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tokens: from the Kerr solution is found, this approach is not suitable to measure the deviation from the Kerr geometry and it is necessary to use a different method. Among the many proposed parametric black-hole spacetimes in literature, here we use the Johannsen metric (Johannsen 2013 ). In its simplest form, which is the version employed in our work, the Johannsen metric has only one deformation parameter, named α 13 (see Johannsen 2013 for the origin of this parameter). In Boyer–Lindquist coordinates, the line element reads (we use units in which G N = c = 1)where , , , andFor α 13 = 0, we recover the Kerr metric. In order to have a regular exterior region, we have to impose (as in the Kerr metric, for there is no event horizon and the central singularity is naked) and the following restriction on α 13 (Tripathi et al. 2018 ) Note that α 13 enters the metric coefficients g tt , g tφ , and g φφ . It thus affects the structure of the accretion disk, modifying the Keplerian gas motion and moving the ISCO radius. Qualitatively speaking, α 13 > 0 ( 0) increases (decreases) the strength of the gravitational force, so it moves the ISCO radius to higher (lower) values and this explains the strong correlation with the spin parameter in the plots that will be presented in the next sections. 3. Data Reduction and Analysis LMC X-1 was discovered in 1969 as the first extragalactic X-ray binary (Mark et al. 1969 ; Price et al. 1971 ). The system consists of a stellar-mass black hole and an O-giant companion star. The distance of the source, the black-hole mass, and the inclination angle of the orbit, which are three key-quantities in the continuum-fitting method, have been estimated to be D = 48.10 ± 2.22 kpc, M = 10.91 ± 1.54 M ⊙ , and i = 3638 ± 202, respectively (Gou et al. 2009 ; Orosz et al. 2009 ). LMC X-1 is characterized by a quite stable bolometric luminosity, which is about 16% of its Eddington luminosity L Edd (Gou et al. 2009 ) and thus nicely meets the standard criterion required to use the continuum-fitting method: sources with an accretion luminosity in the range 5%–30% L Edd (McClintock et al. 2014 ). The measurement of the spin parameter of the black hole in LMC X-1 using the continuum-fitting method was presented in Gou et al. ( 2009 ), and here we follow that study. There are 55 pointed observations of LMC X-1 with the Proportional Counter Array (PCA) on board RXTE (Swank 1999 ). To use the continuum-fitting method, it is desirable to choose thermal dominant spectral data, which are defined by three conditions (Remillard McClintock 2006 ): (i) the flux of the thermal component accounts for more than 75% of the total 2–20 keV unabsorbed flux, (ii) the root mean square (rms) variability in the power density spectrum in the 0.1–10 Hz range is lower than 0.075, and (iii) quasi-periodic oscillations are absent or very weak. Imposing these three conditions, we only have three observations, which are named “gold spectra” in Gou et al. ( 2009 ) as