Quantum Dynamics of Lorentzian Spacetime Foam

A simple spacetime wormhole, which evolves classically from zero throat radius to a maximum value and recontracts, can be regarded as one possible mode of fluctuation in the microscopic ``spacetime foam'' first suggested by Wheeler. The dynamics of a particularly simple version of such a wormhole can be reduced to that of a single quantity, its throat radius; this wormhole thus provides a ``minisuperspace model'' for a structure in Lorentzian-signature foam. The classical equation of motion for the wormhole throat is obtained from the Einstein field equations and a suitable equation of state for the matter at the throat. Analysis of the quantum behavior of the hole then proceeds from an action corresponding to that equation of motion. The action obtained simply by calculating the scalar curvature of the hole spacetime yields a model with features like those of the relativistic free particle. In particular the Hamiltonian is nonlocal, and for the wormhole cannot even be given as a differential operator in closed form. Nonetheless the general solution of the Schr\"odinger equation for wormhole wave functions, i.e., the wave-function propagator, can be expressed as a path integral. Too complicated to perform exactly, this can yet be evaluated via a WKB approximation. The result indicates that the wormhole, classically stable, is quantum-mechanically unstable: A Feynman-Kac decomposition of the WKB propagator yields no spectrum of bound states. Though an initially localized wormhole wave function may oscillate for many classical expansion/recontraction periods, it must eventually leak to large radius values. The possibility of such a mode unstable against growth, combined withComment: 37 pages, 93-

Four-Body Effects in Globular Cluster Black Hole Coalescence

In the high density cores of globular clusters, multibody interactions are expected to be common, with the result that black holes in binaries are hardened by interactions. It was shown by Sigurdsson & Hernquist (1993) and others that 10 solar mass black holes interacting exclusively by three-body encounters do not merge in the clusters themselves, because recoil kicks the binaries out of the clusters before the binaries are tight enough to merge. Here we consider a new mechanism, involving four-body encounters. Numerical simulations by a number of authors suggest that roughly 20-50% of binary-binary encounters will eject one star but leave behind a stable hierarchical triple. If the orbital plane of the inner binary is strongly tilted with respect to the orbital plane of the outer object, a secular Kozai resonance, first investigated in the context of asteroids in the Solar System, can increase the eccentricity of the inner body significantly. We show that in a substantial fraction of cases the eccentricity is driven to a high enough value that the inner binary will merge by gravitational radiation, without a strong accompanying kick. Thus the merged object remains in the cluster; depending on the binary fraction of black holes and the inclination distribution of newly-formed hierarchical triples, this mechanism may allow massive black holes to accumulate through successive mergers in the cores of globular clusters. It may also increase the likelihood that stellar-mass black holes in globular clusters will be detectable by their gravitational radiation.Comment: Submitted to ApJ Letters (includes emulateapj.sty

Black holes and a scalar field in an expanding universe

We consider a model of an inhomogeneous universe including a massless scalar field, where the inhomogeneity is assumed to consist of many black holes. This model can be constructed by following Lindquist and Wheeler, which has already been investigated without including scalar field to show that an averaged scale factor coincides with that of the Friedmann model. In this work we construct the inhomogeneous universe with an massless scalar field, where we assume that the averaged scale factor and scalar field are given by those of the Friedmann model including a scalar field. All of our calculations are carried out in the framework of Brans-Dicke gravity. In constructing the model of an inhomogeneous universe, we define the mass of a black hole in the Brans-Dicke expanding universe which is equivalent to ADM mass if the mass evolves adiabatically, and obtain an equation relating our mass to the averaged scalar field and scale factor. As the results we find that the mass has an adiabatic time dependence in a sufficiently late stage of the expansion of the universe, and that the time dependence is qualitatively diffenrent according to the sign of the curvature of the universe: the mass increases decelerating in the closed universe case, is constant in the flat case and decreases decelerating in the open case. It is also noted that the mass in the Einstein frame depends on time. Our results that the mass has a time dependence should be retained even in the general scalar-tensor gravitiy with a scalar field potential. Furthermore, we discuss the relation of our results to the uniqueness theorem of black hole spacetime and gravitational memory effect.Comment: 16 pages, 3 tables, 5 figure

van Vleck determinants: traversable wormhole spacetimes

Calculating the van Vleck determinant in traversable wormhole spacetimes is an important ingredient in understanding the physical basis behind Hawking's chronology protection conjecture. This paper presents extensive computations of this object --- at least in the short--throat flat--space approximation. An important technical trick is to use an extension of the usual junction condition formalism to probe the full Riemann tensor associated with a thin shell of matter. Implications with regard to Hawking's chronology protection conjecture are discussed. Indeed, any attempt to transform a single isolated wormhole into a time machine results in large vacuum polarization effects sufficient to disrupt the internal structure of the wormhole before the onset of Planck scale physics, and before the onset of time travel. On the other hand, it is possible to set up a putative time machine built out of two or more wormholes, each of which taken in isolation is not itself a time machine. Such ``Roman configurations'' are much more subtle to analyse. For some particularly bizarre configurations (not traversable by humans) the vacuum polarization effects can be arranged to be arbitrarily small at the onset of Planck scale physics. This indicates that the disruption scale has been pushed down into the Planck slop. Ultimately, for these configurations, questions regarding the truth or falsity of Hawking's chronology protection can only be addressed by entering the uncharted wastelands of full fledged quantum gravity.Comment: 42 pages, ReV_TeX 3.

Is Quantum Spacetime Foam Unstable?

A very simple wormhole geometry is considered as a model of a mode of topological fluctutation in Planck-scale spacetime foam. Quantum dynamics of the hole reduces to quantum mechanics of one variable, throat radius, and admits a WKB analysis. The hole is quantum-mechanically unstable: It has no bound states. Wormhole wave functions must eventually leak to large radii. This suggests that stability considerations along these lines may place strong constraints on the nature and even the existence of spacetime foam.Comment: 15 page

Ejection of Supermassive Black Holes from Galaxy Cores

[Abridged] Recent numerical relativity simulations have shown that the emission of gravitational waves during the merger of two supermassive black holes (SMBHs) delivers a kick to the final hole, with a magnitude as large as 4000 km/s. We study the motion of SMBHs ejected from galaxy cores by such kicks and the effects on the stellar distribution using high-accuracy direct N-body simulations. Following the kick, the motion of the SMBH exhibits three distinct phases. (1) The SMBH oscillates with decreasing amplitude, losing energy via dynamical friction each time it passes through the core. Chandrasekhar's theory accurately reproduces the motion of the SMBH in this regime if 2 < ln Lambda < 3 and if the changing core density is taken into account. (2) When the amplitude of the motion has fallen to roughly the core radius, the SMBH and core begin to exhibit oscillations about their common center of mass. These oscillations decay with a time constant that is at least 10 times longer than would be predicted by naive application of the dynamical friction formula. (3) Eventually, the SMBH reaches thermal equilibrium with the stars. We estimate the time for the SMBH's oscillations to damp to the Brownian level in real galaxies and infer times as long as 1 Gyr in the brightest galaxies. Ejection of SMBHs also results in a lowered density of stars near the galaxy center; mass deficits as large as five times the SMBH mass are produced for kick velocities near the escape velocity. We compare the N-body density profiles with luminosity profiles of early-type galaxies in Virgo and show that even the largest observed cores can be reproduced by the kicks, without the need to postulate hypermassive binary SMBHs. Implications for displaced AGNs and helical radio structures are discussed.Comment: 18 pages, The Astrophysical Journal, in press. Replaced with revised versio

Rates and Characteristics of Intermediate Mass Ratio Inspirals Detectable by Advanced LIGO

Gravitational waves (GWs) from the inspiral of a neutron star (NS) or stellar-mass black hole (BH) into an intermediate-mass black hole (IMBH) with mass between ~50 and ~350 solar masses may be detectable by the planned advanced generation of ground-based GW interferometers. Such intermediate mass ratio inspirals (IMRIs) are most likely to be found in globular clusters. We analyze four possible IMRI formation mechanisms: (1) hardening of an NS-IMBH or BH-IMBH binary via three-body interactions, (2) hardening via Kozai resonance in a hierarchical triple system, (3) direct capture, and (4) inspiral of a compact object from a tidally captured main-sequence star; we also discuss tidal effects when the inspiraling object is an NS. For each mechanism we predict the typical eccentricities of the resulting IMRIs. We find that IMRIs will have largely circularized by the time they enter the sensitivity band of ground-based detectors. Hardening of a binary via three-body interactions, which is likely to be the dominant mechanism for IMRI formation, yields eccentricities under 10^-4 when the GW frequency reaches 10 Hz. Even among IMRIs formed via direct captures, which can have the highest eccentricities, around 90% will circularize to eccentricities under 0.1 before the GW frequency reaches 10 Hz. We estimate the rate of IMRI coalescences in globular clusters and the sensitivity of a network of three Advanced LIGO detectors to the resulting GWs. We show that this detector network may see up to tens of IMRIs per year, although rates of one to a few per year may be more plausible. We also estimate the loss in signal-to-noise ratio that will result from using circular IMRI templates for data analysis and find that, for the eccentricities we expect, this loss is negligible.Comment: Accepted for publication in ApJ; revised version reflects changes made to the article during the acceptance proces

Gauge Invariant Hamiltonian Formalism for Spherically Symmetric Gravitating Shells

The dynamics of a spherically symmetric thin shell with arbitrary rest mass and surface tension interacting with a central black hole is studied. A careful investigation of all classical solutions reveals that the value of the radius of the shell and of the radial velocity as an initial datum does not determine the motion of the shell; another configuration space must, therefore, be found. A different problem is that the shell Hamiltonians used in literature are complicated functions of momenta (non-local) and they are gauge dependent. To solve these problems, the existence is proved of a gauge invariant super-Hamiltonian that is quadratic in momenta and that generates the shell equations of motion. The true Hamiltonians are shown to follow from the super-Hamiltonian by a reduction procedure including a choice of gauge and solution of constraint; one important step in the proof is a lemma stating that the true Hamiltonians are uniquely determined (up to a canonical transformation) by the equations of motion of the shell, the value of the total energy of the system, and the choice of time coordinate along the shell. As an example, the Kraus-Wilczek Hamiltonian is rederived from the super-Hamiltonian. The super-Hamiltonian coincides with that of a fictitious particle moving in a fixed two-dimensional Kruskal spacetime under the influence of two effective potentials. The pair consisting of a point of this spacetime and a unit timelike vector at the point, considered as an initial datum, determines a unique motion of the shell.Comment: Some remarks on the singularity of the vector potantial are added and some minor corrections done. Definitive version accepted in Phys. Re

The gravitational wave rocket

Einstein's equations admit solutions corresponding to photon rockets. In these a massive particle recoils because of the anisotropic emission of photons. In this paper we ask whether rocket motion can be powered only by the emission of gravitational waves. We use the double series approximation method and show that this is possible. A loss of mass and gain in momentum arise in the second approximation because of the emission of quadrupole and octupole waves.Comment: 10 pages LaTe

Interpolating the Stage of Exponential Expansion in the Early Universe: a possible alternative with no reheating

In the standard picture, the inflationary universe is in a supercooled state which ends with a short time, large scale reheating period, after which the universe goes into a radiation dominated stage. An alternative is proposed here in which the radiation energy density smoothly decreases all during an inflation-like stage and with no discontinuity enters the subsequent radiation dominated stage. The scale factor is calculated from standard Friedmann cosmology in the presence of both radiation and vacuum energy density. A large class of solutions confirm the above identified regime of non-reheating inflation-like behavior for observationally consistent expansion factors and not too large a drop in the radiation energy density. One dynamical realization of such inflation without reheating is from warm inflation type scenarios. However the solutions found here are properties of the Einstein equations with generality beyond slow-roll inflation scenarios. The solutions also can be continuously interpolated from the non-reheating type behavior to the standard supercooled limit of exponential expansion, thus giving all intermediate inflation-like behavior between these two extremes. The temperature of the universe and the expansion factor are calculated for various cases. Implications for baryongenesis are discussed. This non-reheating, inflation-like regime also appears to have some natural features for a universe that is between nearly flat and open.Comment: 26 pages, Latex, 2 figures, In press Physical Review