Buchdahl-Bondi limit in modified gravity: Packing extra effective mass in relativistic compact stars

Abstract

We generalise the Buchdahl-Bondi limit for the case of static, spherically symmetric, relativistic compact stars immersed in Schwarzschild vacuum in f (R)-theory of gravity, subject to very generic regularity, thermodynamic stability and matching conditions. Similar to the case of general relativity, our result is model independent and remains true for any physically realistic equation of state of standard stellar matter. We show that an extra-massive stable star can exist in these theories, with surface redshift larger than 2, which is forbidden in general relativity. This result gives a novel and interesting observational test for validity or otherwise of general relativity and also provides a possible solution to the dark matter problem.

Buchdahl compactness limit for a pure Lovelock static fluid star

“…Clearly, as expected the boundary radius of the star is always greater than the black hole horizon. Buchdahl compactness limit has attracted a lot of attention in literature and it has been considered in various contexts; inclusion of charge and Λ [2][3][4][5], alternative conditions than that of Buchdahl's [6,7], stars on the brane [8,9], in modified gravity theories [10] and in higher dimensions [11,12] as well. More importantly, it could be successively pinned down by the assumption of dominant energy condition [13] and further requiring sound velocity being subluminal [14].…”

Packing extra mass in compact stellar structures: an interplay between Kalb-Ramond field and extra dimensions

“…The above bound on ADM mass M illustrates that given a certain radius r 0 of a compact stellar object, the maximum mass one can associate with it is larger in presence of Kalb-Ramond field. Thus one can pack extra mass into the stellar structure (a similar scenario appears in f (R) gravity as well [20].). This provides an interesting testbed for Kalb-Ramond field.…”

A possible testbed for warped extra dimension from the angle of Buchdahl’s limit

“…This expression along with the decreasing character of ρ av (with r) makes the right hand side of eqn. (35) negative. As a consequence, we get the following inequality:…”

“…(28) indicates that the first term of the right hand side of eqn. (35) is essentially dρ av /dr i.e. = dρav dr .…”

“…This raises an intriguing question, how is the above limit modified if one considers a theory of gravity different from general relativity. This resulted into a large number of work quite extensively in recent times [28,29,30,31,32,33,34,35,36,37] (see also [38,39,40,41,42]).…”