Gravitational Backreaction Research Articles

Black hole horizons and complementarity.

We investigate the effect of gravitational back-reaction on the black hole evaporation process. The standard derivation of Hawking radiation is re-examined and extended by including gravitational interactions between the infalling matter and the outgoing radiation. We find that these interactions lead to substantial effects. In particular, as seen by an outside observer, they lead to a fast growing uncertainty in the position of the infalling matter as it approaches the horizon. We argue that this result supports the idea of black hole complementarity, which states that, in the description of the black hole system appropriate to outside observers, the region behind the horizon does not establish itself as a classical region of space-time. We also give a new formulation of this complementarity principle, which does not make any specific reference to the location of the black hole horizon.

Characteristics of cosmic string scaling configurations.

Using the formalism developed in a previous paper we analyze the cosmological implications of our conclusions concerning the scaling behaviour of a network of cosmic strings, in particular the idea that once gravitational back-reaction becomes important the transient scaling regime so far explored by numerical simulations will be replaced by a new `full scaling' regime, with slightly different parameters. This has consequences for the normalization of the string tension on all scales. We show how the new scaling solutions affect the gravitational wave bound from nucleosynthesis and the milli-second pulsar, and also describe the consequences from large scale structure up to COBE scales.

Closed-form expression for the momentum radiated from cosmic string loops.

We modify the recent analytic formula given by Allen and Casper for the rate at which piecewise linear cosmic string loops lose energy to gravitational radiation to yield the analogous analytic formula for the rate at which loops radiate momentum. The resulting formula (which is exact when the effects of gravitational back-reaction are neglected) is a sum of O(N^4) polynomial and log terms where, N is the total number of segments on the piecewise linear string loop. As illustration, we write the formula explicitly for a simple one-parameter family of loops with N=5. For most loops the large number of terms makes evaluation ``by hand" impractical, but, a computer or symbolic manipulator may by used to yield accurate results. The formula has been used to correct numerical results given in the existing literature. To assist future work in this area, a small catalog of results for a number of simple string loops is provided.

Closed-form expression for the gravitational radiation rate from cosmic strings.

We present a new formula for the rate at which cosmic strings lose energy into gravitational radiation, valid for all piecewise-linear cosmic string loops. At any time, such a loop is composed of $N$ straight segments, each of which has constant velocity. Any cosmic string loop can be arbitrarily-well approximated by a piecewise-linear loop with $N$ sufficiently large. The formula is a sum of $O(N^4)$ polynomial and log terms, and is exact when the effects of gravitational back-reaction are neglected. For a given loop, the large number of terms makes evaluation ``by hand" impractical, but a computer or symbolic manipulator yields accurate results. The formula is more accurate and convenient than previous methods for finding the gravitational radiation rate, which require numerical evaluation of a four-dimensional integral for each term in an infinite sum. It also avoids the need to estimate the contribution from the tail of the infinite sum. The formula has been tested against all previously published radiation rates for different loop configurations. In the cases where discrepancies were found, they were due to errors in the published work. We have isolated and corrected both the analytic and numerical errors in these cases. To assist future work in this area, a small catalog of results for some simple loop shapes is provided.

General solutions for tunneling of scalar fields with quartic potentials in de Sitter space.

The tunneling rates for scalar fields with quartic potentials in de Sitter space in the limit of no gravitational back reaction are calculated numerically and the results are fitted by analytic formulae.

Fermionic theta vacua and long-necked remnants.

We study a vacuum polarization effect in the background of a certain dilatonic extremal black hole, known as the cornucopion. Whenever charged fermions are of any nonzero mass, the gravitational back reaction to a generic value of a $\mathrm{CP}$-nonconserving vacuum angle $\ensuremath{\theta}$ is shown to be important owing to a vacuum energy density which does not vanish deep inside the cornucopion. When the vacuum energy density is positive, this effect creates an extremal horizon at finite physical distance, closing off the infinite neck. We study the geometry of this horizon in some detail and find different physical interpretations for small and large fermion mass. Also, we argue that the conclusion is qualitatively correct despite the inevitable strong coupling.

Evolution of cosmic string configurations.

We extend and develop our previous work on the evolution of a network of cosmic strings. The new treatment is based on an analysis of the probability distribution of the end-to-end distance, or extension, of a randomly chosen segment of left-moving string of given length. The description involves three distinct length scales: \ensuremath{\xi}, related to the overall string density, \ensuremath{\xi}\ifmmode\bar\else\textasciimacron\fi{}, the persistance length along the string, and \ensuremath{\zeta}, describing the small-scale structure, which is an important feature of the numerical simulations that have been done of this problem. An evolution equation is derived describing how the distribution develops in time due to the combined effects of the universal expansion, of intercommuting and loop formation, and of gravitational radiation. With plausible assumptions about the unknown parameters in the model, we confirm the conclusions of our previous study that if gravitational radiation and small-scale structure effects are neglected the two dominant length scales both scale in proportion to the horizon size. When the extra effects are included, we find that while \ensuremath{\xi} and \ensuremath{\xi}\ifmmode\bar\else\textasciimacron\fi{} grow, \ensuremath{\zeta} initially does not. Eventually, however, it does appear to scale, at a much lower level, due to the effects of gravitational back reaction.

Small-scale structure on cosmic strings.

We extend a linear-kink model of small-scale structure on cosmic strings and show how it is equivalent to an earlier two-scale model. By reconsidering the connection between the rate of loop production and the linear-kink density we correctly predict the build-up of small-scale structure currently seen in those simulations which neglect the gravitational back reaction. After including the gravitational back reaction we determine the full evolution of the small-scale structure, coupled to loop production and gravitational radiation. We confirm that the inclusion of the gravitational back reaction leads inevitably to the scaling of this structure, and that as many as ${10}^{4}$ kinks may persist on an horizon-sized segment of string.

From wormhole to time machine: Remarks on Hawking's chronology protection conjecture.

The recent interest in ``time machines'' has been largely fueled by the apparent ease with which such systems may be formed in general relativity, given relatively benign initial conditions such as the existence of traversable wormholes or of infinite cosmic strings. This rather disturbing state of affairs has led Hawking to formulate his Chronology Protection Conjecture, whereby the formation of ``time machines'' is forbidden. This paper will use several simple examples to argue that the universe appears to exhibit a ``defense in depth'' strategy in this regard. For appropriate parameter regimes Casimir effects, wormhole disruption effects, and gravitational back reaction effects all contribute to the fight against time travel. Particular attention is paid to the role of the quantum gravity cutoff. For the class of model problems considered it is shown that the gravitational back reaction becomes large before the Planck scale quantum gravity cutoff is reached, thus supporting Hawking's conjecture.

Effects of gravitational back reaction on small-scale structure of cosmic strings.

Effects of gravitational back reaction on small-scale structure of cosmic strings.

Gravitational self-interactions of cosmic strings.

We study the gravitational back reaction of local cosmic-string loops as they shrink due to gravitational radiation. We chart the evolution of the shape and radiation rate of the loops. Cusps survive gravitational back reaction, but are weakened. Asymmetric string trajectories radiate momentum and hence undergo a rocket effect, but the effect is not very significant. Typically, a string loop's center-of-mass velocity is changed by $\ensuremath{\Delta}v\ensuremath{\sim}0.1c$. Trajectories that have few modes and that are non-self-intersecting remain so almost until the end of the string's lifetime. We also study highly kinky loops. Small kinks decay very quickly, the decay time for a kink of size $l$ being given by $t{(l)}_{\mathrm{decay}}\ensuremath{\sim}{({\ensuremath{\Gamma}}_{\mathrm{kink}}G\ensuremath{\mu})}^{\ensuremath{-}1}l$, where ${\ensuremath{\Gamma}}_{\mathrm{kink}}\ensuremath{\sim}50$. We argue that this limits the smallest relevant structures on long strings in networks to a fraction (${\ensuremath{\Gamma}}_{\mathrm{kink}}G\ensuremath{\mu}$) of the size of the horizon, and that this will also set the scale for loops produced off a network. This, coupled with results from string network simulations and millisecond-pulsar constraints, limits the string tension to $G\ensuremath{\mu}<2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. This is far from ruling out the cosmic-string scenario of galaxy formation.

Dynamics of cosmic string.

We consider various aspects of the dynamics of cosmic string, many of which are special to four spacetime dimensions. When a loop fragments we show how the properties of the original loop, and those of the daughter loops, are related. We discuss the construction of solutions for a string loop of various types, emphasizing the properties of loops with kinks. Since the number of cusps does not increase during fragmentation, most loops may not have cusps. We provide a geometrical argument that cusps are not smoothed by the self-gravity of the string. An estimate of the gravitational back reaction near a cusp is compatible with this result. We discover a relation between self-intersections of a loop and cusps, and discuss various ways in which a loop is expected to evolve as it loses mass to radiation. The cusps which occur at kinks may be detectable if the string is superconducting.