2016/06/30 by Naresh Dadhich, Sumanta Chakraborty · 46 citations
Mathematics · Physics and Astronomy · #Astrophysics #Black Holes and Theoretical Physics #Classical mechanics #Compact space #Cosmology and Gravitation Theories #Einstein #Einstein field equations #Geometry #Gravitation #Gravitational field #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Perfect fluid #Physics #Schwarzschild radius #Star (game theory) #Surface (topology) #astro-ph.HE #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.95.064059
published in Physical review. D/Physical review. D. 95(6) (American Physical Society) · Revised; Title Changed; 11 pages; no figures
openalex publication_date 2017/03/30 · arxiv created 2017/06/05 · arxiv updated 2017/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We obtain the Buchdahl compactness limit for a pure Lovelock static fluid star and verify that the limit following from the uniform-density Schwarzschild's interior solution, which is universal irrespective of the gravitational theory (Einstein or Lovelock), is true in general. In terms of surface potential \mathrm\ensuremathΦ(r), it means at the surface of the star r=r0, \mathrm\ensuremathΦ(r0)<2N(d\ensuremath-N\ensuremath-1)/(d\ensuremath-1)2, where d and N indicate spacetime dimensions and Lovelock order, respectively. For a given N, \mathrm\ensuremathΦ(r0) is maximum for d=2N+2, while it is always 4/9, Buchdahl's limit, for d=3N+1. It is also remarkable that for N=1 Einstein gravity, or for pure Lovelock in d=3N+1, Buchdahl's limit is equivalent to the criterion that gravitational field energy exterior to the star must be less than half its gravitational mass, having no reference to the interior at all.