arXiv subjects

A. A. Coley

Publications and source records attributed to A. A. Coley.

At least 19 recordsLinked to original sources

arXiv2026

Horizon Singularities in the Schwarzschild Geometry of the Teleparallel Equivalent of General Relativity

Certain torsion scalar invariants are known to diverge at the horizon of the Schwarzschild solution in the Teleparallel Equivalent of General Relativity (TEGR), obstructing its interpretation as a black hole spacetime. We show that Schwarzschild TEGR geometries split into two distinct subclasses determined by the Lorentz sector of the geometry -- the elements of the tetrad and spin connection not encoded in the metric but appearing in the torsion. In the regular subclass, the divergences are absent and the horizon belongs to the manifold, supporting a consistent black hole interpretation. In the singular subclass, the divergences are genuine and the horizon is excluded from the manifold. As part of this analysis, we clarify the role of inertial contributions in teleparallel gravity, showing that the proper frame does not, by itself, eliminate inertial effects and that the horizon singularities are independent of the inertial structure of the frame. Using three independent approaches -- the inertial frame condition, horizon-penetrating coordinates, and the horizon regularity criterion -- we determine the complete class of Lorentz sector functions compatible with a regular horizon in Schwarzschild TEGR geometries. For this class, all torsion scalar invariants remain finite at the horizon and analytic extensions across it are admitted.

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arXiv2026

On non-vacuum black holes in new general relativity

New general relativity (NGR) is a torsion-based modification of general relativity whose Lagrangian depends on three free parameters, $(c_{a}, c_{v}, c_{t})$. A subset of the parameter space is physically admissible, namely that which simultaneously ensures ghost-freedom, propagation of a spin-2 mode, and a consistent Newtonian limit. In this work we analyze static and spherically symmetric configurations in NGR, both in vacuum and in the presence of a perfect fluid and an electromagnetic field, under the assumption of the existence of a local black-hole horizon. We find that the mere existence of such configurations forces the free parameters into regions associated with known pathological models: theories that either contain ghost instabilities, do not propagate a spin-2 mode, or lack a Newtonian limit. The remaining geometries are regular at the horizon, so the obstruction is not a breakdown of the geometry but a breakdown of the underlying theory. We therefore conclude that, within the class of models examined, NGR does not admit physically meaningful non-trivial black holes distinct from those of the teleparallel equivalent of general relativity.

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arXiv2025

On black holes in new general relativity

New General Relativity (NGR) is a class of teleparallel theories defined by three free parameters, effectively reduced to two after appropriate normalization, which are subject to experimental constraints. In this framework, matter couples minimally to the metric, ensuring that test particles follow geodesics and that null congruence expansions can be employed to detect local horizons. Assuming such horizons exist, we demonstrate that all physically viable NGR models--including the Teleparallel Equivalent of General Relativity (TEGR) and the one-parameter Hayashi and Shirafuji model (1P-H&S)--inevitably exhibit divergences in torsion scalars at the local horizon. This singular behavior obstructs the interpretation of these models and their associated teleparallel geometries as black hole configurations.

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arXiv2024

Locally-homogeneous Riemann-Cartan geometries with the largest symmetry group

The symmetry frame formalism is an effective tool for computing the symmetries of a Riemann-Cartan geometry and, in particular, in metric teleparallel geometries. In the case of non-vanishing torsion in a four dimensional Riemann-Cartan geometry, the Minkowski geometry is the only geometry admitting ten affine frame symmetries. Excluding this geometry, the maximal number of affine frame symmetries is seven. A natural question is to ask what four dimensional geometries admit a seven-dimensional group of affine frame symmetries. Such geometries are locally homogeneous and admit the largest isotropy group permitted, and hence are called maximally isotropic. Using the symmetry frame formalism to compute affine frame symmetries along with the additional structure of the torsion tensor, we employ the Cartan-Karlhede algorithm to determine all possible seven-dimensional symmetry groups for Riemann-Cartan geometries.

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arXiv2024

Spherically symmetric teleparallel geometries

We are interested in the development of spherically symmetric geometries in $F(T)$ teleparallel gravity which are of physical importance. We first express the general forms for the spherically symmetric frame and the zero curvature, metric compatible, spin connection. We then analyse the antisymmetric field equations (the solutions of which split into two cases, which we subsequently consider separately), and derive and analyse the resulting symmetric field equations. In order to further study the applications of spherically symmetric teleparallel models, we study $3$ subcases in which there is an additional affine symmetry so that the resulting field equations reduce to a system of ordinary differential equations. First, we study static spherical symmetric geometries and solve the antisymmetric field equations and subsequently derive the full set of symmetric field equations. In particular, we investigate vacuum spacetimes and obtain a number of new solutions. Second, we consider an additional affine frame symmetry in order to expand the affine frame symmetry group to that of a spatially homogeneous Kantowski-Sachs geometry. Third, we study the special case of spherical symmetry with an additional fourth similarity affine vector.

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arXiv2023

The JWST and standard cosmology

Recent observations from the James Webb Space Telescope have identified a population of massive galaxy sources ($\mathrm{>10^{10}\ M_\odot}$) at $z>7-10$, formed less than 700 Myr after the Big Bang. Such massive galaxies do not have enough time to form within the standard cosmological model, and hence these observations significantly challenge standard cosmology. A number of possible solutions to this problem have been put forward, including an enhancement of the gravitational force in a modified theory of gravity and the claim that massive primordial black holes, which were created in the early universe before galaxy formation, might provide seeds for galaxies and black holes to subsequently form. We discuss two more exotic possibilities. Black holes can persist through a cosmological bounce and constitute large seeds formed in the previous cosmic cycle existing before current galaxy formation. And spikes, both incomplete spikes that occur in the early initial oscillatory regime of general cosmological models and permanent spikes that can form in inhomogeneous models at later times, could provide a mechanism for generating large structures early in the Universe.

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arXiv2023

Spatially Homogeneous Teleparallel Gravity: Bianchi I

Using a recently developed algorithm that chooses preferred coordinates and a preferred co-frame, we will determine the completely general Bianchi type I teleparallel geometry. In using this algorithm, any remaining gauge freedom is allocated to the choice of spin connection. We then solve the symmetry constraints placed on the spin connection to derive a general class of Bianchi type I teleparallel geometries. We find that this general class of Bianchi type I teleparallel geometries breaks naturally into two sub-classes. We then illustrate some simple power-law solutions in $F(T)$ teleparallel gravity for each case to illustrate the differences.

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arXiv2023

Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity

Symmetry assumptions on the geometrical framework have provided successful mechanisms to develop physically meaningful solutions to many problems. In tele-parallel gravity, invariance of the frame and spin-connection under a group of motions defines an affine symmetry group. Here, we assume there exists a three-dimensional group of affine symmetries acting simply transitively on a spatial hypersurface and that this group of symmetry actions defines our affine frame symmetry group. We determine the general form of the co-frame and spin connection for each spatially homogeneous Bianchi type. We then construct the corresponding field equations for $f(T)$ tele-parallel gravity. We show that if the symmetry group is of Bianchi type A ($I$, $II$, $VI_0$, $VII_0$, $VIII$ or $IX$) then there exists a co-frame/spin connection pair that is consistent with the antisymmetric part of the field equations of $f(T)$ tele-parallel gravity. For those geometries having a Bianchi type B symmetry group ($IV$, $V$, $VI_h$, $VII_h$), we find that in general these geometries are inconsistent with the antisymmetric part of the $f(T)$ tele-parallel gravity field equations unless the theory reduces to an analog of General Relativity with a cosmological constant.

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arXiv2023

The equilibrium condition in gravitational collapse and its application to a cosmological scenario

We discuss the equilibrium conditions of the gravitational collapse of a spherically symmetric matter cloud. We analyze the spinor structure of a general collapsing space-time and redefine the equilibrium conditions by using Cartan scalars. We qualitatively investigate the equilibrium configuration of a two-fluid system consisting of a dust-like fluid and a fluid with a negative equation of state. We use our results to investigate certain cosmological scenarios where dark energy can cluster inside the over-dense regions of dark matter and together reaches a stable configuration. We compare the outcomes of our work with existing work where the virialization technique is used to stabilize the two-fluid system.

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arXiv2023

A frame based approach to computing symmetries with non-trivial isotropy groups

A frame approach to determining the most general solution admitting a desired symmetry group has been examined previously in Riemannian and teleparallel geometries with some success. In teleparallel geometries, one must determine the general form of the frame and spin connection to generate a general solution admitting the desired symmetry group. Current approaches often rely on the use of the proper frame, where the spin connection is zero. However this leads to particular theoretical and practical problems. In this paper we introduce an entirely general approach to determining the most general Riemann-Cartan geometries which admit a given symmetry group and apply these results to teleparallel geometries. To illustrate the approach we determine the most general geometries, with the minimal number of arbitrary functions, for particular choices of symmetry groups with dimension one, three, six and seven. In addition, we rigorously show how the teleparallel analogues of the Robertson-Walker, de Sitter and Einstein static spacetimes can be determined.

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arXiv2022

Symmetric Teleparallel Geometries

In teleparallel gravity and, in particular, in $F(T)$ teleparallel gravity, there is a challenge in determining an appropriate (co-)frame and its corresponding spin connection to describe the geometry. Very often, the "proper" frame, the frame in which all inertial effects are absent, is not the simplest (e.g, diagonal) (co-)frame. The determination of the frame and its corresponding spin connection for $F(T)$ teleparallel gravity theories when there exist affine symmetries is of much interest. In this paper we present the general form of the coframe and its corresponding spin connection for teleparallel geometries which are invariant under a $G_6$ group of affine symmetries. The proper coframe and the corresponding $F(T)$ field equations are also shown for these Teleparallel Robertson Walker (TRW) geometries. Further, with the addition of an additional affine symmetry, it is possible to define a Teleparallel de Sitter (TdS) geometry.

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arXiv2021

Geometric Horizons: A Frame Approach

In the numerical investigation of the physical merger of two black holes, it is crucial to locate a black hole locally. This is usually done utilizing an apparent horizon. An alternative proposal is to identify a geometric horizon (GH), which is characterized by a surface in the spacetime on which the curvature tensor or its covariant derivatives are algebraically special. This necessitates the choice of a special null frame, which we shall refer to as an algebraically preferred null frame (APNF). The GH is then identified by surfaces of vanishing scalar curvature invariants but, unfortunately, these are difficult to compute. However, the algebraic nature of a GH means that the APNF plays a central role and suggests a null frame approach to characterizing the GH. Indeed, if we employ the Cartan-Karlhede algorithm to completely fix the null frame invariantly, then all of the remaining non vanishing components of the curvature tensor and its covariant derivatives are Cartan scalars. Hence the GH is characterized by the vanishing of certain Cartan scalars. A null frame approach is useful in the numerical investigation of the merger of two black holes in general, but we will focus on the application to identifying a GH. We begin with a review of the use of APNF and GH in previous work. The APNF is then defined and chosen so that the Weyl tensor is algebraically special, and we must examine the covariant derivatives of the Weyl tensor in this frame. We show how to invariantly fix the null frame, and hence characterize the APNF, and describe how to then identify the GH using the zero-set of certain Cartan scalars. Our ultimate aim is to apply this frame formalism to the numerical collapse of two black holes. As an example, we investigate the axisymmetric evolution of a two black hole Kastor-Traschen spacetime.

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arXiv2021

Teleparallel geometries not characterized by their scalar polynomial torsion invariants

A teleparallel geometry is an n-dimensional manifold equipped with a frame basis and an independent spin connection. For such a geometry, the curvature tensor vanishes and the torsion tensor is non-zero. A straightforward approach to characterizing teleparallel geometries is to compute scalar polynomial invariants constructed from the torsion tensor and its covariant derivatives. An open question has been whether the set of all scalar polynomial torsion invariants, $\mathcal{I}_T$ uniquely characterize a given teleparallel geometry. In this paper we show that the answer is no and construct the most general class of teleparallel geometries in four dimensions which cannot be characterized by $\mathcal{I}_T$. As a corollary we determine all teleparallel geometries which have vanishing scalar polynomial torsion invariants.

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arXiv2021

An invariant characterization of the quasi-spherical Szekeres dust models

The quasi-spherical Szekeres dust solutions are a generalization of the spherically symmetric Lemaitre-Tolman-Bondi dust models where the spherical shells of constant mass are non-concentric. The quasi-spherical Szekeres dust solutions can be considered as cosmological models and are potentially models for the formation of primordial black holes in the early universe. Any collapsing quasi-spherical Szekeres dust solution where an apparent horizon covers all shell-crossings that will occur can be considered as a model for the formation of a black hole. In this paper we will show that the apparent horizon can be detected by a Cartan invariant. We will show that particular Cartan invariants characterize properties of these solutions which have a physical interpretation such as: the expansion or contraction of spacetime itself, the relative movement of matter shells, shell-crossings and the appearance of necks and bellies.

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arXiv2020

Persistence in black hole lattice cosmological models

Dynamical solutions for an evolving multiple network of black holes near a cosmological bounce dominated by a scalar field are investigated. In particular, we consider the class of black hole lattice models in a hyperspherical cosmology, and we focus on the special case of eight regularly-spaced black holes with equal masses when the model parameter $κ> 1$. We first derive exact time evolving solutions of instantaneously-static models, by utilizing perturbative solutions of the constraint equations that can then be used to develop exact 4D dynamical solutions of the Einstein field equations. We use the notion of a geometric horizon, which can be characterized by curvature invariants, to determine the black hole horizon. We explicitly compute the invariants for the exact dynamical models obtained. As an application, we discuss whether black holes can persist in such a universe that collapses and then subsequently bounces into a new expansionary phase. We find evidence that in the physical models under investigation (and particularly for $κ> 1$) the individual black holes do not merge before nor at the bounce, so that consequently black holes can indeed persist through the bounce.

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arXiv2020

Theoretical Cosmology

We review current theoretical cosmology, including fundamental and mathematical cosmology and physical cosmology (as well as cosmology in the quantum realm), with an emphasis on open questions.

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arXiv2020

Symmetry and Equivalence in Teleparallel Gravity

In theories such as teleparallel gravity and its extensions, the frame basis replaces the metric tensor as the primary object of study. A choice of coordinate system, frame basis and spin-connection must be made to obtain a solution from the field equations of a given teleparallel gravity theory. It is worthwhile to express solutions in an invariant manner in terms of torsion invariants to distinguish between different solutions. In this paper we discuss the symmetries of teleparallel gravity theories, describe the classification of the torsion tensor and its covariant derivative and define scalar invariants in terms of the torsion. In particular, we propose a modification of the Cartan-Karlhede algorithm for geometries with torsion (and no curvature or nonmetricity). The algorithm determines the dimension of the symmetry group for a solution and suggests an alternative frame-based approach to calculating symmetries. We prove that the only maximally symmetric solution to any theory of gravitation admitting a non-zero torsion tensor is Minkowski space. As an illustration we apply the algorithm to six particular exact teleparallel geometries. From these examples we notice that the symmetry group of the solutions of a teleparallel gravity theory is potentially smaller than their metric-based analogues in General Relativity.

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arXiv2020

Cartan Invariants and Event Horizon Detection, Extended Version

We show that it is possible to locate the event horizons of a black hole (in arbitrary dimensions) as the zeros of certain Cartan invariants. This approach accounts for the recent results on the detection of stationary horizons using scalar polynomial curvature invariants, and improves upon them since the proposed method is computationally less expensive. As an application, we produce Cartan invariants that locate the event horizons for various exact four-dimensional and five-dimensional stationary, asymptotically flat (or (anti) de Sitter) black hole solutions and compare the Cartan invariants with the corresponding scalar curvature invariants that detect the event horizon. In particular, for each of the four-dimensional examples we express the scalar polynomial curvature invariants introduced by Abdelqader and Lake in terms of the Cartan invariants and show a direct relationship between the scalar polynomial curvature invariants and the Cartan invariants that detect the horizon.

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