16 research outputs found

### Colliding Plane Impulsive Gravitational Waves

When two non-interacting plane impulsive gravitational waves undergo a
head-on collision, the vacuum interaction region between the waves after the
collision contains backscattered gravitational radiation from both waves. The
two systems of backscattered waves have each got a family of rays (null
geodesics) associated with them. We demonstrate that if it is assumed that a
parameter exists along each of these families of rays such that the modulus of
the complex shear of each is equal then Einstein's vacuum field equations, with
the appropriate boundary conditions, can be integrated systematically to reveal
the well-known solutions in the interaction region. In so doing the mystery
behind the origin of such solutions is removed. With the use of the field
equations it is suggested that the assumption leading to their integration may
be interpreted physically as implying that the energy densities of the two
backscattered radiation fields are equal. With the use of different boundary
conditions this approach can lead to new collision solutions.Comment: 21 pages, LaTeX2

### Colliding Plane Waves in Einstein-Maxwell Theory

Recently a simple solution of the vacuum Einstein-Maxwell field equations was given describing a plane electromagnetic shock wave sharing its wave front with a plane gravitational impulse wave. We present here an exact solution of the vacuum Einstein-Maxwell field equations describing the head-on collision of such a wave with a plane gravitational impulse wave. The solution has the Penrose-Khan solution and a solution obtained by Griffiths as separate limiting cases

### 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.

### On the extension of the concept of Thin Shells to The Einstein-Cartan Theory

This paper develops a theory of thin shells within the context of the
Einstein-Cartan theory by extending the known formalism of general relativity.
In order to perform such an extension, we require the general non symmetric
stress-energy tensor to be conserved leading, as Cartan pointed out himself, to
a strong constraint relating curvature and torsion of spacetime. When we
restrict ourselves to the class of space-times satisfying this constraint, we
are able to properly describe thin shells and derive the general expression of
surface stress-energy tensor both in its four-dimensional and in its
three-dimensional intrinsic form. We finally derive a general family of static
solutions of the Einstein-Cartan theory exhibiting a natural family of null
hypersurfaces and use it to apply our formalism to the construction of a null
shell of matter.Comment: Latex, 21 pages, 1 combined Latex/Postscript figure; Accepted for
publication in Classical and Quantum Gravit

### Some Physical Consequences of Abrupt Changes in the Multipole Moments of a Gravitating Body

The Barrab\`es-Israel theory of light-like shells in General Relativity is
used to show explicitly that in general a light-like shell is accompanied by an
impulsive gravitational wave. The gravitational wave is identified by its
Petrov Type N contribution to a Dirac delta-function term in the Weyl conformal
curvature tensor (with the delta-function singular on the null hypersurface
history of the wave and shell). An example is described in which an
asymptotically flat static vacuum Weyl space-time experiences a sudden change
across a null hypersurface in the multipole moments of its isolated axially
symmetric source. A light-like shell and an impulsive gravitational wave are
identified, both having the null hypersurface as history. The stress-energy in
the shell is dominated (at large distance from the source) by the jump in the
monopole moment (the mass) of the source with the jump in the quadrupole moment
mainly responsible for the stress being anisotropic. The gravitational wave
owes its existence principally to the jump in the quadrupole moment of the
source confirming what would be expected.Comment: 26 pages, tex, no figures, to appear in Phys.Rev.

### Peeling properties of lightlike signals in General Relativity

The peeling properties of a lightlike signal propagating through a general
Bondi-Sachs vacuum spacetime and leaving behind another Bondi-Sachs vacuum
space-time are studied. We demonstrate that in general the peeling behavior is
the conventional one which is associated with a radiating isolated system and
that it becomes unconventional if the asymptotically flat space-times on either
side of the history of the light-like signal tend to flatness at future null
infinity faster than the general Bondi-Sachs space-time. This latter situation
occurs if, for example, the space-times in question are static Bondi-Sachs
space- times.Comment: 14 pages, LaTeX2

### Plane Light-Like Shells and Impulsive Gravitational Waves in Scalar-Tensor Theories of Gravity

We study gravitational plane impulsive waves and electromagnetic shock waves
in a scalar-tensor theory of gravity of the Brans-Dicke type. In vacuum, we
present an exact solution of Brans-Dicke's field equations and give an example
in which a plane impulsive gravitational wave and a null shell of matter
coexist on the same hypersurface. In the homogenous case, we characterize them
by their surface energy density and wave amplitude and discuss the inhomogenous
case. We also give an exact solution of the Brans-Dicke's field equations in
the electrovacuum case which admits a true curvature singularity and use it to
built an example where a plane impulsive gravitational wave and an
electromagnetic shock wave have the same null hypersurface as history of their
wave fronts and propagate independently and decoupled from a null shell of
matter. This last solution is shown to correspond to the space-time describing
the interaction region resulting from the collision of two electromagnetic
shock waves leading to the formation of two gravitational impulsive waves. The
properties of this solution are discussed and compared to those of the
Bell-Szekeres solution of general relativity.Comment: 19 pages, latex, 1 figure, accepted for publication in Class. Quant.
Gra