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Sean A. Hayward

Publications and source records attributed to Sean A. Hayward.

At least 37 records · Page 2Linked to original sources
arXiv2004

Energy conservation for dynamical black holes

An energy conservation law is described, expressing the increase in mass-energy of a general black hole in terms of the energy densities of the infalling matter and gravitational radiation. For a growing black hole, this first law of black-hole dynamics is equivalent to an equation of Ashtekar & Krishnan, but the new integral and differential forms are regular in the limit where the black hole ceases to grow. An effective gravitational-radiation energy tensor is obtained, providing measures of both ingoing and outgoing, transverse and longitudinal gravitational radiation on and near a black hole. Corresponding energy-tensor forms of the first law involve a preferred time vector which plays the role for dynamical black holes which the stationary Killing vector plays for stationary black holes. Identifying an energy flux, vanishing if and only if the horizon is null, allows a division into energy-supply and work terms, as in the first law of thermodynamics. The energy supply can be expressed in terms of area increase and a newly defined surface gravity, yielding a Gibbs-like equation, with a similar form to the so-called first law for stationary black holes.

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arXiv2004

How to make a traversable wormhole from a Schwarzschild black hole

The theoretical construction of a traversable wormhole from a Schwarzschild black hole is described, using analytic solutions in Einstein gravity. The matter model is pure phantom radiation (pure radiation with negative energy density) and the idealization of impulsive radiation is employed.

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arXiv2004

Kerr black holes in horizon-generating form

New coordinates are given which describe non-degenerate Kerr black holes in dual-null foliations based on the outer (or inner) horizons, generalizing the Kruskal form for Schwarzschild black holes. The construction involves an area radius for the transverse surfaces and a generalization of the Regge-Wheeler radial function, both functions of the original radial coordinate only.

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arXiv2003

The light cone at infinity

A recent refinement of Penrose's conformal framework for asymptotically flat space-times is summarized. The key idea concerns advanced and retarded conformal factors, which allow a rigid description of infinity as a locally metric light cone. In the new framework, the Bondi-Sachs energy-flux integrals of ingoing and outgoing gravitational radiation decay at spatial infinity such that the total radiated energy is finite, and the Bondi-Sachs energy-momentum has a unique limit at spatial infinity, coinciding with the uniquely rendered ADM energy-momentum.

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arXiv2003

Spatial and null infinity via advanced and retarded conformal factors

A new approach to space-time asymptotics is presented, refining Penrose's idea of conformal transformations with infinity represented by the conformal boundary of space-time. Generalizing examples such as flat and Schwarzschild space-times, it is proposed that the Penrose conformal factor be a product of advanced and retarded conformal factors, which asymptotically relate physical and conformal null (light-like) coordinates and vanish at future and past null infinity respectively, with both vanishing at spatial infinity. A correspondingly refined definition of asymptotic flatness at both spatial and null infinity is given, including that the conformal boundary is locally a light cone, with spatial infinity as the vertex. It is shown how to choose the conformal factors so that this asymptotic light cone is locally a metric light cone. The theory is implemented in the spin-coefficient (or null-tetrad) formalism by a simple joint transformation of the spin-metric and spin-basis (or metric and tetrad). The advanced and retarded conformal factors may be used as expansion parameters near the respective null infinity, together with a dependent expansion parameter for both spatial and null infinity, essentially inverse radius. Asymptotic regularity conditions on the spin-coefficients are proposed, based on the conformal boundary locally being a smoothly embedded metric light cone. These conditions ensure that the Bondi-Sachs energy-flux integrals of ingoing and outgoing gravitational radiation decay at spatial infinity such that the total radiated energy is finite, and that the Bondi-Sachs energy-momentum has a unique limit at spatial infinity, coinciding with the uniquely rendered ADM energy-momentum.

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arXiv2003

Recent progress in wormhole dynamics

Space-time wormholes were introduced in Wheeler's idea of space-time foam. Traversible wormholes as defined by Morris & Thorne became popular as potential short cuts across the universe and even time machines. More recently, the author proposed a general theory of wormhole dynamics, unified with black-hole dynamics. This article gives a brief review of the above ideas and summarizes progress on wormhole dynamics in the last year. Firstly, a numerical study of dynamical perturbations of the first Morris-Thorne wormhole showed it to be unstable, either collapsing to a black hole or exploding to an inflationary universe. This provides a mechanism for inflating a wormhole from space-time foam to usable size. Intriguing critical behaviour was also discovered. Secondly, a wormhole solution supported by pure radiation was discovered and used to find analytic examples of dynamic wormhole processes which were also recently found in a two-dimensional dilaton gravity model: the construction of a traversible wormhole from a Schwarzschild black hole and vice versa, and the enlargement or reduction of the wormhole.

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arXiv2002

Construction and enlargement of dilatonic wormholes by impulsive radiation

The dynamical behavior of traversable wormholes and black holes under impulsive radiation is studied in an exactly soluble dilaton gravity model. Simple solutions are presented where a traversable wormhole is constructed from a black hole, or the throat of a wormhole is stably enlarged or reduced. These solutions illustrate the basic operating principles needed to construct similar analytic solutions in full Einstein gravity.

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arXiv2002

Fate of the first traversible wormhole: black-hole collapse or inflationary expansion

We study numerically the stability of Morris & Thorne's first traversible wormhole, shown previously by Ellis to be a solution for a massless ghost Klein-Gordon field. Our code uses a dual-null formulation for spherically symmetric space-time integration, and the numerical range covers both universes connected by the wormhole. We observe that the wormhole is unstable against Gaussian pulses in either exotic or normal massless Klein-Gordon fields. The wormhole throat suffers a bifurcation of horizons and either explodes to form an inflationary universe or collapses to a black hole, if the total input energy is respectively negative or positive. As the perturbations become small in total energy, there is evidence for critical solutions with a certain black-hole mass or Hubble constant. The collapse time is related to the initial energy with an apparently universal critical exponent. For normal matter, such as a traveller traversing the wormhole, collapse to a black hole always results. However, carefully balanced additional ghost radiation can maintain the wormhole for a limited time. The black-hole formation from a traversible wormhole confirms the recently proposed duality between them. The inflationary case provides a mechanism for inflating, to macroscopic size, a Planck-sized wormhole formed in space-time foam.

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arXiv2002

Black holes and traversible wormholes: a synthesis

A unified framework for black holes and traversible wormholes is described, where both are locally defined by outer trapping horizons, two-way traversible for wormholes and one-way traversible for black or white holes. In a two-dimensional dilaton gravity model, examples are given of: construction of wormholes from black holes; operation of wormholes for transport, including back-reaction; maintenance of an operating wormhole; and collapse of wormholes to black holes. In spherically symmetric Einstein gravity, several exotic matter models supporting wormhole solutions are proposed: ghost scalar fields, exotic fluids and pure ghost radiation.

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arXiv2002

Gravitational Energy in Spherical Symmetry

Various properties of the Misner-Sharp spherically symmetric gravitational energy E are established or reviewed. In the Newtonian limit of a perfect fluid, E yields the Newtonian mass to leading order and the Newtonian kinetic and potential energy to the next order. For test particles, the corresponding Hajicek energy is conserved and has the behaviour appropriate to energy in the Newtonian and special-relativistic limits. In the small-sphere limit, the leading term in E is the product of volume and the energy density of the matter. In vacuo, E reduces to the Schwarzschild energy. At null and spatial infinity, E reduces to the Bondi-Sachs and Arnowitt-Deser-Misner energies respectively. The conserved Kodama current has charge E. A sphere is trapped if E>r/2, marginal if E=r/2 and untrapped if E 0, and temporal and untrapped if E<0. On an untrapped sphere, E is non-decreasing in any outgoing spatial or null direction, assuming the dominant energy condition. It follows that E>=0 on an untrapped spatial hypersurface with regular centre, and E>=r_0/2 on an untrapped spatial hypersurface bounded at the inward end by a marginal sphere of radius r_0. All these inequalities extend to the asymptotic energies, recovering the Bondi-Sachs energy loss and the positivity of the asymptotic energies, as well as proving the conjectured Penrose inequality for black or white holes. Implications for the cosmic censorship hypothesis and for general definitions of gravitational energy are discussed.

gr-qc↗
arXiv2002

Wormholes supported by pure ghost radiation

Traversible wormhole space-times are found as static, spherically symmetric solutions to the Einstein equations with ingoing and outgoing pure ghost radiation, i.e. pure radiation with negative energy density. Switching off the radiation causes the wormhole to collapse to a Schwarzschild black hole.

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arXiv2001

Dilatonic wormholes: construction, operation, maintenance and collapse to black holes

The CGHS two-dimensional dilaton gravity model is generalized to include a ghost Klein-Gordon field, i.e. with negative gravitational coupling. This exotic radiation supports the existence of static traversible wormhole solutions, analogous to Morris-Thorne wormholes. Since the field equations are explicitly integrable, concrete examples can be given of various dynamic wormhole processes, as follows. (i) Static wormholes are constructed by irradiating an initially static black hole with the ghost field. (ii) The operation of a wormhole to transport matter or radiation between the two universes is described, including the back-reaction on the wormhole, which is found to exhibit a type of neutral stability. (iii) It is shown how to maintain an operating wormhole in a static state, or return it to its original state, by turning up the ghost field. (iv) If the ghost field is turned off, either instantaneously or gradually, the wormhole collapses into a black hole.

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arXiv2001

Gravitational radiation, energy and reaction on quasi-spherical black holes

Gravitational radiation is locally defined where the wavefronts are roughly spherical. A local energy tensor is defined for the gravitational radiation. Including this energy tensor as a source in the truncated Einstein equations describes gravitational radiation reaction, such as back-reaction on a roughly spherical black hole. The energy-momentum in a canonical frame is covariantly conserved. The strain to be measured by a distant detector is simply defined.

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arXiv2001

Gravitational-wave dynamics and black-hole dynamics: second quasi-spherical approximation

Gravitational radiation with roughly spherical wavefronts, produced by roughly spherical black holes or other astrophysical objects, is described by an approximation scheme. The first quasi-spherical approximation, describing radiation propagation on a background, is generalized to include additional non-linear effects, due to the radiation itself. The gravitational radiation is locally defined and admits an energy tensor, satisfying all standard local energy conditions and entering the truncated Einstein equations as an effective energy tensor. This second quasi-spherical approximation thereby includes gravitational radiation reaction, such as the back-reaction on the black hole. With respect to a canonical flow of time, the combined energy-momentum of the matter and gravitational radiation is covariantly conserved. The corresponding Noether charge is a local gravitational mass-energy. Energy conservation is formulated as a local first law relating the gradient of the gravitational mass to work and energy-supply terms, including the energy flux of the gravitational radiation. Zeroth, first and second laws of black-hole dynamics are given, involving a dynamic surface gravity. Local gravitational-wave dynamics is described by a non-linear wave equation. In terms of a complex gravitational- radiation potential, the energy tensor has a scalar-field form and the wave equation is an Ernst equation, holding independently at each spherical angle. The strain to be measured by a distant detector is simply defined.

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arXiv2000

Quasi-spherical approximation for rotating black holes

We numerically implement a quasi-spherical approximation scheme for computing gravitational waveforms for coalescing black holes, testing it against angular momentum by applying it to Kerr black holes. As error measures, we take the conformal strain and specific energy due to spurious gravitational radiation. The strain is found to be monotonic rather than wavelike. The specific energy is found to be at least an order of magnitude smaller than the 1% level expected from typical black-hole collisions, for angular momentum up to at least 70% of the maximum, for an initial surface as close as $r=3m$.

gr-qc↗
arXiv2000

Quasi-local first law of black-hole dynamics

A property well known as the first law of black hole is a relation among infinitesimal variations of parameters of stationary black holes. We consider a dynamical version of the first law, which may be called the first law of black hole dynamics. The first law of black hole dynamics is derived without assuming any symmetry or any asymptotic conditions. In the derivation, a definition of dynamical surface gravity is proposed. In spherical symmetry it reduces to that defined recently by one of the authors (SAH).

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