2,320 research outputs found
Decay of the Maxwell field on the Schwarzschild manifold
We study solutions of the decoupled Maxwell equations in the exterior region
of a Schwarzschild black hole. In stationary regions, where the Schwarzschild
coordinate ranges over , we obtain a decay rate of
for all components of the Maxwell field. We use vector field methods
and do not require a spherical harmonic decomposition.
In outgoing regions, where the Regge-Wheeler tortoise coordinate is large,
, we obtain decay for the null components with rates of
, , and . Along the event horizon and in ingoing regions, where ,
and when , all components (normalized with respect to an ingoing null
basis) decay at a rate of C \uout^{-1} with \uout=t+r_* in the exterior
region.Comment: 37 pages, 5 figure
Self-Similar Scalar Field Collapse: Naked Singularities and Critical Behaviour
Homothetic scalar field collapse is considered in this article. By making a
suitable choice of variables the equations are reduced to an autonomous system.
Then using a combination of numerical and analytic techniques it is shown that
there are two classes of solutions. The first consists of solutions with a
non-singular origin in which the scalar field collapses and disperses again.
There is a singularity at one point of these solutions, however it is not
visible to observers at finite radius. The second class of solutions includes
both black holes and naked singularities with a critical evolution (which is
neither) interpolating between these two extremes. The properties of these
solutions are discussed in detail. The paper also contains some speculation
about the significance of self-similarity in recent numerical studies.Comment: 27 pages including 5 encapsulated postcript figures in separate
compressed file, report NCL94-TP1
Designing cost-sharing methods for Bayesian games
We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria, have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE).We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players
On Linear Congestion Games with Altruistic Social Context
We study the issues of existence and inefficiency of pure Nash equilibria in
linear congestion games with altruistic social context, in the spirit of the
model recently proposed by de Keijzer {\em et al.} \cite{DSAB13}. In such a
framework, given a real matrix specifying a particular
social context, each player aims at optimizing a linear combination of the
payoffs of all the players in the game, where, for each player , the
multiplicative coefficient is given by the value . We give a broad
characterization of the social contexts for which pure Nash equilibria are
always guaranteed to exist and provide tight or almost tight bounds on their
prices of anarchy and stability. In some of the considered cases, our
achievements either improve or extend results previously known in the
literature
On the Impact of Fair Best Response Dynamics
In this work we completely characterize how the frequency with which each
player participates in the game dynamics affects the possibility of reaching
efficient states, i.e., states with an approximation ratio within a constant
factor from the price of anarchy, within a polynomially bounded number of best
responses. We focus on the well known class of congestion games and we show
that, if each player is allowed to play at least once and at most times
any best responses, states with approximation ratio times the
price of anarchy are reached after best
responses, and that such a bound is essentially tight also after exponentially
many ones. One important consequence of our result is that the fairness among
players is a necessary and sufficient condition for guaranteeing a fast
convergence to efficient states. This answers the important question of the
maximum order of needed to fast obtain efficient states, left open by
[9,10] and [3], in which fast convergence for constant and very slow
convergence for have been shown, respectively. Finally, we show
that the structure of the game implicitly affects its performances. In
particular, we show that in the symmetric setting, in which all players share
the same set of strategies, the game always converges to an efficient state
after a polynomial number of best responses, regardless of the frequency each
player moves with
Global existence problem in -Gowdy symmetric IIB superstring cosmology
We show global existence theorems for Gowdy symmetric spacetimes with type
IIB stringy matter. The areal and constant mean curvature time coordinates are
used. Before coming to that, it is shown that a wave map describes the
evolution of this system
A New Lower Bound for Deterministic Truthful Scheduling
We study the problem of truthfully scheduling tasks to selfish
unrelated machines, under the objective of makespan minimization, as was
introduced in the seminal work of Nisan and Ronen [STOC'99]. Closing the
current gap of on the approximation ratio of deterministic truthful
mechanisms is a notorious open problem in the field of algorithmic mechanism
design. We provide the first such improvement in more than a decade, since the
lower bounds of (for ) and (for ) by
Christodoulou et al. [SODA'07] and Koutsoupias and Vidali [MFCS'07],
respectively. More specifically, we show that the currently best lower bound of
can be achieved even for just machines; for we already get
the first improvement, namely ; and allowing the number of machines to
grow arbitrarily large we can get a lower bound of .Comment: 15 page
Best Approximation to a Reversible Process in Black-Hole Physics and the Area Spectrum of Spherical Black Holes
The assimilation of a quantum (finite size) particle by a
Reissner-Nordstr\"om black hole inevitably involves an increase in the
black-hole surface area. It is shown that this increase can be minimized if one
considers the capture of the lightest charged particle in nature. The
unavoidable area increase is attributed to two physical reasons: the Heisenberg
quantum uncertainty principle and a Schwinger-type charge emission (vacuum
polarization). The fundamental lower bound on the area increase is ,
which is smaller than the value given by Bekenstein for neutral particles.
Thus, this process is a better approximation to a reversible process in
black-hole physics. The universality of the minimal area increase is a further
evidence in favor of a uniformly spaced area spectrum for spherical quantum
black holes. Moreover, this universal value is in excellent agreement with the
area spacing predicted by Mukhanov and Bekenstein and independently by Hod.Comment: 10 page
Quantum Creation of Black Hole by Tunneling in Scalar Field Collapse
Continuously self-similar solution of spherically symmetric gravitational
collapse of a scalar field is studied to investigate quantum mechanical black
hole formation by tunneling in the subcritical case where, classically, the
collapse does not produce a black hole.Comment: t clarification of the quantization method in Sec. IV, version to
appear in PR
Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms
We reconsider the well-studied Selfish Routing game with affine latency
functions. The Price of Anarchy for this class of games takes maximum value
4/3; this maximum is attained already for a simple network of two parallel
links, known as Pigou's network. We improve upon the value 4/3 by means of
Coordination Mechanisms.
We increase the latency functions of the edges in the network, i.e., if
is the latency function of an edge , we replace it by
with for all . Then an
adversary fixes a demand rate as input. The engineered Price of Anarchy of the
mechanism is defined as the worst-case ratio of the Nash social cost in the
modified network over the optimal social cost in the original network.
Formally, if \CM(r) denotes the cost of the worst Nash flow in the modified
network for rate and \Copt(r) denotes the cost of the optimal flow in the
original network for the same rate then [\ePoA = \max_{r \ge 0}
\frac{\CM(r)}{\Copt(r)}.]
We first exhibit a simple coordination mechanism that achieves for any
network of parallel links an engineered Price of Anarchy strictly less than
4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25.
Then, for the case of two parallel links, we describe an optimal mechanism; its
engineered Price of Anarchy lies between 1.191 and 1.192.Comment: 17 pages, 2 figures, preliminary version appeared at ESA 201
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