Universality of the Buchdahl sphere

Abstract

Buchdahl sphere, the limiting stable isotropic stellar structure without exotic matter, plays a very important role, as far as the near horizon physics is concerned. This is because, the radius of the Buchdahl sphere lies between the horizon and the photon sphere, such that the signal arising from gravitational wave and black hole shadow will mimic that of a black hole. Here, we show certain universal properties associated with the Buchdahl sphere, in the sense that these properties will not change even if electric charge is included in the stellar structure. Moreover, these universal properties transcend general relativity and holds good in pure Lovelock theories of gravity as well. Using these universalities, we have proposed a Buchdahl limit for rotating stellar configuration. Finally, the universality of the Buchdahl limit in terms of the gravitational and non-gravitational field energies and also in terms of the photon sphere is also discussed.

Extending the weak cosmic censorship conjecture to the charged Buchdahl star by employing the gedanken experiments

“…In this paper, the main aim is to extend WCCC to a non black hole compact object like BS. This question is motivated by the fact that the latter does share almost all the properties with the former [55,59]. It is indeed the most compact non black hole object [56].…”

“…Note that the characterization, Φ(r) = 1/2, 4/9 respectively for black hole (BH) and Buchdahl star (BS) is universal irrespective of object being uncharged and non-rotating or otherwise. It is remarkable that BS shares almost all BH properties [59] including, in particular, the extremal limit which for the charged case is Q 2 /M 2 > 9/8 > 1. So an extremal BS is over-extremal relative to BH.…”

Extending the weak cosmic censorship conjecture to charged Buchdahl star by employing the gedanken experiments

“…In this paper, the main aim is to extend WCCC to a non black hole compact object like BS. This question is motivated by the fact that the latter does share almost all the properties with the former [56,58]. It is indeed the most compact non black hole object [57].…”

“…Note that the characterization, Φ(r) = 1/2, 4/9 respectively for black hole (BH) and Buchdahl star (BS) is universal irrespective of object being uncharged and non-rotating or otherwise. It is remarkable that BS shares almost all BH properties [58] including, in particular, the extremal limit which for the charged case is…”