arXiv subjects

Mark D. Roberts

Publications and source records attributed to Mark D. Roberts.

At least 19 recordsLinked to original sources

arXiv2019

The Lanczos Potential for Bianchi Spacetime

The form and application of the Lanczos potential for Bianchi spacetime are studied. The Lanczos potential is found in some specific cases then the general case studied. It leads to two coupled first order partial differential equations which although they so far have not been solved in general can be solved for many configurations. The application is to cosmic energetics: in other words to the study of the energy of the gravitational and other fields in the Universe.

gr-qc↗

arXiv2019

Hybrid imploding scalar and ads spacetime

A solution to the massless scalar cosmological constant field equations is presented. The solution has imploding scalar and parts of anti-deSitter or deSitter spacetime as limiting cases. Some of the solutions properties are discussed however not much can be said because of the contrasting properties of imploding scalar and deSitter spacetimes.

gr-qc↗

arXiv2018

Rotational Dimensional Reduction

Rotational energy dissipation in the solar system confines the planets to the ecliptic, this can be thought of as a dimensional reduction from three dimensions to two. It is argued that the same mechanism restricts five dimensional matter to four dimensional spacetime. The result is sensitive to geometric configuration but not to force law. Although the mechanism provides a qualitative description it as yet makes no quantitative prediction.

gr-qc↗

arXiv2017

Quantum Imploding Scalar Fields

The d'Alembertian $\Boxϕ=0$ has solution $ϕ=f(v)/r$, where $f$ is a function of a null coordinate $v$, and this allows creation of a divergent singularity out of nothing. In scalar-Einstein theory a similar situation arises both for the scalar field and also for curvature invariants such as the Ricci scalar. Here what happens in canonical quantum gravity is investigated. Two minispace Hamiltonian systems are set up: extrapolation and approximation of these indicates that the quantum mechanical wavefunction can be finite at the origin.

gr-qc↗

arXiv2016

Non-metric Quantum Cosmology

Scalar-tensor theory has arbitrary functions of the scalar field in front of the geometric and scalar terms in the Lagrangain. The extent to which these arbitrary functions appear in the Wheeler-deWitt wavefunction of mini-super Robertson-Walker spacetimes is discussed. The function of the scalar field in front of the Einstein-Hilbert action allows a current to be constructed which suggests transfer from matter to geometry of aspects of the wavefunction.

gr-qc↗

arXiv2015

Causality in scalar-Einstein waves

A wavelike scalar-Einstein solution is found and indicating vectors constructed from the Bel-Robinson tensor are used to study which objects co-move with the wave and whether gravitational energy transfer is null.

gr-qc↗

arXiv2014

A Characteristic Particle Length

It is argued that there are characteristic intervals associated with any particle that can be derived without reference to the speed of light $c$. Such intervals are inferred from zeros of wavefunctions which are solutions to the Schrödinger equation. The characteristic length is $\ell=β^2\hbar^2/(8Gm^3)$, where $β=3.8\dots$; this length might lead to observational effects on objects the size of a virus.

physics.gen-ph↗

arXiv2011

A Fluid Generalization of Membranes

In a certain sense a perfect fluid is a generalization of a point particle. This leads to the question as to what is the corresponding generalization for extended objects. The lagrangian formulation of a perfect fluid is much generalized and this has as a particular example a fluid which is a classical generalization of a membrane, however there is as yet no indication of any relationship between their quantum theories.

hep-th↗

arXiv2011

Halo Spacetime

It is shown that constant galactic rotation curves require a logarithmic potential in both newtonian and relativistic theory. In newtonian theory the density vanishes asymptotically, but there are a variety of possibilities for perfect fluid einstein theory.

astro-ph↗

arXiv2010

String theory explanation of galactic rotation

The unique spherically symmetric metric which has vanishing weyl tensor, is asymptotically desitter, and can model constant galactic rotation curves is presented. Two types of field equations are shown to have this metric as an exact solution. The first is palatini varied scalar-tensor theory. The second is the low energy limit of string theory modified by inclusion of a contrived potential.

gr-qc↗

arXiv2010

Quadratic field equations on the brane

It is shown that four dimensional vacuum Einstein solutions simply embedded in five dimensions obey the Gauss-Bonnet-Einstein field equations: $G_{ab}+αGB_{ab}+δ^{55}_{ab}α\exp(-2χ/\sqrtα)GB_4=0$ and the Pauli-Einstein equations $G_{ab}-3αP_{ab}/5=0$, and the Bach-Einstein equations $B_{ab}=0$. General equations are calculated for which these and similar results follow. It is briefly argued that such field equations could be significant on large distance scales.

gr-qc↗

arXiv2010

The Relative Motion of Membranes

The relative classical motion of membranes is governed by an equation of the form D(hessian D separation)=riemann times separation times momentum. This is a generalization of the geodesic deviation equation and can be derived from a simple lagrangian. Quantum mechanically the picture is less clear. Some quantizations of the classical equations are attempted so that the question as to whether the Universe started with a quantum fluctuation can be addressed.

gr-qc↗

arXiv2009

The Kasner Brane

Solutions are found to field equations constructed from the Pauli, Bach and Gauss-Bonnet quadratic tensors to the Kasner and Kasner brane spacetimes in up to five dimensions. A double Kasner space is shown to have a vacuum solution. Brane solutions in which the bulk components of the Einstein tensor vanish are also looked at and for four branes a solution similar to radiation Robertson-Walker spacetime is found. Matter trapping of a test scalar field and a test perfect fluid are investigated using energy conditions.

gr-qc↗

arXiv2009

Constructing Spacetime from the String Worldsheet

In a certain sense riemannian geometry can be thought of as geometry built up from the finslerian properties of point particles. The generalization of this to where the geometry is built up from the finslerian properties of string and membranes is investigated. Solely classical arguments suggest a physical interpretation in which microscopic strings are directly related to macroscopic geometry; alternatively the resulting geometry can be interpretated as that describing microsopic spacetime.

gr-qc↗

arXiv2009

The clebsch potential approach to fluid lagrangians

The clebsch potential approach to fluid lagrangians is developed in order to establish contact with other approaches to fluids. Three variants of the perfect fluid approach are looked at. The first is an explicit linear lagrangian constructed directly from the clebsch potentials, this has fixed equation of state and explicit expression for the pressure but is less general than a perfect fluid. The second is lagrangians more general than that of a perfect fluid which are constructed from higher powers of the comoving vector. The third is lagrangians depending on two vector fields which can represent both density flow and entropy flow.

gr-qc↗

arXiv2009

Fractional Derivative Cosmology

The degree by which a function can be differentiated need not be restricted to integer values. Usually most of the field equations of physics are taken to be second order, curiosity asks what happens if this is only approximately the case and the field equations are nearly second order. For Robertson-Walker cosmology there is a simple fractional modification of the Friedman and conservation equations. In general fractional gravitational equations similar to Einstein's are hard to define as this requires fractional derivative geometry. What fractional derivative geometry might entail is briefly looked at and it turns out that even asking very simple questions in two dimensions leads to ambiguous or intractable results. A two dimensional line element which depends on the Gamma-function is looked at.

gr-qc↗

arXiv2009

New Five Dimensional Spherical Vacuum Solutions

A new five dimensional spherical vacuum solution is both dervied and its signature, curvature and truncation discussed. Its truncation leads to a four dimensional spacetime with similiar stress to those found by charge-free Kaluza-Klein compactification. Various other restrictions to four dimensions are looked at to see if they have stresses consisting of electromagnetic fields or quadratic tensors. The solution is extended to the brane picture where the extended space is found to obey field equations with metric stress derivable from a lagrangian dependent on brane function and kaluza scalar.

gr-qc↗

arXiv2008

The Lanczos potential and Chern-Simons theory

A new tensor $D$ is introduced which is constructed from the Lanczos potential and is of the same form as that of the Weyl tensor $C$ expressed in terms of the Lanczos potential except that covariant differentiation is replaced by transvection with a vector $v$. The new tensor has associated invariants $C\cdot D$ and $D^2$, the first of these can be interpreted as a Chern-Simons term for Weyl $C^2$ gravity. Both invariants allow various tensors to be constructed and some of the properties of these are investigated by using exact examples.

gr-qc↗