Exact gravitational field of a string

Abstract

The exact spacetime metric representing the exterior of a static cylindrically symmetric string is found, The geometry is conical, with a deficit angle of 8m Gp, , where p, is the linear energy density of the string. The results of Vilenkin, obtained using linearized gravity, are thus shown to be correct to all orders in Gp, .Strings with Gp,~4 are found to collapse the exterior spacetime, resulting in dimensional reduction.

Influences of a topological defect on the spin Hall effect

“…In last few decades, this subject has drawn special attention in several areas of physics ranging from condensed-matter physics to cosmology [17][18][19][20][21][22][23][24][25][26], such as the defect formed at phase transitions in the earliest history of the universe [17], the cosmic string [17][18][19][20], the domain wall [20][21][22][23][24][25], and the global monopole [26], etc. In particular, cosmic-string theory provides a bridge between the physical descriptions of microscopic and macroscopic scales and then generates extensive discussions on various quantum problems.…”

LETTER: Cosmological Constant, Conical Defect and Classical Tests of General Relativity

“…For very small effects the parameter b itself may be written as b = 1 − ǫ, where ǫ is a small dimensionless param-eter quantifying the conical defect. In particular, for ǫ = 0 the spherically symmetric line element is recovered whereas for a conical defect generated by a cosmic string one has ǫ = 8Gµ/c 2 , where µ is the mass per unit length of the string [11,12].…”

“…However, in order to compare the results with the astronomical observations, the simplest way is provided by the method of sucessive aproximation. The first order correction may easily be obtained by considering the perturbative expansion, u ∼ = u 0 +u 1 (u 1 << u 0 ), where u 0 is given by (12). The application of the standard perturbative procedure to this extended framework is justifiable because the last two terms in (11) are small in comparison to the Newtonian contribution.…”

Cylindrical Sources in Full Einstein and Brans-Dicke Gravity

“…Some years later, Hiscock [4], motivated by the possibility of theories which may lead to values of Gµ closer to one, showed that Vilenkin's results are actually valid to all orders in Gµ. As a source, he considered a thick cylinder of radius a with uniform tension and linear mass density, whose tensor is…”