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George F. R. Ellis

Publications and source records attributed to George F. R. Ellis.

At least 19 recordsLinked to original sources
arXiv2026

Reframing the Free Will Debate: The Universe is Not Deterministic

Free will discourse is primarily centred around the thesis of determinism. Much of the literature takes determinism as its starting premise, assuming it true for the sake of discussion, and then proceeds to present arguments for why, if determinism is true, free will would be either possible or impossible. This is reflected in the theoretical terrain of the debate, with the primary distinction currently being between compatibilists and incompatibilists and not, as one might expect, between free will realists and skeptics. The aim of this paper is twofold. First, we argue that there is no reason to accept such a framing. We show that, on the basis of modern physics, there is no good evidence that physical determinism of any variety provides an accurate description of our universe and lots of evidence against such a view. Moreover, we show that this analysis extends equally to the sort of indeterministic worldviews endorsed by many libertarian philosophers and their skeptics, a worldview which we refer to as determinism plus randomness. The papers secondary aim is therefore to present an alternative conception of indeterminism, which is more in line with the empirical evidence from physics. It is this indeterministic worldview, we suggest, that ought to be the central focus of a reframed philosophy of free will.

physics.hist-ph↗
arXiv2020

Tidal forces are gravitational waves

In this paper we show in a covariant and gauge invariant way that in general relativity, tidal forces are actually a hidden form of gravitational waves. This must be so because gravitational effects cannot occur faster than the speed of light. Any two body gravitating system, where the bodies are orbiting around each other, may generate negligible gravitational waves, but it is via these waves that non-negligible tidal forces (causing shape distortions) act on these bodies. Although the tidal forces are caused by the electric part of the Weyl tensor, we transparently show that some small time varying magnetic part of the Weyl tensor with non zero curl must be present in the system that mediates the tidal forces via gravitational wave type effects. The outcome is a new test of whether gravitational effects propagate at the speed of light.

gr-qc↗
arXiv2020

Stephen William Hawking: A Biographical Memoir

Stephen Hawking's contributions to the understanding of gravity, black holes and cosmology were truly immense. They began with the singularity theorems in the 1960s followed by his discovery that black holes have an entropy and consequently a finite temperature. Black holes were predicted to emit thermal radiation, what is now called Hawking radiation. He pioneered the study of primordial black holes and their potential role in cosmology. His organisation of and contributions to the Nuffield Workshop in 1982 consolidated the picture that the large-scale structure of the universe originated as quantum fluctuations during the inflationary era. Work on the interplay between quantum mechanics and general relativity resulted in his formulation of the concept of the wavefunction of the universe. The tension between quantum mechanics and general relativity led to his struggles with the information paradox concerning deep connections between these fundamental areas of physics. These achievements were all accomplished following the diagnosis during the early years of Stephen's studies as a post-graduate student in Cambridge that he had incurable motor neuron disease -- he was given two years to live. Against all the odds, he lived a further 55 years. The distinction of his work led to many honours and he became a major public figure, promoting with passion the needs of disabled people. His popular best-selling book A Brief History of Time made cosmology and his own work known to the general public worldwide. He became an icon for science and an inspiration to all.

physics.hist-ph↗
arXiv2019

Direct Detection of Universal Expansion by Holonomy in the McVittie Spacetime

In general relativity the parallel transfer of a vector around a closed curve in spacetime, or along two curves which together form a closed loop, usually results in a nonzero deficit angle between the vector's initial and final positions. We show that such holonomy in the McVittie spacetime, which represents a gravitating object imbedded in an expanding universe, can in principle be used to directly detect the expansion of the universe, for example by measuring changes in the components of a gyroscopic spin axis. Although such changes are of course small, they are large enough (\D S \sim 10^{-7}) that they could conceivably be measured if the real universe behaved like the McVittie spacetime. The real problem is that virialization will lead to domains decoupled from the global expansion on a scale much larger than that of the solar system, making such an experiment infeasible probably even in principle. Nevertheless the effect is of interest in relation to ongoing discussions, dating back at least to Einstein and Straus, which concern the relationship between the expansion of the universe and local systems.

gr-qc↗
arXiv2018

Transferring Energy in General Relativity

A problem in general relativity is, how the gravitational field can transfer energy and momentum between different distant places. The issue is that matter stress tensor is locally conserved, with no explicit interaction with the free gravitational field, which is represented by the Weyl tensor. In this paper we explicitly construct an interaction tensor for free gravity and matter, that depicts the interplay between the energy momentum tensor of free gravity, which is taken to be the symmetric two index square root of Bell-Robinson tensor, and matter. This is examined both in the case of Coulomb-like Petrov type D spacetimes and radiation like Petrov type N spacetimes, where a unique square root exists. The first case generalises the Tweedledum and Tweedledee thought experiment regarding gravitational induction in Newtonian gravity to general relativistic scenarios, and the second gives a proposal for how gravitational radiation can transfer energy and momentum between distant objects separated by a vacuum.

gr-qc↗
arXiv2017

Rotating and twisting locally rotationally symmetric spacetimes: a general solution

In this paper we derive a general solution for the most general rotating and twisting locally rotationally symmetric spacetimes. This is achieved in three steps. First we decompose the manifold via 1+1+2 semi-tetrad formalism that yields a set of geometrical and thermodynamic scalars for the spacetime. We then recast the Einstein field equations in terms of evolution and propagation of these scalars. It is then shown that this class of spacetimes must possess self similarity and we use this property to solve for these scalars, thus obtaining a general solution. This solution has a number of very interesting cosmological or astrophysical consequences which we discuss in detail.

gr-qc↗
arXiv2017

4-dimensional spacetimes from 2-dimensional conformal null data

In this paper we investigate whether the holographic principle proposed in string theory has a classical counterpart in general relativity theory. We show that there is a partial correspondence: at least in the case of vacuum Petrov type D spacetimes that admit a non-trivial Killing tensor, which encompass all the astrophysical black hole spacetimes, there exists a one to one correspondence between gravity in bulk and a two dimensional classical conformal scalar field on a null boundary.

gr-qc↗
arXiv2016

Foliation dependence of black hole apparent horizons in spherical symmetry

Numerical studies of gravitational collapse to black holes make use of apparent horizons, which are intrinsically foliation-dependent. We expose the problem and discuss possible solutions using the Hawking quasilocal mass. In spherical symmetry, we present a physically sensible approach to the problem by restricting to spherically symmetric spacetime slicings. In spherical symmetry the apparent horizons are gauge-independent in any spherically symmetric foliation but physical quantities associated with them, such as surface gravity and temperature, are not. The widely used comoving and Kodama foliations, which are of particular interest, are discussed in detail.

gr-qc↗
arXiv2016

New class of LRS spacetimes with simultaneous rotation and spatial twist

We establish the existence and find the necessary and sufficient conditions for a new class of solutions of Locally Rotationally Symmetric spacetimes that have non vanishing rotation and spatial twist simultaneously. We transparently show that the existence of such solutions demand non vanishing and bounded heat flux and these solutions are self similar. We provide a brief algorithm indicating how to solve the system of field equations with the given Cauchy data on an initial spacelike Cauchy surface. Finally we argue that these solutions can be used as a first approximation from spherical symmetry to study rotating, inhomogeneous, dynamic and radiating astrophysical stars.

gr-qc↗
arXiv2016

Current observations with a decaying cosmological constant allow for chaotic cyclic cosmology

We use the phase plane analysis technique of Madsen and Ellis to consider a universe with a true cosmological constant as well as a cosmological "constant" that is decaying. Time symmetric dynamics for the inflationary era allows eternally bouncing models to occur. Allowing for scalar field dynamic evolution, we find that if dark energy decays in the future, chaotic cyclic universes exist provided the spatial curvature is positive. This is particularly interesting in light of current observations which do not yet rule out either closed universes or possible evolution of the cosmological constant. We present only a proof of principle, with no definite claim on the physical mechanism required for the present dark energy to decay.

astro-ph.CO↗
arXiv2016

Constructing black hole entropy from gravitational collapse

Based on a recent proposal for the gravitational entropy of free gravitational fields, we investigate the thermodynamic properties of black hole formation through gravitational collapse in the framework of the semitetrad 1+1+2 covariant formalism. In the simplest case of an Oppenheimer-Snyder-Datt collapse we prove that the change in gravitational entropy outside a collapsing body is related to the variation of the surface area of the body itself, even before the formation of horizons. As a result, we are able to relate the Bekenstein-Hawking entropy of the black hole endstate to the variation of the vacuum gravitational entropy outside the collapsing body.

gr-qc↗
arXiv2015

The KLT relations in unimodular gravity

With this article, we initiate a systematic study of some of the symmetry properties of unimodular gravity, building on much of the known structure of general relativity, and utilising the powerful technology developed in that context. In particular, we show, up to four-points and tree-level, that the KLT relations of perturbative gravity hold for tracefree or unimodular gravity.

hep-th↗
arXiv2015

100 Years of General Relativity

This is Chapter 1 in the book General Relativity and Gravitation: A Centennial Perspective, Edited by Abhay Ashtekar (Editor in Chief), Beverly Berger, James Isenberg, Malcolm MacCallum. Publisher: Cambridge University Press (June, 2015). It gives a survey of themes that have been developed during the 100 years of progress in general relativity theory.

gr-qc↗
arXiv2015

Particle creation from the quantum stress tensor

Among the different methods to derive particle creation, finding the quantum stress tensor expectation value gives a covariant quantity which can be used for examining the back-reaction issue. However this tensor also includes vacuum polarization in a way that depends on the vacuum chosen. Here we review different aspects of particle creation by looking at energy conservation and at the quantum stress tensor. It will be shown that in the case of general spherically symmetric black holes that have a \emph{dynamical horizon}, as occurs in a cosmological context, one cannot have pair creation on the horizon because this violates energy conservation. This confirms the results obtained in other ways in a previous paper [25]. Looking at the expectation value of the quantum stress tensor with three different definitions of the vacuum state, we study the nature of particle creation and vacuum polarization in black hole and cosmological models, and the associated stress energy tensors. We show that the thermal temperature that is calculated from the particle flux given by the quantum stress tensor is compatible with the temperature determined by the affine null parameter approach. Finally, it will be shown that in the spherically symmetric dynamic case, we can neglect the backscattering term and only consider the s-waves term near the future apparent horizon.

gr-qc↗
arXiv2015

Ricci Time in the Lemaitre-Tolman Model and the Block Universe

It is common to think of our universe according to the "block universe" concept, which says that spacetime consists of many "stacked" 3-surfaces, labelled by some kind of proper time, $τ$. Standard ideas do not distinguish past and future, but Ellis "evolving block universe" tries to make a fundamental distinction. One proposal for this proper time is the proper time measured along the timelike Ricci eigenlines, starting from the big bang. This work investigates the shape of the "Ricci time" surfaces relative to the the null surfaces. We use the Lemaitre-Tolman metric as our inhomogeneous spacetime model, and we find the necessary and sufficient conditions for these $\{τ$= constant$\}$ surfaces, $S(τ)$, to be spacelike or timelike. Furthermore, we look at the effect of strong gravity domains by determining the location of timelike $S$ regions relative to apparent horizons. We find that constant Ricci time surfaces are always spacelike near the big bang, while at late times (near the crunch or the extreme far future), they are only timelike under special circumstances. At intermediate times, timelike $S$ regions are common unless the variation of the bang time is restricted. The regions where these surfaces become timelike are often adjacent to apparent horizons, but always outside them, and in particular timelike $S$ regions do not occur inside black holes.

gr-qc↗
arXiv2014

Cosmic Matter Flux May Turn Hawking Radiation Off

An astrophysical (cosmological) black hole forming in a cosmological context will be subject to a flux of infalling matter and radiation, which will cause the outer apparent horizon (a marginal trapping surface) to be spacelike \cite{ellisetal14}. As a consequence the radiation emitted close to the apparent horizon no longer arrives at infinity with a diverging redshift. Standard calculations of the emission of Hawking radiation then indicate that no blackbody radiation is emitted to infinity by the black hole in these circumstances, hence there will also then be no black hole evaporation process due to emission of such radiation as long as the matter flux is significant. The essential adiabatic condition (eikonal approximation) for black hole radiation gives a strong limit to the black holes that can emit Hawking radiation. We give the mass range for the black holes that can radiate, according to their cosmological redshift, for the special case of the cosmic blackbody radiation (CBR) influx (which exists everywhere in the universe). At a very late stage of black hole formation when the CBR influx decays away, the black hole horizon becomes first a slowly evolving horizon and then an isolated horizon; at that stage, black hole radiation will start. This study suggests that the primordial black hole evaporation scenario should be revised to take these considerations into account.

gr-qc↗
arXiv2014

Cosmic background radiation in the vicinity of a Schwarzschild black hole: no classic firewall

The Cosmic Blackbody Background Radiation pervades the entire Universe, and so falls into every astrophysical black hole. The blueshift of the infalling photons, measured by a static observer, is infinite at the event horizon. This raises a question as to whether a "firewall" of high energy density may form just outside the horizon, or whether the effect can be attributed exclusively to a singular behavior of the static observer's frame at the horizon. In principle, the presence of such firewall may alter the motion of the infalling matter, influence the black hole evolution, or even invalidate the {\it vacuum} Einstein field equation solution as a realistic approximation for black holes. In this paper we show by means of analytic calculations that all these effects indeed exist, but their magnitude is typically negligibly small, even though the matter stress tensor is divergent in the static frame at $r=2M$. That is not surprising because of the divergent relation of that frame to a freely falling frame as $r \rightarrow 2M$; however it represents a kind of classical analogue for the Black Hole Complementarity principle that has been proposed for quantum effects near a black hole. What is perhaps more surprising is the divergence of the radiation stress tensor for massive particles moving on circular geodesic orbits for values of $r$ approaching $r = 3M$. However such orbits will not occur for infalling matter in realistic accretion discs.

gr-qc↗