Exact Solutions of Einstein's Field Equations
Exact Solutions of Einstein's Field Equations
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DOI：
10.1007/s10773-006-9104-5
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发表时间：
2004-01
影响因子：
1.4
通讯作者：
P. Negi
中科院分区：
文献类型：
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作者：
P. Negi
我们研究了文献中各种众所周知的精确解，以研究Negi和Durgapal [Gravitation and Cosmology 7，37（2001）]中最近获得的标准，该标准应在流体静力平衡状态下由任何静态和球对称解实现。可以看出，这一标准是满足只有（i）正规的解决方案有一个消失的表面密度与压力，和（ii）奇异的解决方案，对应于一个非零密度在表面的配置。另一方面，对应于非零面密度的正则解不满足这个标准。在此基础上，我们指出，为了得到与广义相对论流体静力平衡态相容的精确解或物态方程，外史瓦西解本身为考虑物质内部的密度分布类型提供了必要条件。具有有限中心和非零表面密度的正则解不满足Negi和Durgapal（2001）给出的标准，实际上不满足Schwarzschild外解所建立的“实际质量”的要求。在这方面唯一可能的规则解是由均匀（齐次）密度分布表示的。这个判据为任何静态和球形结构（包括核心-包络模型）与广义相对论的结构（即广义相对论中的流体静力平衡状态）相容提供了一个充分必要条件。因此，它可以找到应用程序，以构建适当的核心包络模型的恒星物体，如中子星，并可用于测试各种状态方程的致密核物质和模型的相对论性星星集群与任意大的中心红移。
We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in Negi and Durgapal [Gravitation and Cosmology7, 37 (2001)] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic equilibrium. It is seen that this criterion is fulfilled only by (i) the regular solutions having a vanishing surface density together with pressure, and (ii) the singular solutions corresponding to a non-vanishing density at the surface of the configuration. On the other hand, the regular solutions corresponding to a non-vanishing surface density do not fulfill this criterion. Based upon this investigation, we point out that the exterior Schwarzschild solution itself provides necessary conditions for the types of the density distributions to be considered inside the mass, in order to obtain exact solutions or equations of state compatible with the state of hydrostatic equilibrium in general relativity. The regular solutions with finite centre and non-zero surface densities which do not fulfill the criterion given by Negi and Durgapal (2001), in fact, cannot meet the requirement of the‘actual mass’, set up by exterior Schwarzschild solution. The only regular solution which could be possible in this regard is represented by uniform (homogeneous) density distribution. This criterion provides a necessary and sufficient condition for any static and spherical configuration (including core-envelope models) to be compatible with the structure of general relativity [that is, the state of hydrostatic equilibrium in general relativity]. Thus, it may find application to construct the appropriate core-envelope models of stellar objects like neutron stars and may be used to test various equations of state for dense nuclear matter and the models of relativistic star clusters with arbitrary large central redshifts.