Charged Quark Stars and Extreme Compact Objects in Regularized 4D Einstein-Gauss-Bonnet Gravity (2406.12933v2)

Abstract: Since the derivation of a well-defined $D\rightarrow 4$ limit for 4 dimensional Einstein Gauss-Bonnet (4DEGB) gravity coupled to a scalar field, there has been interest in testing it as an alternative to Einstein's general theory of relativity. Using the Tolman-Oppenheimer-Volkoff (TOV) equations modified for charge and 4DEGB gravity, we model the stellar structure of charged, non-interacting quark stars. We find that increasing the Gauss-Bonnet coupling constant $\alpha$ or the charge $Q$ both tend to increase the mass-radius profiles of quark stars described by this theory, allowing a given central pressure to support larger quark stars in general. We also derive a generalization of the Buchdahl bound for charged stars in 4DEGB gravity. As in the uncharged case, we find that quark stars can exist below the general relativistic Buchdahl bound (BB) and Schwarzschild radius $R=2M$, due to the lack of a mass gap between black holes and compact stars in the 4DEGB theory. Even for $\alpha$ well within current observational constraints, we find that quark star solutions in this theory can describe Extreme Compact Charged Objects (ECCOs), objects whose radii are smaller than what is allowed by general relativity.

• The paper integrates modified TOV equations with a scalar field and charge in 4D Einstein-Gauss-Bonnet gravity to study charged quark stars.
• Numerical results show quark star mass and radius increase with the Gauss-Bonnet coupling or charge, and derive a generalized Buchdahl bound and implications for extreme compact objects (ECCOs).
• Investigating charged quark stars in modified gravity like 4DEGB offers crucial insights into dense matter under extreme conditions, potentially allowing observational substantiation of such theories via detecting ECCOs.

Insights into Charged Quark Stars in Regularized 4D Einstein-Gauss-Bonnet Gravity

The paper, "Charged Quark Stars and Extreme Compact Objects in Regularized 4D Einstein-Gauss-Bonnet Gravity," provides a detailed exploration of stellar structures within the framework of the modified theory of gravity known as 4D Einstein-Gauss-Bonnet (4DEGB) gravity. This investigation is framed within the context of charged quark stars—a class of compact astrophysical objects that offer a fertile testing ground for extending general relativity via higher curvature modifications.

Theoretical Foundations and Methodology

The authors capitalize on the significant postponements in the detectability of deviations from general relativity. Specifically, they paper the implications of a well-defined 4D limit of the Einstein-Gauss-Bonnet (EGB) theory, which is of considerable interest since it provides second-order field equations, reminiscent of regular general relativity, while incorporating higher-dimensional effects. The research paper describes the integration of the Tolman-Oppenheimer-Volkoff (TOV) equations for stellar equilibrium with modifications due to both a scalar field and the presence of charge under the 4DEGB framework.

Numerical Analysis and Results

Crucially, the paper investigates how variations in the Gauss-Bonnet coupling parameter ($\alpha$) and additional charge ($Q$) influence the stellar mass-radius profiles. The results indicate a notable enlargement in mass and radius of quark stars with either increasing $\alpha$ or $Q$, suggesting a shift in stability regimes and the maximum mass sustainment compared to standard general relativistic predictions.

One of the significant contributions of the paper is the derivation of a generalized Buchdahl bound applicable to charged compact stars within the 4DEGB gravity scenario. This bound is central in determining the possible configurations of compact objects and connects seamlessly to the threshold beyond which a star collapses into a black hole. Furthermore, the research derives implications on the existence of extreme compact charged objects (ECCOs), which exhibit radii that potentially dip below those established by the Buchdahl limit in GR.

Implications and Future Outlook

The exploration of quark stars under modified theories like the 4DEGB is pivotal for understanding dense astrophysical objects in environments surpassing the explanatory capacity of conventional GR. Notably, the authors posit that observing such ECCOs could substantiate the presence and physical legitimacy of the 4DEGB modifications. Such an occurrence would not only bolster alternative gravitational theories but also shed light on the true nature and behavior of matter under extreme conditions.

The findings in this paper pave pathways for further studies, particularly in high-energy astrophysics, where exploration could enhance understanding of phenomena such as gravitational wave emissions from compact star mergers and the properties of matter under extreme magnetic or gravitational fields. Continuing inquiries could well integrate rotational dynamics to assess stability further and explore detailed oscillation modes within these modified gravity frameworks.

Conclusion

In conclusion, this paper's robust exploration of charged quark stars within 4DEGB gravity extends the current understanding of compact stellar objects. It provides crucial insights into the behavior of matter influenced by higher curvature gravitational effects. While present findings carve a promising route for novel astrophysical predictions, comprehensive exploration—and perhaps more stringent observational constraints—will continue to be seminal in evaluating the viability of such modified theories of gravity.