arXiv subjects

Douglas M. Eardley

Publications and source records attributed to Douglas M. Eardley.

16 recordsLinked to original sources

arXiv2015

A Variational Principle for Asymptotically Randall-Sundrum Black Holes

We prove the following variational principle for asymptotically Randall-Sundrum (RS) black holes, based on the first law of black hole mechanics: Instantaneously static initial data that extremizes the mass yields a static black hole, for variations at fixed apparent horizon area, AdS curvature length, cosmological constant, brane tensions, and RS brane warp factors. This variational principle is valid with either two branes (RS1) or one brane (RS2), and is applicable to variational trial solutions.

gr-qc↗

arXiv2015

First Law and a Variational Principle for Static Asymptotically Randall-Sundrum Black Holes

We give a new, intrinsic, mass definition for spacetimes asymptotic to the Randall-Sundrum braneworld models, RS1 and RS2. For this mass, we prove a first law for static black holes, including variations of the bulk cosmological constant, brane tensions, and RS1 interbrane distance. Our first law defines a thermodynamic volume and a gravitational tension that are braneworld analogs of the corresponding quantities in asymptotically AdS black hole spacetimes and asymptotically flat compactifications, respectively. We also prove the following related variational principle for asymptotically RS black holes: instantaneously static initial data that extremizes the mass yields a static black hole, for variations at fixed apparent horizon area, AdS curvature length, cosmological constant, brane tensions, and RS brane warp factors. This variational principle is valid with either two branes (RS1) or one brane (RS2), and is applicable to variational trial solutions.

gr-qc↗

arXiv2015

Stability and Binding Energy of Small Asymptotically Randall-Sundrum Black Holes

We study the binding of a small black hole to a positive-tension brane in the second Randall-Sundrum scenario (RS2) with orbifold symmetry. We find that a small black hole on the brane has substantial gravitational binding energy to the brane, and is stable against escaping into the bulk. This result can be applied in other models with an orbifold-symmetric brane. We also find a novel static black hole, which is completely localized off the brane and is unstable against translations transverse to the brane. Our results are obtained analytically by applying a variational principle to black hole initial data. This paper is the second in a series on asymptotically RS black holes.

gr-qc↗

arXiv2002

Classical Black Hole Production in High-Energy Collisions

We investigate classical formation of a D-dimensional black hole in a high energy collision of two particles. The existence of an apparent horizon is related to the solution of an unusual boundary-value problem for Poisson's equation in flat space. For sufficiently small impact parameter, we construct solutions giving such apparent horizons in D=4. These supply improved estimates of the classical cross-section for black hole production, and of the mass of the resulting black holes. We also argue that a horizon can be found in a region of weak curvature, suggesting that these solutions are valid starting points for a semiclassical analysis of quantum black hole formation.

gr-qc↗

arXiv2000

Puncture of gravitating domain walls

We investigate the semi-classical instability of vacuum domain walls to processes where the domain walls decay by the formation of closed string loop boundaries on their worldvolumes. Intuitively, a wall which is initially spherical may `pop', so that a hole corresponding to a string boundary component on the wall, may form. We find instantons, and calculate the rates, for such processes. We show that after puncture, the hole grows exponentially at the same rate that the wall expands. It follows that the wall is never completely thermalized by a single expanding hole; at arbitrarily late times there is still a large, thin shell of matter which may drive an exponential expansion of the universe. We also study the situation where the wall is subjected to multiple punctures. We find that in order to completely annihilate the wall by this process, at least four string loops must be nucleated. We argue that this process may be relevant in certain brane-world scenarios, where the universe itself is a domain wall.

hep-th↗

arXiv1997

Quantum Decay of Domain Walls in Cosmology II: Hamiltonian Approach

This paper studies the decay of a large, closed domain wall in a closed universe. Such walls can form in the presence of a broken, discrete symmetry. We study a novel process of quantum decay for such a wall, in which the vacuum fluctuates from one discrete state to another throughout one half of the universe, so that the wall decays into pure field energy. Equivalently, the fluctuation can be thought of as the nucleation of a second closed domain wall of zero size, followed by its growth by quantum tunnelling and its collision with the first wall, annihilating both. We therefore study the 2-wall system coupled to a spherically symmetric gravitational field. We derive a simple form of the 2-wall action, use Dirac quantization, obtain the 2-wall wave function for annihilation, find from it the barrier factor for this quantum tunneling, and thereby get the decay probability. This is the second paper of a series.

gr-qc↗

arXiv1997

Quantum Decay of Domain Walls In Cosmology I: Instanton Approach

This paper studies the decay of a large, closed domain wall in a closed universe. Such walls can form in the presence of a broken, discrete symmetry. We introduce a novel process of quantum decay for such a wall, in which the vacuum fluctuates from one discrete state to another throughout one half of the universe, so that the wall decays into pure field energy. Equivalently, the fluctuation can be thought of as the nucleation of a second domain wall of zero size, followed by its growth by quantum tunnelling and its collision with the first wall, annihilating both. The barrier factor for this quantum tunneling is calculated by guessing and verifying a Euclidean instanton for the two-wall system. We also discuss the classical origin and evolution of closed, topologically spherical domain walls in the early universe, through a "budding-off" process involving closed domain walls larger than the Hubble radius. This paper is the first of a series on this subject.

gr-qc↗

arXiv1997

Black Hole Boundary Conditions and Coordinate Conditions

This paper treats boundary conditions on black hole horizons for the full 3+1D Einstein equations. Following a number of authors, the apparent horizon is employed as the inner boundary on a space slice. It is emphasized that a further condition is necessary for the system to be well posed; the ``prescribed curvature conditions" are therefore proposed to complete the coordinate conditions at the black hole. These conditions lead to a system of two 2D elliptic differential equations on the inner boundary surface, which coexist nicely to the 3D equation for maximal slicing (or related slicing conditions). The overall 2D/3D system is argued to be well posed and globally well behaved. The importance of ``boundary conditions without boundary values" is emphasized. This paper is the first of a series. This revised version makes minor additions and corrections to the previous version.

gr-qc↗

arXiv1996

Comment on "Instabilities in Close Neutron Star Binaries"

In a recent Physical Review Letter, Wilson and Mathews presented some interesting numerical calculations of a system of two equally massive neutron stars in strong-field gravity. In particular they estimated the innermost stable circular orbit in their system. Here we point out a possibly important consequence of their results: Their calculated configurations have total angular momentum $J$ and total mass $M$ too large to form any Kerr black hole: $J>M^2$, in constrast to previous calculations of the innermost stable circular orbit.

gr-qc↗

arXiv1995

Criticality and Bifurcation in the Gravitational Collapse of a Self-Coupled Scalar Field

We examine the gravitational collapse of a non-linear sigma model in spherical symmetry. There exists a family of continuously self-similar solutions parameterized by the coupling constant of the theory. These solutions are calculated together with the critical exponents for black hole formation of these collapse models. We also find that the sequence of solutions exhibits a Hopf-type bifurcation as the continuously self-similar solutions become unstable to perturbations away from self-similarity.

gr-qc↗

arXiv1995

Critical Exponents and Stability at the Black Hole Threshold for a Complex Scalar Field

This paper continues a study on Choptuik scaling in gravitational collapse of a complex scalar field at the threshold for black hole formation. We perform a linear perturbation analysis of the previously derived complex critical solution, and calculate the critical exponent for black hole mass, $γ\approx 0.387106$. We also show that this critical solution is unstable via a growing oscillatory mode.

gr-qc↗

arXiv1995

S-Duality at the Black Hole Threshold in Gravitational Collapse

We study gravitational collapse of the axion/dilaton field in classical low energy string theory, at the threshold for black hole formation. A new critical solution is derived that is spherically symmetric and continuously self-similar. The universal scaling and echoing behavior discovered by Choptuik in gravitational collapse appear in a somewhat different form. In particular, echoing takes the form of SL(2,R) rotations (cf. S-duality). The collapse leaves behind an outgoing pulse of axion/dilaton radiation, with nearly but not exactly flat spacetime within it.

gr-qc↗

arXiv1995

NONLINEAR WAVE EQUATIONS FOR RELATIVITY

Graviational radiation is described by canonical Yang-Mills wave equations on the curved space-time manifold, together with evolution equations for the metric in the tangent bundle. The initial data problem is described in Yang-Mills scalar and vector potentials, resulting in Lie-constraints in addition to the familiar Gauss-Codacci relations.

gr-qc↗

arXiv1995

Behavior of Friedmann-Robertson-Walker Cosmological Models in Scalar-Tensor Gravity

We analyze solutions to Friedmann-Robertson-Walker cosmologies in Brans-Dicke theory, where a scalar field is coupled to gravity. Matter is modelled by a $γ$-law perfect fluid, including false-vacuum energy as a special case. Through a change of variables, we reduce the field equations from fourth order to second order, and they become equivalent to a two-dimensional dynamical system. We then analyze the entire solution space of this dynamical system, and find that many qualitative features of these cosmologies can be gleaned, including standard non-inflationary or extended inflationary expansion, but also including bifurcations of stable or unstable expansion or contraction, noninflationary vacuum-energy dominated models, and several varieties of ``coasting," ``bouncing," ``hesitating," and ``vacillating" universes. It is shown that inflationary dogma, which states that a universe with curvature and dominated by inflationary matter will always approach a corresponding flat-space solution at late times, does not hold in general for the scalar-tensor theory, but rather that the occurence of inflation depends upon the initial energy of the scalar field relative to the expansion rate. In the case of flat space ($k=0$), the dynamical system formalism generates some previously known exact power-law solutions.

gr-qc↗

arXiv1994

Universal Scaling and Echoing in Gravitational Collapse of a Complex Scalar Field

This paper studies gravitational collapse of a complex scalar field at the threshold for black hole formation, assuming that the collapse is spherically symmetric and continuously self-similar. A new solution of the coupled Einstein-scalar field equations is derived, after a small amount of numerical work with ordinary differential equations. The universal scaling and echoing behavior discovered by Choptuik in spherically symmetrical gravitational collapse appear in a somewhat different form. Properties of the endstate of the collapse are derived: The collapse leaves behind an irregular outgoing pulse of scalar radiation, with exactly flat spacetime within it.

gr-qc↗

arXiv1994

Gravitational Collapse of Vacuum Gravitational Field Configurations

This paper proves a theorem about the existence of an apparent horizon in general relativity, which applies equally well to vacuum configurations and matter configurations. The theorem uses the reciprocal of the surface-to-volume ratio of a region on a space slice to measure the radius of the region, and uses the minimum value $K_{\rm min}$ of certain components of the extrinsic curvature to measure the strengh of the gravitational field in the region. The theorem proves that, if the product of the radius times $K_{\rm min}$ is larger than unity, then an apparent horizon must form, signalling the formation of a black hole.

gr-qc↗