Higher dimensional generalization of the Buchdahl-Vaidya-Tikekar model for a supercompact star

Avas Khugaev, Naresh Dadhich, and Alfred Molina
Phys. Rev. D 94, 064065 – Published 22 September 2016

Abstract

We obtain higher-dimensional solutions for a supercompact star for the Buchdahl-Vaidya-Tikekar metric ansatz. In particular, Vaidya and Tikekar characterized the 3-geometry by a parameter, K, which is related to the sign of a density gradient. It turns out that the key pressure isotropy equation continues to have the same Gauss form and, hence, four-dimensional solutions can be taken over to higher dimensions with K satisfying the relation, Kn=(K4n+4)/(n3), where the subscript refers to the dimension of spacetime. Further, K0 is required (otherwise, the density would have the undesirable feature of increasing with radius), and the equality indicates a constant density star described by the Schwarzschild interior solution. This means that, for a given K4, the maximum dimension could only be n=K4+4. Otherwise, Kn will turn negative.

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  • Received 29 March 2016

DOI:https://doi.org/10.1103/PhysRevD.94.064065

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Avas Khugaev*

  • Institute of Nuclear Physics, Tashkent 100214, Uzbekistan

Naresh Dadhich

  • Centre for Theoretical Physics, Jamia Millia, Islamia, New Delhi, 110025, India and Inter-University Center for Astronomy and Astrophysics, Post Bag 4, Pune 411 007, India

Alfred Molina

  • Departament de Física Quàntica i Astrofísica, Institut de Ciéncies del Cosmos, Universitat de Barcelona, Barcelona 08028, Spain

  • *avaskhugaev@mail.ru
  • nkd@iucaa.in
  • alfred.molina.ub.edu

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Issue

Vol. 94, Iss. 6 — 15 September 2016

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