2,715 research outputs found
Causal sets and conservation laws in tests of Lorentz symmetry
Many of the most important astrophysical tests of Lorentz symmetry also
assume that energy-momentum of the observed particles is exactly conserved. In
the causal set approach to quantum gravity a particular kind of Lorentz
symmetry holds but energy-momentum conservation may be violated. We show that
incorrectly assuming exact conservation can give rise to a spurious signal of
Lorentz symmetry violation for a causal set. However, the size of this spurious
signal is much smaller than can be currently detected and hence astrophysical
Lorentz symmetry tests as currently performed are safe from causal set induced
violations of energy-momentum conservation.Comment: 8 pages, matches version published in PR
An Elementary Proof of the Existence and Uniqueness Theorem for the Navier-Stokes Equations
We give a geometric approach to proving know regularity and existence
theorems for the 2D Navier-Stokes Equations. We feel this point of view is
instructive in better understanding the dynamics. The technique is inspired by
constructions in the Dynamical Systems.Comment: 15 Page
Mechanics of universal horizons
Modified gravity models such as Ho\v{r}ava-Lifshitz gravity or
Einstein-{\ae}ther theory violate local Lorentz invariance and therefore
destroy the notion of a universal light cone. Despite this, in the infrared
limit both models above possess static, spherically symmetric solutions with
"universal horizons" - hypersurfaces that are causal boundaries between an
interior region and asymptotic spatial infinity. In other words, there still
exist black hole solutions. We construct a Smarr formula (the relationship
between the total energy of the spacetime and the area of the horizon) for such
a horizon in Einstein-{\ae}ther theory. We further show that a slightly
modified first law of black hole mechanics still holds with the relevant area
now a cross-section of the universal horizon. We construct new analytic
solutions for certain Einstein-{\ae}ther Lagrangians and illustrate how our
results work in these exact cases. Our results suggest that holography may be
extended to these theories despite the very different causal structure as long
as the universal horizon remains the unique causal boundary when matter fields
are added.Comment: Minor clarifications. References update
Seemingly stable chemical kinetics can be stable, marginally stable or unstable
We present three examples of chemical reaction networks whose ordinary differential equation scaling limits are almost identical and in all cases stable. Nevertheless, the Markov jump processes associated to these reaction networks display the full range of behaviors: one is stable (positive recurrent), one is unstable (transient) and one is marginally stable (null recurrent). We study these differences and characterize the invariant measures by Lyapunov function techniques. In particular, we design a natural set of such functions which scale homogeneously to infinity, taking advantage of the same scaling behavior of the reaction rates
The Theory of a Quantum Noncanonical Field in Curved Spacetimes
Much attention has been recently devoted to the possibility that quantum
gravity effects could lead to departures from Special Relativity in the form of
a deformed Poincar\`e algebra. These proposals go generically under the name of
Doubly or Deformed Special Relativity (DSR). In this article we further explore
a recently proposed class of quantum field theories, involving noncanonically
commuting complex scalar fields, which have been shown to entail a DSR-like
symmetry. An open issue for such theories is whether the DSR-like symmetry has
to be taken as a physically relevant symmetry, or if in fact the "true"
symmetries of the theory are just rotations and translations while boost
invariance has to be considered broken. We analyze here this issue by extending
the known results to curved spacetime under both of the previous assumptions.
We show that if the symmetry of the free theory is taken to be a DSR-like
realization of the Poincar\'e symmetry, then it is not possible to render such
a symmetry a gauge symmetry of the curved physical spacetime. However, it is
possible to introduce an auxiliary spacetime which allows to describe the
theory as a standard quantum field theory in curved spacetime. Alternatively,
taking the point of view that the noncanonical commutation of the fields
actually implies a breakdown of boost invariance, the physical spacetime
manifold has to be foliated in surfaces of simultaneity and the field theory
can be coupled to gravity by making use of the ADM prescription.Comment: 9 pages, no figure
Development of an internal restraint system for an integrated restraint-pressure suit system Report, 7 Jun. 1965 - 28 Jun. 1966
Internal restraint system, composed of liquid filled garment and separate auxiliary system, for integrated restraint pressure suit for acceleration protection and thermal transpor
About Locality and the Relativity Principle Beyond Special Relativity
Locality of interactions is an essential ingredient of Special Relativity.
Recently, a new framework under the name of relative locality
\cite{AmelinoCamelia:2011bm} has been proposed as a way to consider Planckian
modifications of the relativistic dynamics of particles. We note in this paper
that the loss of absolute locality is a general feature of theories beyond
Special Relativity with an implementation of a relativity principle. We give an
explicit construction of such an implementation and compare it both with the
previously mentioned framework of relative locality and the so-called Doubly
Special Relativity theories.Comment: 10 pages, no figure
Detecting Vanishing Dimensions Via Primordial Gravitational Wave Astronomy
Lower-dimensionality at higher energies has manifold theoretical advantages
as recently pointed out. Moreover, it appears that experimental evidence may
already exists for it - a statistically significant planar alignment of events
with energies higher than TeV has been observed in some earlier cosmic ray
experiments. We propose a robust and independent test for this new paradigm.
Since (2+1)-dimensional spacetimes have no gravitational degrees of freedom,
gravity waves cannot be produced in that epoch. This places a universal maximum
frequency at which primordial waves can propagate, marked by the transition
between dimensions. We show that this cut-off frequency may be accessible to
future gravitational wave detectors such as LISA.Comment: Somewhat expanded version with discussions that could not fit into
the PRL version; references adde
Sensitivity of Hawking radiation to superluminal dispersion relations
We analyze the Hawking radiation process due to collapsing configurations in
the presence of superluminal modifications of the dispersion relation. With
such superluminal dispersion relations, the horizon effectively becomes a
frequency-dependent concept. In particular, at every moment of the collapse,
there is a critical frequency above which no horizon is experienced. We show
that, as a consequence, the late-time radiation suffers strong modifications,
both quantitative and qualitative, compared to the standard Hawking picture.
Concretely, we show that the radiation spectrum becomes dependent on the
measuring time, on the surface gravities associated with different frequencies,
and on the critical frequency. Even if the critical frequency is well above the
Planck scale, important modifications still show up.Comment: 14 pages, 7 figures. Extensive paragraph added in conclusions to
clarify obtained result
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