## Abstract

In a recent report, Carballo-Rubio [R. Carballo-Rubio, Stellar Equilibrium in Semiclassical Gravity, Phys. Rev. Lett. 120, 061102 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.061102] utilizes the semi-classical theory of gravity to obtain a generalized Tolman-Oppenheimer-Volkoff (TOV) equation. This model has a new coupling constant lp implying two different modified TOV equation forms characterized by the sign of p′. The negative branch reduces to the ordinary GR-TOV in the limit of lp→0, while the positive one does not. In the positive branch, Carballo-Rubio was able to find the exact solutions using the constant-λ 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)PRLTAO0031-900710.1103/PhysRevLett.120.061102]. 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) 096JHEPFG1029-847910.1007/JHEP03(2018)096] using constant energy density ρ=ρ0 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 ρ=p/w+ρ0 with w=1 and w=1/3. In general, we obtain that the range of lp is very restricted and must not be equal to rc. Here rc is the starting point of integration located at the center of the star. While lp should be set to be much larger than Planck length LPl. Consequently, the mass-radius curves for the various value of lp for both w cases are still indistinguishable from the standard GR-TOV results. Hence from the negative branch of p′(r), the additional free parameter lp does not provide a significant effect compared to the standard GR-TOV equation results, even though lp is not in the limit of lp→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) 011JCAPBP1475-751610.1088/1475-7516/2019/04/011] 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.

Original language | English |
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Article number | 123536 |

Journal | Physical Review D |

Volume | 103 |

Issue number | 12 |

DOIs | |

Publication status | Published - 15 Jun 2021 |