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

TL;DR

This paper introduces a new exact solution in Freund-Nambu scalar-tensor gravity that generalizes the JNW naked singularity, analyzes particle dynamics and QPOs, and uses observational data to constrain the model's parameters.

Contribution

It presents a novel parametrized scalar-tensor solution extending the JNW spacetime and constrains its parameters using astrophysical QPO data.

Findings

The scalar field profile is modified by parameter q.

QPO frequencies depend on parameters n, g_s, and q.

Model parameters q and g_s are constrained by observational data.

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 $\mu$. 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.