

gr-qc↗

arXiv2020

Observer-based invariants for cosmological models

We consider the equivalence problem for cosmological models in four-dimensional gravity theories. A cosmological model is considered as a triple $(M, {\bf g},{\bf u})$ consisting of a spacetime $(M, {\bf g})$ and a preferred normalized time-like vector field ${\bf u}$ tangent to a congruence of fundamental observers. We introduce a modification of the Cartan-Karlhede algorithm by restricting to frames adapted to ${\bf u}$ and including the covariant derivatives of ${\bf u}$ along with the Riemann tensor and its covariant derivatives. To fix the frame we make use of quantities relative to the fundamental observers, such as the anisotropic pressure tensor, energy flux vector, electric and magnetic parts of the Weyl tensor and the kinematical quantities of ${\bf u}$. This provides a simpler way to construct a list of invariants relative to the fundamental observers that completely characterizes the model, independent of coordinates. As an illustration of the algorithm, we consider several well-known cosmological models from General Relativity.

gr-qc↗

arXiv2019

Differential invariants of Kundt waves

Kundt waves belong to the class of spacetimes which are not distinguished by their scalar curvature invariants. We address the equivalence problem for the metrics in this class via scalar differential invariants with respect to the equivalence pseudo-group of the problem. We compute and finitely represent the algebra of those on the generic stratum and also specify the behavior for vacuum Kundt waves. The results are then compared to the invariants computed by the Cartan-Karlhede algorithm.

gr-qc↗

arXiv2017

Identification of black hole horizons using scalar curvature invariants

We introduce the concept of a geometric horizon, which is a surface distinguished by the vanishing of certain curvature invariants which characterize its special algebraic character. We motivate its use for the detection of the event horizon of a stationary black hole by providing a set of appropriate scalar polynomial curvature invariants that vanish on this surface. We extend this result by proving that a non-expanding horizon, which generalizes a Killing horizon, coincides with the geometric horizon. Finally, we consider the imploding spherically symmetric metrics and show that the geometric horizon identifies a unique quasi-local surface corresponding to the unique spherically symmetric marginally trapped tube, implying that the spherically symmetric dynamical black holes admit a geometric horizon. Based on these results, we propose a suite of conjectures concerning the application of geometric horizons to more general dynamical black hole scenarios.

gr-qc↗

arXiv2013

Vacuum Kundt Waves

We discuss the invariant classification of vacuum Kundt waves using the Cartan-Karlhede algorithm, and the upper bound on the number of iterations of the Karlhede algorithm to classify the vacuum Kundt waves. By choosing a particular coordinate system we partially construct the canonical coframe used in the classification to study the functional dependence of the invariants arising at each iteration of the algorithm. We provide a new upper bound $q \leq 4$ and show this bound is sharp by analyzing the subclass of Kundt waves with invariant count beginning with (0,1,...) to show that the class with invariant count $(0,1,3,4,4)$ exists. This class of vacuum Kundt waves is shown to be unique as the only set of metrics requiring the fourth covariant derivatives of the curvature. We conclude with an invariant classification of the vacuum Kundt waves using a suite of invariants.

gr-qc↗

arXiv2012

Spacetimes with all scalar curvature invariants in terms of the Cosmological Constant

In this letter we provide an invariant characterization for all spacetimes with all polynomial scalar invariants constructed from the Riemann tensor and its covariant derivatives vanishing except those zeroth order curvature invariants expressed as polynomials in $Λ$, the cosmological constant. Using this invariant description we provide explicit forms for the metric.

gr-qc↗

arXiv2012

Isometries in higher dimensional CCNV spacetimes

We study the class of higher-dimensional Kundt metrics admitting a covariantly constant null vector, known as CCNV spacetimes. We pay particular attention to those CCNV spacetimes with constant (polynomial) curvature invariants (CSI). We investigate the existence of an additional isometry in CCNV spacetimes, by studying the Killing equations for the general form of the CCNV metric. In particular, we list all CCNV spacetimes allowing an additional non-spacelike 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 CCNV spacetimes with an additional isometry as well as the subset of these spacetimes in which the isometry is non-spacelike for all values v.

math-ph↗

arXiv2012

Killing vectors in higher dimensional spacetimes with constant scalar curvature invariants

We study the existence of a non-spacelike isometry, ζ, in higher dimensional Kundt spacetimes with constant scalar curvature invariants (CSI). We present the particular forms for the null or timelike Killing vectors and a set of constraints for the metric functions in each case. Within the class of N dimensional CSI Kundt spacetimes, admitting a non-spacelike isometry, we determine which of these can admit a covariantly constant null vector that also satisfy ζ_{[a;b]} = 0.

math.DG↗

arXiv2012

Vacuum Plane Waves; Cartan Invariants and physical interpretation

As an application of the Cartan invariants obtained using the Karlhede algorithm, we study a simple subclass of the PP-wave spacetimes, the gravitational plane waves. We provide an invariant classification of these spacetimes and then study a few notable subcases: the linearly polarized plane waves, the weak-field circularly polarized waves, and another class of plane waves found by imposing conditions on the set of invariants. As we study these spacetimes we relate the invariant structure (i.e., Cartan scalars) to the physical description of these spacetimes using the geodesic deviation equations relative to timelike geodesic observers.

gr-qc↗

arXiv2012

Invariant classification of vacuum PP-waves

We solve the equivalence problem for vacuum PP-wave spacetimes by employing the Karlhede algorithm. Our main result is a suite of Cartan invariants that allows for the complete invariant classification of the vacuum pp-waves. In particular, we derive the invariant characterization of the G2 and G3 sub-classes in terms of these invariants. It is known [Collins91] that the invariant classification of vacuum pp-waves requires at most the fourth order covariant derivative of the curvature tensor, but no specific examples requiring the fourth order were known. Using our comprehensive classification, we prove that the q<=4 bound is sharp and explicitly describe all such maximal order solutions.

gr-qc↗