Eur. Phys. J. C (2014) 74:2952
DOI 10.1140/epjc/s10052-014-2952-x
Regular Article - Theoretical Physics
Higher-dimensional charged shear-free relativistic models
with heat flux
Y. Nyonyi
a
, S. D. Maharaj
b
, K. S. Govinder
c
Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal,
Private Bag 54001, Durban 4000, South Africa
Received: 13 May 2014 / Accepted: 23 June 2014 / Published online: 11 July 2014
© The Author(s) 2014. This article is published with open access at Springerlink.com
Abstract We analyze shear-free spherically symmetric rel-
ativistic models of gravitating fluids with heat flow and elec-
tric charge defined on higher-dimensional manifolds. The
solution to the Einstein–Maxwell system is governed by the
pressure isotropy condition, which depends on the space-time
dimension. We study this highly nonlinear partial differen-
tial equation using Lie’s group theoretic approach. The Lie
symmetry generators that leave the equation invariant are
determined. We provide exact solutions to the gravitational
potentials using the first symmetry admitted by the equation.
Our new exact solutions contain the earlier results for the
four-dimensional case. Using the other Lie generators, we
are able to provide solutions to the gravitational potentials or
reduce the order of the master equation to a first order non-
linear differential equation. We also find expressions for the
causal and Eckart temperatures and show their dependence
on the dimension.
1 Introduction
In this paper, we study charged shear-free spherically sym-
metric gravitating fluids defined on higher-dimensional man-
ifolds. The idea of higher dimensions stems from the earlier
attempts of Kaluza [1] and Klein [2] who were motivated
by the desire to unify the fundamental forces of electro-
magnetism and Einstein gravity by introducing a compact
fifth dimension. The discourse of higher-dimensional mod-
els hibernated for over four decades and it was not until the
early 1960s that the early developments to what we have
come to know as String Theory came into existence. This
theory, which requires a higher-dimensional framework, was
initially sought to explain the strong nuclear force but its
a
e-mail: yusuf@aims.ac.za
b
e-mail: maharaj@ukzn.ac.za
c
e-mail: govinder@ukzn.ac.za
peculiar properties made it a good candidate for studying
quantum gravity with a hope of obtaining a unifying grand
theory. In addition, studying models in higher dimensions
provides a platform to understand the nature of the early uni-
verse. It is believed that the universe, in its earlier epoch was
dense and hot (a scenario better explained in higher dimen-
sions), and as a result of expansion the extra dimensions
have compactified to produce the present four-dimensional
universe [3].
The model we study here is for a charged higher-
dimensional shear-free gravitating fluid in the presence of
heat flow; this is intended to extend our earlier study [4]in
four dimensions. This model is very important in studying
both relativistic cosmological and astrophysical processes.
Therefore providing exact solutions to the Einstein–Maxwell
system is a vital aspect in this regard. This is well docu-
mented in Krasinski’s monograph [5] where he points out the
significance of these solutions in understanding the growth
of inhomogeneities, the appearance of singularities, structure
formation, gravitational collapse, and other relativistic stellar
processes. Incorporating heat flow and charge in our model
provides us with a platform for building radiating and grav-
itating models. The intricacies of the model we study are
simplified by considering the shear-free condition. In this
way the generalized pressure isotropy condition reduces to
an equation, containing two independent metric functions,
which is much easier to study and solve. For a comprehen-
sive recent treatment of shear-free heat conducting perfect
fluids see Ivanov [6].
The study of relativistic stars that emit null radiation in the
form of radial heat flow, as established by Santos [7], requires
a nonzero heat flux emanating from the interior space-
time to match with the pressure at the boundary with the
exterior Vaidya space-time. This was extended by Maharaj
et al. [8] to the generalized Vaidya space-time superposing
a null fluid and a string fluid in the exterior energy momen-
tum tensor. The Santos junction condition is also applica-
123
下载后可阅读完整内容，剩余7页未读，立即下载
weixin_38503483
- 粉丝: 8
- 资源: 942
我的内容管理
展开
最新资源
- ***+SQL三层架构体育赛事网站毕设源码
- 深入探索AzerothCore的WoTLK版本开发
- Jupyter中实现机器学习基础算法的教程
- 单变量LSTM时序预测Matlab程序及参数调优指南
- 俄G大神修改版inet下载管理器6.36.7功能详解
- 深入探索Scratch编程世界及其应用
- Aria2下载器1.37.0版本发布，支持aarch64架构
- 打造互动性洗车业务网站-HTML5源码深度解析
- 基于zxing的二维码扫描与生成树形结构示例
- 掌握TensorFlow实现CNN图像识别技术
- 苏黎世理工自主无人机系统开源项目解析
- Linux Elasticsearch 8.3.1 正式发布
- 高效销售采购库管统计软件全新发布
- 响应式网页设计：膳食营养指南HTML源码
- 心心相印婚礼主题响应式网页源码 - 构建专业前端体验
- 期末复习指南：数据结构关键操作详解
资源上传下载、课程学习等过程中有任何疑问或建议，欢迎提出宝贵意见哦~我们会及时处理！
点击此处反馈
