C. Barrabès

Stochastically Fluctuating Black-Hole Geometry, Hawking Radiation and the Trans-Planckian Problem

We study the propagation of null rays and massless fields in a black hole fluctuating geometry. The metric fluctuations are induced by a small oscillating incoming flux of energy. The flux also induces black hole mass oscillations around its average value. We assume that the metric fluctuations are described by a statistical ensemble. The stochastic variables are the phases and the amplitudes of Fourier modes of the fluctuations. By averaging over these variables, we obtain an effective propagation for massless fields which is characterized by a critical length defined by the amplitude of the metric fluctuations: Smooth wave packets with respect to this length are not significantly affected when they are propagated forward in time. Concomitantly, we find that the asymptotic properties of Hawking radiation are not severely modified. However, backward propagated wave packets are dissipated by the metric fluctuations once their blueshifted frequency reaches the inverse critical length. All these properties bear many resemblances with those obtained in models for black hole radiation based on a modified dispersion relation. This strongly suggests that the physical origin of these models, which were introduced to confront the trans-Planckian problem, comes from the fluctuations of the black hole geometry.

Singular Null Hypersurfaces in General Relativity: Light-Like Signals from Violent Astrophysical Events

General Description of an Impulsive Light-Like Signal Illustrations and Implications of the Bianchi Identities Light-Like Boosts Spherically Symmetric Null Shells Collisions of Plane Impulsive Light-Like Signals Impulsive Light-Like Signals in Alternative Theories of Gravity.

Advanced general relativity : gravity waves spinning particles and black holes

Preface 1. Minkowskian space-time 2. Plane gravitational waves 3. Equations of motion 4. Inhomogeneous aspects of cosmology 5. Black holes 6. Higher dimensional black holes Appendix A: Notation Appendix B: Transport law For k along r=0 Appendix C: Some useful scalar products References Index

Some physical consequences of abrupt changes in the multipole moments of a gravitating body

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 dipole moment mainly responsible for the stress being anisotropic. The gravitational wave owes its existence prrincipally to the jump in th quadrupole moment of the source confirming what would be expected. This serves as a model of a cataclysmic astrophysical event such as a supernova.

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 lightlike 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.

DETECTION OF IMPULSIVE LIGHT-LIKE SIGNALS IN GENERAL RELATIVITY

The principal purpose of this paper is to study the effect of an impulsive light-like signal on neighbouring test particles. Such a signal can in general be unambiguously decomposed into a light-like shell of null matter and an impulsive gravitational wave. Our results are: (a) If there is anisotropic stress in the light-like shell then test particles initially moving in the signal front are displaced out of this 2-surface after encountering the signal; (b) For a light-like shell with no anisotropic stress accompanying a gravitational wave the effect of the signal on test particles moving in the signal front is to displace them relative to each other with the usual distortion due to the gravitational wave diminished by the presence of the light-like shell. An explicit example for a plane-fronted signal is worked out.

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.

Generating a cosmological constant with gravitational waves

A technique is given to derive the well known Bell–Szekeres solution of the Einstein–Maxwell vacuum field equations describing the space-time and the Maxwell field following the head-on collision of two homogeneous, plane, electromagnetic shock waves. The analogue of this technique is then utilized to construct the space-time model of the gravitational field following the head-on collision of two homogeneous, plane, gravitational shock waves. The latter collision, which is followed by a pair of impulsive gravitational waves and a pair of light like shells traveling away from each other, provides a mechanism for generating a cosmological constant which may be important in the theoretical description of dark energy.

A CLASS OF COLLISIONS OF PLANE IMPULSIVE LIGHT-LIKE SIGNALS IN GENERAL RELATIVITY

We present a systematic study of collisions of homogeneous, plane- fronted, impulsive light-like signals which do not interact after head-on collision. For the head-on collision of two such signals, six real parameters are involved, three from each of the incoming signals. We find two necessary conditions to be satisfied by these six parameters for the signals to be noninteracting after collision. We then solve the collision problem in the general case when these necessary conditions hold. After collision the two signals focus each other at Weyl curvature singularities on each others signal front. Our family of solutions contains some known collision solutions as special cases.

IMPULSIVE LIGHT-LIKE SIGNALS

A general characterisation of an impulsive light–like signal was given1,2. The signal may consist of a shell of null matter and/or an impulsive gravitational wave. Both parts of the signal can be unambiguously identified3,4. The signals can be used to model bursts of gravitational radiation and light– like matter accompanying cataclysmic events such as supernovae and neutron star collisions. Also in high speed collisions of compact objects such as black–holes or neutron stars the gravitational fields of these objects resemble those of impulsive light–like signals when the objects are boosted to the speed of light. Several examples of impulsive light–like signals were presented, in particular those produced by recoil effects5 and by the Aichelburg–Sexl boost of an isolated gravitating multipole source6. The detection of these signals was also discussed7.