9,937 research outputs found

### Stability of naked singularities and algebraically special modes

We show that algebraically special modes lead to the instability of naked
singularity spacetimes with negative mass. Four-dimensional negative-mass
Schwarzschild and Schwarzschild-de Sitter spacetimes are unstable. Stability of
the Schwarzschild-anti-de Sitter spacetime depends on boundary conditions. We
briefly discuss the generalization of these results to charged and rotating
singularities.Comment: 6 pages. ReVTeX4. v2: Minor improvements and extended discussion on
boundary conditions. Version to appear in Phys. Rev.

### The Bell-Szekeres Solution and Related Solutions of the Einstein-Maxwell Equations

A novel technique for solving some head-on collisions of plane homogeneous
light-like signals in Einstein-Maxwell theory is described. The technique is a
by-product of a re-examination of the fundamental Bell-Szekeres solution in
this field of study. Extensions of the Bell-Szekeres collision problem to
include light-like shells and gravitational waves are described and a family of
solutions having geometrical and topological properties in common with the
Bell-Szekeres solution is derived.Comment: 18 pages, Latex fil

### Electrodynamics in Friedmann-Robertson-Walker Universe: Maxwell and Dirac fields in Newman-Penrose formalism

Maxwell and Dirac fields in Friedmann-Robertson-Walker spacetime is
investigated using the Newman-Penrose method. The variables are all separable,
with the angular dependence given by the spin-weighted spherical harmonics. All
the radial parts reduce to the barrier penetration problem, with mostly
repulsive potentials representing the centrifugal energies. Both the helicity
states of the photon field see the same potential, but that of the Dirac field
see different ones; one component even sees attractive potential in the open
universe. The massless fields have the usual exponential time dependencies;
that of the massive Dirac field is coupled to the evolution of the cosmic scale
factor $a$. The case of the radiation filled flat universe is solved in terms
of the Whittaker function. A formal series solution, valid in any FRW universe,
is also presented. The energy density of the Maxwell field is explicitly shown
to scale as $a^{-4}$. The co-moving particle number density of the massless
Dirac field is found to be conserved, but that of the massive one is not.
Particles flow out of certain regions, and into others, creating regions that
are depleted of certain linear and angular momenta states, and others with
excess. Such current of charged particles would constitute an electric current
that could generate a cosmic magnetic field. In contrast, the energy density of
these massive particles still scales as $a^{-4}$.Comment: 18 pages including 9 figure

### Can binary mergers produce maximally spinning black holes?

Gravitational waves carry away both energy and angular momentum as binary
black holes inspiral and merge. The relative efficiency with which they are
radiated determines whether the final black hole of mass $M_f$ and spin $S_f$
saturates the Kerr limit ($\chi_f \equiv S_f/M_f^2 \leq 1$). Extrapolating from
the test-particle limit, we propose expressions for $S_f$ and $M_f$ for mergers
with initial spins aligned or anti-aligned with the orbital angular momentum.
We predict the the final spin at plunge for equal-mass non-spinning binaries to
better than 1%, and that equal-mass maximally spinning aligned mergers lead to
nearly maximally spinning final black holes ($\chi_f \simeq 0.9988$). We also
find black holes can always be spun up by aligned mergers provided the mass
ratio is small enough.Comment: 4 pages, 6 figues, sublitted to PR

### Stellar Dynamics and Black Holes

Chandrasekhar's most important contribution to stellar dynamics was the
concept of dynamical friction. I briefly review that work, then discuss some
implications of Chandrasekhar's theory of gravitational encounters for motion
in galactic nuclei.Comment: Talk presented at the "Chandrasekhar Centenary Conference" (2010

### Spontaneous symmetry breaking in rotating condensates of ultracold atoms

We describe an equilibrium state of a rotating trapped atomic condensate,
which is characterized by a non-zero internal circulation and spontaneous
breaking of the rotational O(2) symmetry with all three major semiaxes of the
condensate having different values. The macroscopic rotation of the condensate
is supported by a mesh of quantized vortices, whose number density is a
function of internal circulation. The oscillation modes of this state are
computed and the Goldstone mode associated with the loss of the symmetry is
identified. The possible avenues for experimental identification this state are
discussed.Comment: v1: 4 pages, 3 figures; v2: 5 pages, 4 figures, minor changes,
matches published versio

### Dipole Perturbations of the Reissner-Nordstrom Solution: The Polar Case

The formalism developed by Chandrasekhar for the linear polar perturbations
of the Reissner-Nordstrom solution is generalized to include the case of dipole
(l=1) perturbations. Then, the perturbed metric coefficients and components of
the Maxwell tensor are computed.Comment: 16 pages, LaTeX, no figures. Submitted for publication in Physical
Review

### Equilibration, generalized equipartition, and diffusion in dynamical Lorentz gases

We prove approach to thermal equilibrium for the fully Hamiltonian dynamics
of a dynamical Lorentz gas, by which we mean an ensemble of particles moving
through a $d$-dimensional array of fixed soft scatterers that each possess an
internal harmonic or anharmonic degree of freedom to which moving particles
locally couple. We establish that the momentum distribution of the moving
particles approaches a Maxwell-Boltzmann distribution at a certain temperature
$T$, provided that they are initially fast and the scatterers are in a
sufficiently energetic but otherwise arbitrary stationary state of their free
dynamics--they need not be in a state of thermal equilibrium. The temperature
$T$ to which the particles equilibrate obeys a generalized equipartition
relation, in which the associated thermal energy $k_{\mathrm B}T$ is equal to
an appropriately defined average of the scatterers' kinetic energy. In the
equilibrated state, particle motion is diffusive

### The Effect of Sources on the Inner Horizon of Black Holes

Single pulse of null dust and colliding null dusts both transform a regular
horizon into a space-like singularity in the space of colliding waves. The
local isometry between such space-times and black holes extrapolates these
results to the realm of black holes. However, inclusion of particular scalar
fields instead of null dusts creates null singularities rather than space-like
ones on the inner horizons of black holes.Comment: Final version to appear in PR

### Stellar Pulsations excited by a scattered mass

We compute the energy spectra of the gravitational signals emitted when a
mass m is scattered by the gravitational field of a star of mass M >> m. We
show that, unlike black holes in similar processes, the quasi-normal modes of
the star are excited, and that the amount of energy emitted in these modes
depends on how close the exciting mass can get to the star.Comment: 23 pages, 6 figures, RevTe

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