471 research outputs found
Decay of the Cosmological Constant. Equivalence of Quantum Tunneling and Thermal Activation in Two Spacetime Dimensions
We study the decay of the cosmological constant in two spacetime dimensions
through production of pairs. We show that the same nucleation process looks as
quantum mechanical tunneling (instanton) to one Killing observer and as thermal
activation (thermalon) to another. Thus, we find another striking example of
the deep interplay between gravity, thermodynamics and quantum mechanics which
becomes apparent in presence of horizons.Comment: 11 pages, 6 figure
p-Brane Dyons and Electric-magnetic Duality
We discuss dyons, charge quantization and electric-magnetic duality for
self-interacting, abelian, p-form theories in the spacetime dimensions D=2(p+1)
where dyons can be present. The corresponding quantization conditions and
duality properties are strikingly different depending on whether p is odd or
even. If p is odd one has the familiar eg'-ge'= 2nh, whereas for even p one
finds the opposite relative sign, eg'+ge'= 2nh. These conditions are obtained
by introducing Dirac strings and taking due account of the multiple
connectedness of the configuration space of the strings and the dyons. A
two-potential formulation of the theory that treats the electric and magnetic
sources on the same footing is also given.
Our results hold for arbitrary gauge invariant self-interaction of the fields
and are valid irrespective of their duality properties.Comment: 33 pages, 1 figur
Black hole entropy calculations based on symmetries
Symmetry based approaches to the black hole entropy problem have a number of
attractive features; in particular they are very general and do not depend on
the details of the quantization method. However we point out that, of the two
available approaches, one faces conceptual problems (also emphasized by
others), while the second contains certain technical flaws. We correct these
errors and, within the new, improved scheme, calculate the entropy of
3-dimensional black holes. We find that, while the new symmetry vector fields
are well-defined on the ``stretched horizon,'' and lead to well-defined
Hamiltonians satisfying the expected Lie algebra, they fail to admit a
well-defined limit to the horizon. This suggests that, although the formal
calculation can be carried out at the classical level, its real, conceptual
origin probably lies in the quantum theory.Comment: 14 pages, Latex, CGPG-01/1-
Gravity from the extension of spatial diffeomorphisms
The possibility of the extension of spatial diffeomorphisms to a larger
family of symmetries in a class of classical field theories is studied. The
generator of the additional local symmetry contains a quadratic kinetic term
and a potential term which can be a general (not necessarily local) functional
of the metric. From the perspective of the foundation of Einstein's gravity our
results are positive: The extended constraint algebra is either that of
Einstein's gravity, or ultralocal gravity. If our goal is a simple modification
of Einstein's gravity that for example makes it perturbatively renormalizable,
as has recently been suggested, then our results show that there is no such
theory within this class.Comment: 34 page
Parallel transport on non-Abelian flux tubes
I propose a way of unambiguously parallel transporting fields on non-Abelian
flux tubes, or strings, by means of two gauge fields. One gauge field
transports along the tube, while the other transports normal to the tube.
Ambiguity is removed by imposing an integrability condition on the pair of
fields. The construction leads to a gauge theory of mathematical objects known
as Lie 2-groups, which are known to result also from the parallel transport of
the flux tubes themselves. The integrability condition is also shown to be
equivalent to the assumption that parallel transport along nearby string
configurations are equal up to arbitrary gauge transformations. Attempts to
implement this condition in a field theory leads to effective actions for
two-form fields.Comment: significant portions of text rewritten, references adde
Hamiltonian Time Evolution for General Relativity
Hamiltonian time evolution in terms of an explicit parameter time is derived
for general relativity, even when the constraints are not satisfied, from the
Arnowitt-Deser-Misner-Teitelboim-Ashtekar action in which the slicing density
is freely specified while the lapse is not.
The constraint ``algebra'' becomes a well-posed evolution system for the
constraints; this system is the twice-contracted Bianchi identity when
. The Hamiltonian constraint is an initial value constraint which
determines and hence , given .Comment: 4 pages, revtex, to appear in Phys. Rev. Let
Self-accelerated Universe
It is widely believed that the large redshifts for distant supernovae are
explained by the vacuum energy dominance, or, in other words, by the
cosmological constant in Einstein's equations, which is responsible for the
anti-gravitation effect. A tacit assumption is that particles move along a
geodesic for the background metric. This is in the same spirit as the consensus
regarding the uniform Galilean motion of a free electron. However, there is a
runaway solution to the Lorentz--Dirac equation governing the behavior of a
radiating electron, in addition to the Galilean solution. Likewise, a runaway
solution to the entire system of equations, both gravitation and matter
equations of motion including, may provide an alternative explanation for the
accelerated expansion of the Universe, without recourse to the hypothetic
cosmological constant.Comment: 11 pages; Talk at the 9th Adriatic Meeting, Dubrovnic, Croatia, 4-14
September, 2003, Minor improvement, references added; to appear in ``Progress
in General Relativity and Quantum Cosmology Research'', Nova Science
Publisher
Cosmology in nonrelativistic general covariant theory of gravity
Horava and Melby-Thompson recently proposed a new version of the
Horava-Lifshitz theory of gravity, in which the spin-0 graviton is eliminated
by introducing a Newtonian pre-potential and a local U(1) gauge field
. In this paper, we first derive the corresponding Hamiltonian,
super-momentum constraints, the dynamical equations, and the equations for
and , in the presence of matter fields. Then, we apply the theory to
cosmology, and obtain the modified Friedmann equation and the conservation law
of energy, in addition to the equations for and . When the spatial
curvature is different from zero, terms behaving like dark radiation and
stiff-fluid exist, from which, among other possibilities, bouncing universe can
be constructed. We also study linear perturbations of the FRW universe with any
given spatial curvature , and derive the most general formulas for scalar
perturbations. The vector and tensor perturbations are the same as those
recently given by one of the present authors [A. Wang, Phys. Rev. D{\bf 82},
124063 (2010)] in the setup of Sotiriou, Visser and Weinfurtner. Applying these
formulas to the Minkowski background, we have shown explicitly that the scalar
and vector perturbations of the metric indeed vanish, and the only remaining
modes are the massless spin-2 gravitons.Comment: Revtex4, no figures. Gauge freedom was clarified and typos were
corrected. Version to appear in Physical Reviews
Coulomb field of an accelerated charge: physical and mathematical aspects
The Maxwell field equations relative to a uniformly accelerated frame, and
the variational principle from which they are obtained, are formulated in terms
of the technique of geometrical gauge invariant potentials. They refer to the
transverse magnetic (TM) and the transeverse electric (TE) modes. This gauge
invariant "2+2" decomposition is used to see how the Coulomb field of a charge,
static in an accelerated frame, has properties that suggest features of
electromagnetism which are different from those in an inertial frame. In
particular, (1) an illustrative calculation shows that the Larmor radiation
reaction equals the electrostatic attraction between the accelerated charge and
the charge induced on the surface whose history is the event horizon, and (2) a
spectral decomposition of the Coulomb potential in the accelerated frame
suggests the possibility that the distortive effects of this charge on the
Rindler vacuum are akin to those of a charge on a crystal lattice.Comment: 27 pages, PlainTex. Related papers available at
http://www.math.ohio-state.edu/~gerlac
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