2,058 research outputs found
Self-force on a scalar charge in radial infall from rest using the Hadamard-WKB expansion
We present an analytic method based on the Hadamard-WKB expansion to
calculate the self-force for a particle with scalar charge that undergoes
radial infall in a Schwarzschild spacetime after being held at rest until a
time t = 0. Our result is valid in the case of short duration from the start.
It is possible to use the Hadamard-WKB expansion in this case because the value
of the integral of the retarded Green's function over the particle's entire
past trajectory can be expressed in terms of two integrals over the time period
that the particle has been falling. This analytic result is expected to be
useful as a check for numerical prescriptions including those involving mode
sum regularization and for any other analytical approximations to self-force
calculations.Comment: 22 pages, 2 figures, Physical Review D version along with the
corrections given in the erratu
Point Charge Self-Energy in the General Relativity
Singularities in the metric of the classical solutions to the Einstein
equations (Schwarzschild, Kerr, Reissner -- Nordstr\"om and Kerr -- Newman
solutions) lead to appearance of generalized functions in the Einstein tensor
that are not usually taken into consideration. The generalized functions can be
of a more complex nature than the Dirac \d-function. To study them, a
technique has been used based on a limiting solution sequence. The solutions
are shown to satisfy the Einstein equations everywhere, if the energy-momentum
tensor has a relevant singular addition of non-electromagnetic origin. When the
addition is included, the total energy proves finite and equal to , while
for the Kerr and Kerr--Newman solutions the angular momentum is .
As the Reissner--Nordstr\"om and Kerr--Newman solutions correspond to the point
charge in the classical electrodynamics, the result obtained allows us to view
the point charge self-energy divergence problem in a new fashion.Comment: VI Fridmann Seminar, France, Corsica, Corgeze, 2004, LaTeX, 6 pages,
2 fige
A universal constraint between charge and rotation rate for degenerate black holes surrounded by matter
We consider stationary, axially and equatorially symmetric systems consisting
of a central rotating and charged degenerate black hole and surrounding matter.
We show that always holds provided that a continuous sequence of
spacetimes can be identified, leading from the Kerr-Newman solution in
electrovacuum to the solution in question. The quantity is the black
hole's intrinsic angular momentum per unit mass, its electric charge and
the well known black hole mass parameter introduced by Christodoulou and
Ruffini.Comment: 19 pages, 2 figures, replaced with published versio
Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation
This paper is concerned with a generalized type of Darboux transformations
defined in terms of a twisted derivation satisfying
where is a homomorphism. Such twisted derivations include regular
derivations, difference and -difference operators and superderivatives as
special cases. Remarkably, the formulae for the iteration of Darboux
transformations are identical with those in the standard case of a regular
derivation and are expressed in terms of quasideterminants. As an example, we
revisit the Darboux transformations for the Manin-Radul super KdV equation,
studied in Q.P. Liu and M. Ma\~nas, Physics Letters B \textbf{396} 133--140,
(1997). The new approach we take enables us to derive a unified expression for
solution formulae in terms of quasideterminants, covering all cases at once,
rather than using several subcases. Then, by using a known relationship between
quasideterminants and superdeterminants, we obtain expressions for these
solutions as ratios of superdeterminants. This coincides with the results of
Liu and Ma\~nas in all the cases they considered but also deals with the one
subcase in which they did not obtain such an expression. Finally, we obtain
another type of quasideterminant solutions to the Main-Radul super KdV equation
constructed from its binary Darboux transformations. These can also be
expressed as ratios of superdeterminants and are a substantial generalization
of the solutions constructed using binary Darboux transformations in earlier
work on this topic
van Vleck determinants: geodesic focussing and defocussing in Lorentzian spacetimes
The van Vleck determinant is an ubiquitous object, arising in many physically
interesting situations such as: (1) WKB approximations to quantum time
evolution operators and Green functions. (2) Adiabatic approximations to heat
kernels. (3) One loop approximations to functional integrals. (4) The theory of
caustics in geometrical optics and ultrasonics. (5) The focussing and
defocussing of geodesic flows in Riemannian manifolds. While all of these
topics are interrelated, the present paper is particularly concerned with the
last case and presents extensive theoretical developments that aid in the
computation of the van Vleck determinant associated with geodesic flows in
Lorentzian spacetimes. {\sl A fortiori} these developments have important
implications for the entire array of topics indicated. PACS: 04.20.-q,
04.20.Cv, 04.60.+n. To appear in Physical Review D47 (1993) 15 March.Comment: plain LaTeX, 18 page
Next-to-leading term of the renormalized stress-energy tensor of the quantized massive scalar field in Schwarzschild spacetime. The back reaction
The next-to-leading term of the renormalized stress-energy tensor of the
quantized massive field with an arbitrary curvature coupling in the spacetime
of the Schwarzschild black hole is constructed. It is achieved by functional
differentiation of the DeWitt-Schwinger effective action involving coincidence
limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficients and
The back reaction of the quantized field upon the Schwarzschild black
hole is briefly discussed
Coupling of Linearized Gravity to Nonrelativistic Test Particles: Dynamics in the General Laboratory Frame
The coupling of gravity to matter is explored in the linearized gravity
limit. The usual derivation of gravity-matter couplings within the
quantum-field-theoretic framework is reviewed. A number of inconsistencies
between this derivation of the couplings, and the known results of tidal
effects on test particles according to classical general relativity are pointed
out. As a step towards resolving these inconsistencies, a General Laboratory
Frame fixed on the worldline of an observer is constructed. In this frame, the
dynamics of nonrelativistic test particles in the linearized gravity limit is
studied, and their Hamiltonian dynamics is derived. It is shown that for
stationary metrics this Hamiltonian reduces to the usual Hamiltonian for
nonrelativistic particles undergoing geodesic motion. For nonstationary metrics
with long-wavelength gravitational waves (GWs) present, it reduces to the
Hamiltonian for a nonrelativistic particle undergoing geodesic
\textit{deviation} motion. Arbitrary-wavelength GWs couple to the test particle
through a vector-potential-like field , the net result of the tidal forces
that the GW induces in the system, namely, a local velocity field on the system
induced by tidal effects as seen by an observer in the general laboratory
frame. Effective electric and magnetic fields, which are related to the
electric and magnetic parts of the Weyl tensor, are constructed from that
obey equations of the same form as Maxwell's equations . A gedankin
gravitational Aharonov-Bohm-type experiment using to measure the
interference of quantum test particles is presented.Comment: 38 pages, 7 figures, written in ReVTeX. To appear in Physical Review
D. Galley proofs corrections adde
The warp drive: hyper-fast travel within general relativity
It is shown how, within the framework of general relativity and without the
introduction of wormholes, it is possible to modify a spacetime in a way that
allows a spaceship to travel with an arbitrarily large speed. By a purely local
expansion of spacetime behind the spaceship and an opposite contraction in
front of it, motion faster than the speed of light as seen by observers outside
the disturbed region is possible. The resulting distortion is reminiscent of
the ``warp drive'' of science fiction. However, just as it happens with
wormholes, exotic matter will be needed in order to generate a distortion of
spacetime like the one discussed here.Comment: 10 pages, 1 figure. Not previously available in gr-q
Quantum teleportation between moving detectors in a quantum field
We consider the quantum teleportation of continuous variables modeled by
Unruh-DeWitt detectors coupled to a common quantum field initially in the
Minkowski vacuum. An unknown coherent state of an Unruh-DeWitt detector is
teleported from one inertial agent (Alice) to an almost uniformly accelerated
agent (Rob, for relativistic motion), using a detector pair initially entangled
and shared by these two agents. The averaged physical fidelity of quantum
teleportation, which is independent of the observer's frame, always drops below
the best fidelity value from classical teleportation before the detector pair
becomes disentangled with the measure of entanglement evaluated around the
future lightcone of the joint measurement event by Alice. The distortion of the
quantum state of the entangled detector pair from the initial state can
suppress the fidelity significantly even when the detectors are still strongly
entangled around the lightcone. We point out that the dynamics of entanglement
of the detector pair observed in Minkowski frame or in quasi-Rindler frame are
not directly related to the physical fidelity of quantum teleportation in our
setup. These results are useful as a guide to making judicious choices of
states and parameter ranges and estimation of the efficiency of quantum
teleportation in relativistic quantum systems under environmental influences.Comment: 18 pages, 7 figure
Regularity of Cauchy horizons in S2xS1 Gowdy spacetimes
We study general S2xS1 Gowdy models with a regular past Cauchy horizon and
prove that a second (future) Cauchy horizon exists, provided that a particular
conserved quantity is not zero. We derive an explicit expression for the
metric form on the future Cauchy horizon in terms of the initial data on the
past horizon and conclude the universal relation A\p A\f=(8\pi J)^2 where
A\p and A\f are the areas of past and future Cauchy horizon respectively.Comment: 17 pages, 1 figur
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