Regular Article - Theoretical Physics
Spherically symmetric brane spacetime with bulk gravity
IUCAA, Ganeshkhind, Pune University Campus, Post Bag 4, Pune, 411 007, India
2 Department of Theoretical Physics, Indian Association for the Cultivation of Science, Kolkata, 700032, India
Accepted: 11 December 2014
Published online: 14 January 2015
Introducing term in the five-dimensional bulk action we derive effective Einstein’s equation on the brane using Gauss–Codazzi equation. This effective equation is then solved for different conditions on dark radiation and dark pressure to obtain various spherically symmetric solutions. Some of these static spherically symmetric solutions correspond to black hole solutions, with parameters induced from the bulk. Specially, the dark pressure and dark radiation terms (electric part of Weyl curvature) affect the brane spherically symmetric solutions significantly. We have solved for one parameter group of conformal motions where the dark radiation and dark pressure terms are exactly obtained exploiting the corresponding Lie symmetry. Various thermodynamic features of these spherically symmetric space-times are studied, showing existence of second order phase transition. This phenomenon has its origin in the higher curvature term with gravity in the bulk.
© SIF and Springer-Verlag Berlin Heidelberg, 2015