Anisotropic ultra-compact object in Serrano–Liska gravity model

Abstract

AbstractWe implement a recent model proposed by Serrano–Liska (SL) (Alonso-Serrano and Liška, JHEP, 12:196, 2020) to study the ultra-compact star properties. The matter in the interior star is modeled by the quark model, deducted from QCD theory equipped with anisotropic pressure. Anisotropy is used to increase the compactness of the stars. We intend to see the signature of the “quantum gravity” effect through the SL model in ultra-compact stars. The SL model was motivated by quantum correction appearing in the black hole by adding a logarithmic term in gravity entropy used to derive the effective Einstein field equation. We expect this correction term in the SL model also affects ultra-compact star properties. The SL model with coupling constant$${\tilde{c}}$$c~in logarithmic term equipped with spherically symmetric metric yields correction terms$$\mathscr {O}({\tilde{c}})$$O(c~)that can be expressed by a function$$\varXi (r)$$Ξ(r). The$$\varXi (r)$$Ξ(r)function vanishes at the star’s exterior. We found that the mass-radius relation prediction by the SL model with anisotropic matter deviates from the one predicted by the standard Tolman–Oppenheimer–Volkoff (TOV) equation for$${\tilde{c}}\ge 10^7$$c~≥107m$$^2$$2. We also have a sufficiently deep enough effective potential to produce a quasi-normal mode. We obtain the echo frequency of 15.2 kHz using maximum anisotropic pressure contribution and$${\tilde{c}}= 10^7$$c~=107m$$^2$$2. Because the corresponding effective potential is almost indistinguishable from that of GR, this echo frequency value can be indistinguishable to one of GR, but not comparable to the result from GW170817 data analysis, i.e., 72 Hz. To circumvent this problem, we can decrease the value of echo frequency by increasing the magnitude of$${\tilde{c}}$$c~to orders of magnitude than$${\tilde{c}}= 10^7$$c~=107m$$^2$$2. On the other hand, too large a strength from the logarithmic correction term is not physically favored because we learn from the black hole case that the logarithmic term is expected to be smaller than that of the Bekenstein term. Therefore, more precise gravitation echo measurements are crucial to understand this issue.