arXiv subjects

Peter K S Dunsby

Publications and source records attributed to Peter K S Dunsby.

6 recordsLinked to original sources

arXiv2026

A complete correspondence between the Newman-Penrose and 1+1+2 formalisms

We establish a correspondence between the Newman-Penrose and 1+1+2 semitetrad covariant formalisms by expressing all Newman-Penrose spin coefficients, Ricci scalars, and Weyl scalars in terms of the scalar, vector, and tensor variables of the 1+1+2 decomposition. In addition, we provide some discussions on the correspondence between the gauge structures of the formalisms. This provides a direct dictionary between two widely used approaches to general relativity and gives a geometrical interpretation of Newman-Penrose quantities in terms of covariantly defined 1+1+2 variables. As a simple demonstration, we use this mapping to derive inequalities on the Newman-Penrose scalars and the cosmological constant, which constrains the existence of future outer trapping horizons in spacetimes exhibiting local rotational symmetry.

gr-qc↗

arXiv2024

Gradient conformal stationarity and the CMC condition in LRS spacetimes

We study the existence of gradient conformal Killing vectors (CKVs) in the class of locally rotationally symmetric (LRS) spacetimes which generalizes spherically symmetric spacetimes, and investigate some implications for the evolutionary character of marginally outer trapped surfaces. We first study existence of gradient CKVs via the obtention of a relationship between the Ricci curvature and the gradient of the divergence of the CKV. This provides an alternative set of equations, for which the integrability condition is obtained, to analyze the existence of gradient CKVs. A uniqueness result is obtained in the case of perfect fluids, where it is demonstrated that the Robertson-Walker solution is the unique perfect fluid solution with a nonvanishing pressure, admitting a timelike gradient CKV. The constant mean curvature condition for LRS spacetimes is also obtained, characterized by three distinct conditions which are specified by a set of three scalars. Linear combinations of these scalars, whose vanishing define the constant mean curvature condition, turn out to be related to the evolutions of null expansions of 2-spheres along their null normal directions. As such, some implications for the existence of black holes and the character of the associated horizons are obtained. It is further shown that dynamical black holes of increasing area, with a non-vanishing heat flux across the horizon, will be in equilibrium, with respect to the frame of the conformal observers.

gr-qc↗

arXiv2021

On some locally symmetric embedded spaces with non-negative scalar curvature and their characterization

In this work we perform a general study of properties of a class of locally symmetric embedded hypersurfaces in spacetimes admitting a $1+1+2$ spacetime decomposition. The hypersurfaces are given by specifying the form of the Ricci tensor with respect to the induced metric. These are slices of constant time in the spacetime. Firstly, the form of the Ricci tensor for general hypersurfaces is obtained and the conditions under which the general case reduces to those of constant time slices are specified. We provide a characterization of these hypersurfaces, with key physical quantities in the spacetime playing a role in specifying the local geometry of these hypersurfaces. Furthermore, we investigate the case where these hypersurfaces admit a Ricci soliton structure. The particular cases where the vector fields associated to the solitons are Killing or conformal Killing vector fields are analyzed. Finally, in the context of spacetimes with local rotational symmetry it is shown that, only spacetimes in this class with vanishing rotation and spatial twist can admit the hypersurface types considered, and that the hypersurfaces are necessarily flat. And if such hypersurface do admit a Ricci soliton structure, the soliton is steady, with the components of the soliton field being constants.

gr-qc↗

arXiv2016

The 1+1+2 formalism for Scalar-Tensor gravity

We use the 1+1+2 covariant approach to clarify a number of aspects of spherically symmetric solutions of non-minimally coupled scalar tensor theories. Particular attention is focused on the extension of Birkhoff's theorem and the nature of quasi-local horizons in this context.

gr-qc↗

arXiv2006

Shear dynamics in Bianchi I cosmologies with R^n-gravity

We give the equations governing the shear evolution in Bianchi spacetimes for general f(R)-theories of gravity. We consider the case of R^n-gravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit local rotational symmetry. We find exact solutions and study their behaviour and stability in terms of the values of the parameter n. In particular, we found a set of cosmic histories in which the universe is initially isotropic, then develops shear anisotropies which approaches a constant value.

gr-qc↗

arXiv2006

On inhomogeneous magnetic seed fields and gravitational waves within the MHD limit

In this paper we apply second-order gauge-invariant perturbation theory to investigate the possibility that the non-linear coupling between gravitational waves (GW) and a large scale inhomogeneous magnetic field acts as an amplification mechanism in an `almost' Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe. The spatial inhomogeneities in the magnetic field are consistently implemented using the magnetohydrodynamic (MHD) approximation, which yields an additional source term due to the interaction of the magnetic field with velocity perturbations in the plasma. Comparing the solutions with the corresponding results in our previous work indicates that, on super-horizon scales, the interaction with the spatially inhomogeneous field in the dust regime induces the same boost as the case of a homogeneous field, at least in the ideal MHD approximation. This is attributed to the observation that the MHD induced part of the generated field effectively only contributes on scales where the coherence length of the initial field is less than the Hubble scale. At sub-horizon scales, the GW induced magnetic field is completely negligible in relation to the MHD induced field. Moreover, there is no amplification found in the long-wavelength limit.

gr-qc↗