The growth of curvature near a space-time singularity

1979 ◽  
Vol 10 (12) ◽  
pp. 1005-1006 ◽  
Author(s):  
Frank J. Tipler
Keyword(s):  
Space Time ◽  
Time Singularity

On the collision of impulsive gravitational waves when coupled with fluid motions

1985 ◽  
Vol 402 (1822) ◽  
pp. 37-65 ◽  
Keyword(s):  
Exact Solution ◽  
Gravitational Waves ◽  
Massive Particle ◽  
Natural Generalization ◽  
Space Time ◽  
Direct Result ◽  
Sound Waves ◽  
Time Singularity ◽  
Consistent Extension ◽  
Ultimate Result

An exact solution of Einstein’s equations, with a source derived from a perfect fluid in which the energy density, ε , is equal to the pressure, p , is obtained. The solution describes the space–time following the collision of plane impulsive gravitational waves and is the natural generalization of the Nutku─Halil solution of the vacuum equations, in the region of interaction under similar basic conditions. A consistent extension of the solution, prior to the instant of collision, requires that the fluid in the region of interaction is the direct result of a transformation of incident null-dust (i. e. of massless particles describing null trajectories). The ultimate result of the collision is the development of a space─time singularity, the nature of which is strongly dependent on the amplitude and the character of the sound waves that are present. The distribution of ε that follows the collision has many intriguing features. The solution obtained in this paper provides the first example of an induced transformation of a massless into a massive particle.

Quantum fluctuations near a space–time singularity

1989 ◽  
Vol 67 (10) ◽  
pp. 935-938
Author(s):  
K. D. Krori ◽  
P. Borgohain ◽  
Dipali Das Kar
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Bianchi Type ◽  
Quantum Fluctuations ◽  
Space Time ◽  
Operator Technique ◽  
Time Singularity ◽  
Quantum Uncertainty ◽  
Initial Epoch ◽  
The Universe

The well-known operator technique in quantum mechanics is used to study quantum fluctuations near the space–time singularity using Kantowski–Sachs and Bianchi type VIo metrics. In both cases the wave function of the universe is found to diverge near the space–time singularity, indicating the divergence of the quantum uncertainty near the initial epoch.

CONFORMAL QUANTIZATION AND SPACE-TIME SINGULARITY

1986 ◽  
Vol 01 (01) ◽  
pp. 243-263 ◽  
Author(s):  
P.S. JOSHI ◽  
J.V. NARLIKAR
Keyword(s):  
Probability Measure ◽  
Full Range ◽  
Space Time ◽  
Singular Solutions ◽  
Curvature Singularity ◽  
Field Equations ◽  
Time Singularity ◽  
Previous Conclusion ◽  
Definition Of ◽  
The Universe

This work generalizes earlier results of conformal quantization1,2 that within the full range of space-times conformal to any singular space-time satisfying Einstein’s field equations for minimally coupled matter, the singular solutions form a set of zero-probability measure. A wider definition of space-time singularity that includes the curvature singularity assumed in the earlier work (op. cit.) is adapted and it is shown that the previous conclusion stands even when the present state of the universe is defined by wave functionals that are not necessarily wave packets. Within the present framework of quantum gravity therefore it seems extremely unlikely that the universe had a singular origin.

scholarly journals TOPOLOGICAL FIELD THEORIES AND THE SPACE-TIME SINGULARITY

1992 ◽  
Vol 07 (02) ◽  
pp. 85-91 ◽  
Author(s):  
TOHRU EGUCHI
Keyword(s):  
Field Theory ◽  
Topological Field Theories ◽  
Space Time ◽  
Field Theories ◽  
Two Dimensional ◽  
Time Singularity ◽  
Singular Configurations ◽  
Dimensional Black Hole ◽  
Time Singularities ◽  
Topological Field

Based on a study of recently proposed solution of two-dimensional black hole we argue that the space-time singularities of general relativity may be described by topological field theories (TFTs). We also argue that in general TFT is a field theory which describes singular configurations of a reduced holonomy in its field space.

Some exact solutions of gravitational waves coupled with fluid motions

1985 ◽  
Vol 402 (1823) ◽  
pp. 205-224 ◽  
Keyword(s):  
Exact Solutions ◽  
Gravitational Waves ◽  
Perfect Fluid ◽  
Space Time ◽  
Velocity Of Sound ◽  
Time Singularity ◽  
Einstein's Equations ◽  
The Past ◽  
Velocity Of Light ◽  
Cosmological Solutions

Some exact solutions of Einstein’s equations are found which represent the interaction of gravitational waves with a perfect fluid in which the velocity of sound equals the velocity of light. These solutions, unlike the solutions representing the collision of impulsive gravitational waves, are bounded by a space–time singularity and have some resemblance to cosmological solutions: every time-like trajectory, extended into the past, encounters the singularity. Moreover, in the generic case, matter may be considered as being created at the singularity.

On colliding waves in the Einstein—Maxwell theory

1985 ◽  
Vol 398 (1815) ◽  
pp. 223-259 ◽  
Keyword(s):  
Maxwell Equations ◽  
Plane Waves ◽  
Space Time ◽  
Square Root ◽  
Maxwell Theory ◽  
Time Singularity ◽  
The Relationship ◽  
The Waves ◽  
Natural Way ◽  
Conceptual Difficulties

An exact solution of the Einstein—Maxwell equations is obtained that represents a space-time which describes consistently the collision between two plane impulsive gravitational waves, each supporting an electromagnetic shock-wave. In obtaining the solution, the relationship, which had been established earlier, between the solutions describing stationary black-holes and solutions describing colliding plane-waves, is extended to the Einstein-Maxwell equations (and exploited). The case when the colliding waves are parallelly polarized is analysed in detail to exhibit the singularities and the discontinuities that occur on the null boundaries characteristic of this problem. It is found that the passage of the waves, prior to collision, produces a spray of gravitational and electromagnetic radiation and the collision results in the scattering and the focusing of the waves and the development of a space—time singularity. The solution that is obtained avoids in a natural way certain conceptual difficulties (such as the occurrence of the ‘square root’ of a δ -function and current sheets) that had been anticipated.

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