Year: 2021
Type: article
Abstract: In a recent report, Carballo-Rubio [R. Carballo-Rubio, Stellar Equilibrium in Semiclassical Gravity, Phys. Rev. Lett. 120, 061102 (2018)] utilizes the semi-classical theory of gravity to obtain a generalized Tolman-Oppenheimer-Volkoff (TOV) equation. This model has a new coupling constant ${l}_{p}$ implying two different modified TOV equation forms characterized by the sign of ${p}^{\ensuremath{'}}$. The negative branch reduces to the ordinary GR-TOV in the limit of ${l}_{p}\ensuremath{\rightarrow}0$, while the positive one does not. In the positive branch, Carballo-Rubio was able to find the exact solutions using the constant-$\ensuremath{\lambda}$ trick. In this work, we investigate whether this theory's negative branch can also provide a different feature of the ultra-compact object compared to those obtained from the GR-TOV equation. We use a numerical method to calculate the properties of an ultra-compact object. We tested our code by calculating numerically the pressure profile of the object in a positive branch with the star's radius $R$ in a macroscopic unit by integrating from surface to center. The result reproduces the analytical result of Carballo-Rubio [R. Carballo-Rubio, Stellar Equilibrium in Semiclassical Gravity, Phys. Rev. Lett. 120, 061102 (2018)]. While in a negative branch, we reproduce the pressure profile results of Ho and Matsuo [P. M. Ho and Y. Matsuo, Static black hole and vacuum energy: Thin shell and incompressible fluid, J. High Energy Phys. 03 (2018) 096] using constant energy density $\ensuremath{\rho}={\ensuremath{\rho}}_{0}$ not only by integrating from surface to center but also by integrating from center to surface, respectively. In this work, we study ultra-compact objects with an isotropically ideal fluid matter where we use a simple but physically motivated equation of state $\ensuremath{\rho}=p/w+{\ensuremath{\rho}}_{0}$ with $w=1$ and $w=1/3$. In general, we obtain that the range of ${l}_{p}$ is very restricted and must not be equal to ${r}_{c}$. Here ${r}_{c}$ is the starting point of integration located at the center of the star. While ${l}_{p}$ should be set to be much larger than Planck length ${L}_{\mathrm{Pl}}$. Consequently, the mass-radius curves for the various value of ${l}_{p}$ for both $w$ cases are still indistinguishable from the standard GR-TOV results. Hence from the negative branch of ${p}^{\ensuremath{'}}(r)$, the additional free parameter ${l}_{p}$ does not provide a significant effect compared to the standard GR-TOV equation results, even though ${l}_{p}$ is not in the limit of ${l}_{p}\ensuremath{\rightarrow}0$ anymore. Therefore, similar to the conclusion in [A. Urbano and H. Veerme, On gravitational echoes from ultracompact exotic stars, J. Cosmol. Astropart. Phys. 04 (2019) 011] with GR theory that the ultra-compact objects from negative branch of semi-classical gravity with a linear equation of state are unable to generate demanding gravitational echoes.
Authors: I. Prasetyo, H. S. Ramadhan, A. Sulaksono
Institution: University of Indonesia
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G1746217759
OpenAlex ID: W3165088155