Spherically symmetric vacuum solution in Freund–Nambu scalar–tensor gravity

Abstract We present an exact solution in Freund–Nambu scalar–tensor gravity that extends the Janis–Newman–Winnicour (JNW) naked-singularity spacetime. The metric retains the JNW form governed by parameter n , while a new parameter q deforms the profile of the massive scalar field $$\varphi .$$ φ . Test-particle dynamics incorporate a direct linear coupling $$g_s$$ g s to $$\varphi .$$ φ . We compute the specific angular momentum, innermost stable circular orbit, and radiative efficiency, and derive epicyclic frequencies for quasi-periodic oscillations (QPOs). Within the epicyclic resonance model, the twin-peak QPO frequencies depend on n , q , and $$g_s.$$ g s . A Markov Chain Monte Carlo analysis of microquasars XTE J1550-564 and GRS 1915+105 yields black-hole masses $$M = 8.99 \pm 0.55\,M_\odot $$ M = 8.99 ± 0.55 M ⊙ and $$13.3 \pm 1.0\,M_\odot ,$$ 13.3 ± 1.0 M ⊙ , consistent with previous estimates, and gives the first observational constraints $$q \approx 3,$$ q ≈ 3 , $$g_s \approx 0.45.$$ g s ≈ 0.45 . These distinctive imprints demonstrate that this modified gravity framework provides a viable, testable arena for strong-field physics beyond general relativity.

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