12,438 research outputs found

### Collisions of Shock Waves in General Relativity

We show that the Nariai-Bertotti Petrov type D, homogeneous solution of
Einstein's vacuum field equations with a cosmological constant describes the
space-time in the interaction region following the head-on collision of two
homogeneous, plane gravitational shock waves each initially traveling in a
vacuum containing no cosmological constant. A shock wave in this context has a
step function profile in contrast to an impulsive wave which has a delta
function profile. Following the collision two light-like signals, each composed
of a plane, homogeneous light-like shell of matter and a plane, homogeneous
impulsive gravitational wave, travel away from each other and a cosmological
constant is generated in the interaction region. Furthermore a plane,
light-like signal consisting of an electromagnetic shock wave accompanying a
gravitational shock wave is described with the help of two real parameters, one
for each wave. The head-on collision of two such light-like signals is examined
and we show that if a simple algebraic relation is satisfied between the two
pairs of parameters associated with each incoming light-like signal then the
space-time in the interaction region following the collision is a Bertotti
space-time which is a homogeneous solution of the vacuum Einstein-Maxwell field
equations with a cosmological constant.Comment: Latex file, 10 page

### On The Interaction of Gravitational Waves with Magnetic and Electric Fields

The existence of large--scale magnetic fields in the universe has led to the
observation that if gravitational waves propagating in a cosmological
environment encounter even a small magnetic field then electromagnetic
radiation is produced. To study this phenomenon in more detail we take it out
of the cosmological context and at the same time simplify the gravitational
radiation to impulsive waves. Specifically, to illustrate our findings, we
describe the following three physical situations: (1) a cylindrical impulsive
gravitational wave propagating into a universe with a magnetic field, (2) an
axially symmetric impulsive gravitational wave propagating into a universe with
an electric field and (3) a `spherical' impulsive gravitational wave
propagating into a universe with a small magnetic field. In cases (1) and (3)
electromagnetic radiation is produced behind the gravitational wave. In case
(2) no electromagnetic radiation appears after the wave unless a current is
established behind the wave breaking the Maxwell vacuum. In all three cases the
presence of the magnetic or electric fields results in a modification of the
amplitude of the incoming gravitational wave which is explicitly calculated
using the Einstein--Maxwell vacuum field equations.Comment: 15 pages, Latex file, accepted for publication in Physical Review

### Collision of Shock Waves in Einstein-Maxwell Theory with a Cosmological Constant: A Special Solution

Post-collision space-times of the Cartesian product form M'xM'', where M' and
M'' are two-dimensional manifolds, are known with M' and M'' having constant
curvatures of equal and opposite sign (for the collision of electromagnetic
shock waves) or of the same sign (for the collision of gravitational shock
waves). We construct here a new explicit post-collision solution of the
Einstein-Maxwell vacuum field equations with a cosmological constant for which
M' has constant (nonzero) curvature and M'' has zero curvature.Comment: Latex file, 7 page

### Scattering of High Speed Particles in the Kerr Gravitational Field

We calculate the angles of deflection of high speed particles projected in an
arbitrary direction into the Kerr gravitational field. This is done by first
calculating the light-like boost of the Kerr gravitational field in an
arbitrary direction and then using this boosted gravitational field as an
approximation to the gravitational field experienced by a high speed particle.
In the rest frame of the Kerr source the angles of deflection experienced by
the high speed test particle can then easily be evaluated.Comment: 10 pages, Latex file, accepted for publication in Phys. Rev.

### Colliding Impulsive Gravitational Waves and a Cosmological Constant

We present a space--time model of the collision of two homogeneous, plane
impulsive gravitational waves (each having a delta function profile)
propagating in a vacuum before collision and for which the post collision
space--time has constant curvature. The profiles of the incoming waves are
$k\,\delta(u)$ and $l\,\delta(v)$ where $k, l$ are real constants and $u=0,
v=0$ are intersecting null hypersurfaces. The cosmological constant $\Lambda$
in the post collision region of the space--time is given by $\Lambda=-6\,k\,l$.Comment: 12 pages, Latex file, published pape

### Bursts of Radiation and Recoil Effects in Electromagnetism and Gravitation

The Maxwell field of a charge e which experiences an impulsive acceleration
or deceleration is constructed explicitly by subdividing Minkowskian space-time
into two halves bounded by a future null-cone and then glueing the halves back
together with appropriate matching conditions. The resulting retarded radiation
can be viewed as instantaneous electromagnetic bremsstrahlung. If we similarly
consider a spherically symmetric, moving gravitating mass, to experience an
impulsive deceleration, as viewed by a distant observer, then this is
accompanied by the emission of a light-like shell whose total energy measured
by this observer is the same as the kinetic energy of the source before it
stops. This phenomenon is a recoil effect which may be thought of as a limiting
case of a Kinnersley rocket.Comment: 24 pages LaTeX2e, 2 figures (included). Published in Class. Quant.
Gravit

### Braking--Radiation: An Energy Source for a Relativistic Fireball

If the Schwarzschild black-hole is moving rectilinearly with uniform
3-velocity and suddenly stops, according to a distant observer, then we
demonstrate that this observer will see a spherical light--like shell or
"relativistic fireball" radiate outwards with energy equal to the original
kinetic energy of the black-hole.Comment: 6 pages, LateX2e. Published in Phys. Lett.

### Implications of Spontaneous Glitches in the Mass and Angular Momentum in Kerr Space-Time

The outward-pointing principal null direction of the Schwarzschild Riemann
tensor is null hypersurface-forming. If the Schwarzschild mass spontaneously
jumps across one such hypersurface then the hypersurface is the history of an
outgoing light-like shell. The outward-- pointing principal null direction of
the Kerr Riemann tensor is asymptotically (in the neighbourhood of future null
infinity) null hypersurface-forming. If the Kerr parameters of mass and angular
momentum spontaneously jump across one such asymptotic hypersurface then the
asymptotic hypersurface is shown to be the history of an outgoing light-like
shell and a wire singularity-free spherical impulsive gravitational wave.Comment: 16 pages, TeX, no figures, accepted for publication in Phys. Rev.

### Shear-Free Gravitational Waves in an Anisotropic Universe

We study gravitational waves propagating through an anisotropic Bianchi I
dust-filled universe (containing the Einstein-de-Sitter universe as a special
case). The waves are modeled as small perturbations of this background
cosmological model and we choose a family of null hypersurfaces in this
space-time to act as the histories of the wavefronts of the radiation. We find
that the perturbations we generate can describe pure gravitational radiation if
and only if the null hypersurfaces are shear-free. We calculate the
gauge-invariant small perturbations explicitly in this case. How these differ
from the corresponding perturbations when the background space-time is
isotropic is clearly exhibited.Comment: 32 pages, accepted for publication in Physical Review

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