Equation of states in the curved spacetime of spherical degenerate stars

Abstract

In the study of spherical degenerate stars such as neutron stars, general relativistic effects are incorporated by using Tolman-Oppenheimer-Volkoff equations to describe their interior spacetime. However, the equation of states employed in such studies are invariably computed in flat spacetime. We show that the equation of states computed in the curved spacetime of these stars depend explicitly on the metric function. Further, we show that ignoring such metric-dependent gravitational time dilation effect leads one to grossly underestimate the mass limits of these compact stars.

Do we need equation of state in curved spacetime for neutron stars?

“…( 20). We note that the grand canonical EoS computed in previous works [21,22], which shows an explicit dependence on the gravitational potential Φ, is not compatible with the TOV equation and local thermodynamic relations.…”

“…Recently, some works have reported that the dense matter EoS computed by using quantum field theory in curved spacetime would make a big difference [21,22]. They found that the gravitational time dilation effect leads to a significant increase of the maximum mass of neutron stars.…”

“…On the other hand, theorists are good at computing the grand canonical EoS p = p(T, µ) by using finite temperature field theory in flat spacetime [18]. Some recent works have tried to compute the grand canonical EoS based on the statistic mechanics of quantum fields in curved spacetime [21,22]. Within their approach, the gravitational time dilation effect explicitly influences the grand canonical EoS, i.e., p(T, µ) is different at different position in the gravitational field.…”

“…In previous works [21,22], the gravitational effect is attributed to the gravitational potential Φ(r), i.e., the gravitational time dilation. Since Φ(r) is a single-valued function of r, it is equivalent to assume that the grand canonical EoS may depend explicitly on Φ, i.e.…”

Fermi gas and modified gravity

“…An interesting fact that chemical reactions rates depend on gravity [63] also suggests that any modification to this interaction will also have an effect on the kinetic rate constants of chemical reactions. Apart from this, ignoring the relativistic effects introduced by GR causes underestimation of the limiting masses of compact stars -but computations of equations of state in curved spacetime provide that in the degenerated stars one deals with EoS which depend explicitly on the metric components [64,65], therefore one should expect similar changes in EoS derived from different assumptions on the gravitational interaction. It is mainly manifested by already mentioned enhanced chemical potentials and temperatures [66] which are a part of the equations' set describing a statistical system.…”