4,975 research outputs found
Energy-Momentum Restrictions on the Creation of Gott Time Machines
The discovery by Gott of a remarkably simple spacetime with closed timelike
curves (CTC's) provides a tool for investigating how the creation of time
machines is prevented in classical general relativity. The Gott spacetime
contains two infinitely long, parallel cosmic strings, which can equivalently
be viewed as point masses in (2+1)-dimensional gravity. We examine the
possibility of building such a time machine in an open universe. Specifically,
we consider initial data specified on an edgeless, noncompact, spacelike
hypersurface, for which the total momentum is timelike (i.e., not the momentum
of a Gott spacetime). In contrast to the case of a closed universe (in which
Gott pairs, although not CTC's, can be produced from the decay of stationary
particles), we find that there is never enough energy for a Gott-like time
machine to evolve from the specified data; it is impossible to accelerate two
particles to sufficiently high velocity. Thus, the no-CTC theorems of Tipler
and Hawking are enforced in an open (2+1)-dimensional universe by a mechanism
different from that which operates in a closed universe. In proving our result,
we develop a simple method to understand the inequalities that restrict the
result of combining momenta in (2+1)-dimensional gravity.Comment: Plain TeX, 41 pages incl. 9 figures. MIT-CTP #225
A Relativistic Description of Gentry's New Redshift Interpretation
We obtain a new expression of the Friedmann-Robertson-Walker metric, which is
an analogue of a static chart of the de Sitter space-time. The reduced metric
contains two functions, and , which are interpreted as,
respectively, the mass function and the gravitational potential. We find that,
near the coordinate origin, the reduced metric can be approximated in a static
form and that the approximated metric function, , satisfies the
Poisson equation. Moreover, when the model parameters of the
Friedmann-Robertson-Walker metric are suitably chosen, the approximated metric
coincides with exact solutions of the Einstein equation with the perfect fluid
matter. We then solve the radial geodesics on the approximated space-time to
obtain the distance-redshift relation of geodesic sources observed by the
comoving observer at the origin. We find that the redshift is expressed in
terms of a peculiar velocity of the source and the metric function, ,
evaluated at the source position, and one may think that this is a new
interpretation of {\it Gentry's new redshift interpretation}.Comment: 11 pages. Submitted to Modern Physics Letters
Non-topological solitons as nucleation sites for cosmological phase transitions
I consider quantum field theories that admit charged non-topological solitons
of the Q-ball type, and use the fact that in a first-order cosmological phase
transition, below the critical temperature, there is a value of the soliton
charge above which the soliton becomes unstable and expands, converting space
to the true vacuum, much like a critical bubble in the case of ordinary
tunneling. Using a simple model for the production rate of Q-balls through
charge accretion during a random walk out of equilibrium, I calculate the
probability for the formation of critical charge solitons and estimate the
amount of supercooling needed for the phase transition to be completed.Comment: 20 pages, 2 figures, some comments and references adde
Self Similar Solutions of the Evolution Equation of a Scalar Field in an Expanding Geometry
We consider the functional Schrodinger equation for a self interacting scalar
field in an expanding geometry. By performing a time dependent scale
transformation on the argument of the field we derive a functional Schrodinger
equation whose hamiltonian is time independent but involves a time-odd term
associated to a constraint on the expansion current. We study the mean field
approximation to this equation and generalize in this case, for interacting
fields, the solutions worked out by Bunch and Davies for free fields.Comment: 8 pages, Latex, IPNO/TH 94-3
On the variable-charged black holes embedded into de Sitter space: Hawking's radiation
In this paper we study the Hawking evaporation of masses of variable-charged
Reissner-Nordstrom and Kerr-Newman, black holes embedded into the de Sitter
universe by considering the charge to be function of radial coordinate of the
spherically symmetric metric.Comment: LaTex, p. 2
Trusting versus monitoring: an experiment of endogenous institutional choices
We investigate the problem of deciding between trusting and monitoring, and how this decision affects subsequent behavior, using a laboratory experiment where subjects choose between the Ultimatum and the Yes-No Game. Despite the similarity of the two games in Ultimatum Games responders monitor the allocation proposal, while in Yes-No games responders react without monitoring, i.e. have to rely on trust. We permit either the proposer or responder to make the game choice and analyze how both roles choose between trusting and monitoring, what the ensuing effects of their choices are, and how they vary depending on who has chosen the game. We, also, experimentally vary the cost of monitoring and the responder’s conflict payoff. Since monitoring is usually costly, the amount to share in Yes-No Games (YNG) can exceed that in Ultimatum Games (UG). Regarding the conflict payoff, it can be positive or negative with the former rendering Yes-No interaction a social dilemma. According to our results, proposers (responders) opt for trusting significantly more (less) often than for monitoring. Average offers are higher in Ultimatum than in Yes-No games, but neither UG nor YNG offers depend on who has chosen between games
Telling the other what one knows? Strategic lying in a modified acquiring-a-company experiment with two-sided private information
Lying for a strategic advantage is to be expected in commercial interactions. But would this be more or less obvious when lying could come from either party and question mutually profitable exchange? To explore this, we modify the acquiring-a-company game (Samuelson and Bazerman in Res Exp Econ 3:105–138, 1985) by letting both, buyer and seller, be privately informed. Specifically, the value of the company for the buyer is known only by the seller; whereas, only the buyer is aware by which proportion the sellers evaluation is lower than that of the buyer. Before bargaining, both parties can reveal what they know via cheap-talk numerical messages. Game theoretically, the pooling equilibrium may or may not allow for trade depending on the commonly known expected evaluation discrepancy. By mutually revealing what one knows, one could boost trade and efficiency. Although strategic misreporting prevails quite generally, it is higher for sellers throughout the experiment. Regarding gender, women misreport less, especially as sellers, and offer higher prices
Cosmological Inflation with orbifold moduli as inflatons
Cosmological inflation is studied in the case where the inflaton is the
overall modulus for an orbifold. General forms of the (non-perturbative)
superpotential are considered to ensure that is modular
invariant. We find generically that these models do not produce a potential
flat enough for slow roll to a supersymmetric minimum, although we do find a
model which produces up to 20 e-folds of inflation to a non-supersymmetric
minimum.Comment: LaTeX file, 16 pages including 5 figures, v3 is the published versio
Non-Equilibrium Evolution of Scalar Fields in FRW Cosmologies I
We derive the effective equations for the out of equilibrium time evolution
of the order parameter and the fluctuations of a scalar field theory in
spatially flat FRW cosmologies.The calculation is performed both to one-loop
and in a non-perturbative, self-consistent Hartree approximation.The method
consists of evolving an initial functional thermal density matrix in time and
is suitable for studying phase transitions out of equilibrium. The
renormalization aspects are studied in detail and we find that the counterterms
depend on the initial state. We investigate the high temperature expansion and
show that it breaks down at long times. We also obtain the time evolution of
the initial Boltzmann distribution functions, and argue that to one-loop order
or in the Hartree approximation, the time evolved state is a ``squeezed''
state. We illustrate the departure from thermal equilibrium by numerically
studying the case of a free massive scalar field in de Sitter and radiation
dominated cosmologies. It is found that a suitably defined non-equilibrium
entropy per mode increases linearly with comoving time in a de Sitter
cosmology, whereas it is {\it not} a monotonically increasing function in the
radiation dominated case.Comment: 29 pages, revtex 3.0, 11 figures available upon request, PITT-93-6;
LPTHE-93-52; CMU-HEP-93-2
General Solutions for Tunneling of Scalar Fields with Quartic Potentials
For the theory of a single scalar field with a quartic potential
, we find semi-analytic expressions for the Euclidean action in
both four and three dimensions. The action in four dimensions determines the
quantum tunneling rate at zero temperature from a false vacuum state to the
true vacuum state; similarly, the action in three dimensions determines the
thermal tunneling rate for a finite temperature theory. We show that for all
quartic potentials, the action can be obtained from a one parameter family of
instanton solutions corresponding to a one parameter family of differential
equations. We find the solutions numerically and use polynomial fitting
formulae to obtain expressions for the Euclidean action. These results allow
one to calculate tunneling rates for the entire possible range of quartic
potentials, from the thin-wall (nearly degenerate) limit to the opposite limit
of vanishing barrier height. We also present a similar calculation for
potentials containing terms, which arise in the
one-loop approximation to the effective potential in electroweak theory.Comment: 17 pages, 6 figures not included but available upon request, UM AC
93-
- …