Spherically-symmetrical vacuum solution in Freund-Nambu scalar-tensor gravity

Abstract

Scalar--tensor theories of gravity provide a natural extension of general relativity and may predict naked singularities as alternative compact objects. In this work, we investigate a novel exact solution within the Freud--Nambu scalar--tensor gravity framework, generalizing the Janis--Newman--Winicour (JNW) naked singularity spacetime through the introduction of a parameter $q$ coupled to a real scalar field $\varphi$ with mass $μ$. Although the metric remains identical to the JNW solution, the scalar field profile is modified, providing a parametrized deformation of this class of spacetimes. We analyze particle dynamics in this background, including a direct linear coupling between the test particle and the scalar field characterized by the parameter $g_s$. The influence of these parameters on astrophysical observables is studied through the specific angular momentum, the innermost stable circular orbit (ISCO), and the radiative efficiency of accretion. We also derive the epicyclic frequencies governing oscillatory motion and explore their implications for quasi-periodic oscillations (QPOs) in black hole binaries. Within the epicyclic resonance model, the upper and lower QPO frequencies depend sensitively on the parameters $n$, $g_s$, and $q$. To constrain the model, we perform a Markov Chain Monte Carlo analysis using twin-peak QPO data from the microquasars XTE~J1550--564 and GRS~1915+105. The resulting black hole masses agree with previous estimates and provide the first observational constraints on the parameters $q$ and $g_s$, indicating that modified gravity effects may leave detectable imprints on strong-field astrophysical phenomena.

Figures (8)

• Figure 1: Radial dependencies of specific angular momentum for various values of $g_s$ and $q$ on fixed values of spacetime parameter $n$.
• Figure 2: Dependence of ISCO radius on $n$ for different values of $g_s$ and $q$ parameters. In the left panel, $q$ is fixed as $0.2$. In the right panel, $g_s$ is fixed as $0.2$ and $-0.2$.
• Figure 3: Dependence of the radiative efficiency $\eta$ on the parameter $n$ for different values of $g_s$ and $q$.
• Figure 4: Degeneracy between the scalar-tensor model parameters and the Kerr spin parameter $a$. Each panel shows the ISCO radius as a function of the Kerr spin $a$ (solid curve), along with the ISCO values obtained for different combinations of $q$, $n$, and $g_s$. The intersection points indicate parameter values that produce the same ISCO location as a given Kerr spin.
• Figure 5: Radial dependence of the fundamental frequencies $\nu_r$ and $\nu_\phi$. Left panel: Fixed $g_s = 0.2$ and $n = 0.7$, with $q = 0.2$ (solid), $1.0$ (dashed), and $3.0$ (dotted). Middle panel: Fixed $q = 0.2$ and $n = 0.7$, with $g_s = 0.1$ (solid), $0.2$ (dashed), and $0.3$ (dotted). Right panel: Fixed $g_s = 0.2$ and $q = 0.2$, with $n = 0.5$ (solid), $0.7$ (dashed), and $0.9$ (dotted).