Stationary spacetime from intersecting M-branes

Eternally Inflating Cosmologies From Intersecting Spacelike Branes

“…With multibrane solutions, some dimensions are static or shrink. The required intersection rule is shown to be the same as that suggested for regular solutions in other papers [21,22,23,24]. The last section is devoted to an examination of these solutions in relation to the real Universe.…”

“…(22) is the intersection rule, which has already been suggested for regular solutions in other papers [21,22,23,24].…”

“…General orthogonally intersecting solutions where the metric functions u and v and fields φ and F depend only on one timelike coordinate have also been proposed [23]. A D-brane solution which depends on all the extra space coordinates has been suggested [24]. We assume that the metrics and fields do not depend only on the timelike coordinates y a , a = D − s + 1, · · · , and D, but also on the other perpendicular coordinates y a , a = p + 2, · · · , and D − s. That is to say,…”

Chapter 10. Black Hole Solutions in String Theory

“…In this section we shall explore the null case, where the spacetime admits isometry of a null orbit generated by ∂/∂v. 83) As for the internal space, we assume its Ricci flatness. We suppose that the base space spanned by {x i }, which corresponds to our world space, is a (d − 1)-dimensional flat Euclid space, which can be extended easily to any Ricci flat space without modification.…”

“…We suppose that the base space spanned by {x i }, which corresponds to our world space, is a (d − 1)-dimensional flat Euclid space, which can be extended easily to any Ricci flat space without modification. Under these conditions, we can adopt the following D-dimensional metric form, 83) Consider a q A -brane extending into the directions {y 1 , y α 2 , · · · , y αq A }. If the q A -brane is electrically charged, it is well known that it couples to an n A = q A + 2 form field strength.…”