96 research outputs found
Newtonian limits of warp drive spacetimes
We find a class of warp drive spacetimes possessing Newtonian limits, which
we then determine. The same method is used to compute Newtonian limits of the
Schwarzschild solution and spatially flat Friedmann-Robertson-Walker
cosmological models.Comment: 9 pages; v2: major changes; v3: misprints correcte
Elastic shocks in relativistic rigid rods and balls
We study the free boundary problem for the "hard phase" material introduced
by Christodoulou, both for rods in (1+1)-dimensional Minkowski spacetime and
for spherically symmetric balls in (3+1)-dimensional Minkowski spacetime.
Unlike Christodoulou, we do not consider a "soft phase", and so we regard this
material as an elastic medium, capable of both compression and stretching. We
prove that shocks must be null hypersurfaces, and derive the conditions to be
satisfied at a free boundary. We solve the equations of motion of the rods
explicitly, and we prove existence of solutions to the equations of motion of
the spherically symmetric balls for an arbitrarily long (but finite) time,
given initial conditions sufficiently close to those for the relaxed ball at
rest. In both cases we find that the solutions contain shocks if and only if
the pressure or its time derivative do not vanish at the free boundary
initially. These shocks interact with the free boundary, causing it to lose
regularity.Comment: 22 pages, 3 figures; v2: small changes, matches final published
version; v3: typos in the references fixe
Homogeneous cosmologies from the quasi-Maxwell formalism
We show how to use the quasi-Maxwell formalism to obtain solutions of
Einstein's field equations corresponding to homogeneous cosmologies - namely
Einstein's universe, Godel's universe and the Ozsvath-Farnsworth-Kerr class I
solutions - written in frames for which the associated observers are
stationary.Comment: 15 pages, references adde
Asymptotic Quasinormal Frequencies for Black Holes in Non-Asymptotically Flat Spacetimes
The exact computation of asymptotic quasinormal frequencies is a technical
problem which involves the analytic continuation of a Schrodinger-like equation
to the complex plane and then performing a method of monodromy matching at the
several poles in the plane. While this method was successfully used in
asymptotically flat spacetime, as applied to both the Schwarzschild and
Reissner-Nordstrom solutions, its extension to non-asymptotically flat
spacetimes has not been achieved yet. In this work it is shown how to extend
the method to this case, with the explicit analysis of Schwarzschild de Sitter
and large Schwarzschild Anti-de Sitter black holes, both in four dimensions. We
obtain, for the first time, analytic expressions for the asymptotic quasinormal
frequencies of these black hole spacetimes, and our results match previous
numerical calculations with great accuracy. We also list some results
concerning the general classification of asymptotic quasinormal frequencies in
d-dimensional spacetimes.Comment: JHEP3.cls, 20 pages, 5 figures; v2: added references, typos
corrected, minor changes, final version for JMP; v3: more typos fixe
Spherical linear waves in de Sitter spacetime
We apply Christodoulou's framework, developed to study the Einstein-scalar
field equations in spherical symmetry, to the linear wave equation in de Sitter
spacetime, as a first step towards the Einstein-scalar field equations with
positive cosmological constant. We obtain an integro-differential evolution
equation which we solve by taking initial data on a null cone. As a corollary
we obtain elementary derivations of expected properties of linear waves in de
Sitter spacetime: boundedness in terms of (characteristic) initial data, and a
Price law establishing uniform exponential decay, in Bondi time, to a constant.Comment: 9 pages, 1 figure; v2: minor changes, references added, matches final
published versio
Mathisson's helical motions demystified
The motion of spinning test particles in general relativity is described by
Mathisson-Papapetrou-Dixon equations, which are undetermined up to a spin
supplementary condition, the latter being today still an open question. The
Mathisson-Pirani (MP) condition is known to lead to rather mysterious helical
motions which have been deemed unphysical, and for this reason discarded. We
show that these assessments are unfounded and originate from a subtle (but
crucial) misconception. We discuss the kinematical explanation of the helical
motions, and dynamically interpret them through the concept of hidden momentum,
which has an electromagnetic analogue. We also show that, contrary to previous
claims, the frequency of the helical motions coincides exactly with the
zitterbewegung frequency of the Dirac equation for the electron.Comment: To appear in the Proceedings of the Spanish Relativity Meeting 2011
(ERE2011), "Towards new paradigms", Madrid 29 August - 2 September 201
- …