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Testing the nature of the supermassive object at the Galactic Center
Despite the huge improvements guaranteed by future GRAVITY observations of S0-2 star, these will not be able to unveil the fundamental nature, whether black hole or wormhole, of the central supermassive object. Nevertheless, observing stars orbiting closer to the central gravitational source could allow distinguishing between the black hole and wormhole nature of this object at more than 5σ [1].
In GR, the Black Bounce (BB) metric refers to the one-parameter family of solutions, firstly introduced in [2], described by the following line element:
where we have set G = c = 1. This is a static and spherically symmetric family of solutions tuned by the parameter α. Indeed, setting α=0 returns the Schwarzschild metric. The parameter α defines the so-called throat of the geometry,
Firstly, we have used publicly available astrometric and spectroscopic measurements of S0-2 star to constrain the metric around the supermassive object without finding any evidence either favouring or ruling out the wormhole nature.
Secondly, we have designed a mock catalogue of future observations of S0-2 star mirroring the accuracy and precision of GRAVITY. Afterwards, we firstly tested our methodology showing that our procedure recovers the input model, and subsequently we demonstrated that the constraining power of such a dataset is not enough to distinguish between black hole and wormhole.
Finally, we built some toy models representing stars orbiting much closer to the central object than S0-2. We used these toy models to investigate which are the ideal orbital features and observational strategies to achieve our aim of unveiling the fundamental nature of the central supermassive object, demonstrating that a star with a period of the order of ~5 years and a pericentre distance of ~5 AU could identify the nature of the central object at almost 5σ accuracy.
Table: We report the number of observations that are performed in the regions of the toy star’s orbit (Figure on the left) that we have defined in Figure 8 for the six different mock catalogues that we have built.
Figure: On the left panel we report the 1σ, 3σ and 5σ uppers bound on the parameter α resulting from the posterior distributions (reported on the right panel), as a function of the observational strategy for the Toy star in Table.
Testing super-Planckian hairs with S2 data
We investigate a nonsingular black hole spacetime representing a strong deformation of the Schwarzschild solution with mass M by an additional hair ℓ [3]:
which may be hierarchically larger than the Planck scale. The spacetime is an exact solution of Einstein's equations sourced by an anisotropic fluid. The model presents a de Sitter core and O (ℓ2/r2) slow-decaying corrections to the Schwarzschild solution. These solutions are thermodynamically preferred when 0.2 ≲ℓ/G M ≲0.3 and are characterized by strong deviations in the orbits of test particles from the Schwarzschild case. In particular, we find corrections to the perihelion precession angle scaling linearly with ℓ. We test our model using the available data for the orbits of the S2 star around Sgr A*. These data strongly constrain the value of the hair ℓ, casting an upper bound on it of ∼0.47 G M but do not rule out the possible existence of regular black holes with super-Planckian hair.
Figure: Marginalized posterior probability distribution for the parameter ℓ resulting from our MCMC analysis. We are able to constrain the parameter ℓ by providing a 95% confidence level upper limit of ℓ ≲ 0.019 AU.
Testing Einstein-Maxwell-Dilaton-Axion model with S2 data
We derive new constraints on the dilaton parameter appearing in the spherically-symmetric black hole solution of Einstein-Maxwell-dilaton-axion gravity [4]. We neglected the rotation of the black hole and thus considered the non-rotating limit (a → 0), where both the spin and the axionic field vanish. A pure dilaton BH solution is hence obtained:
where the pseudo-radial coordinate r and mass M are defined as:
This theory emerges from the low energy effective action of the heterotic string theory and has been proven to predict peculiar observational features from the direct imaging of black hole shadows. At a fundamental level, Einstein-Maxwell-dilaton-axion includes additional electromagnetic, dilatonic and axionic fields coupled to the space-time metric. When considering charged non-rotating black hole solutions, the additional fields endow the metric with one extra parameter b, called dilaton parameter, that is theoretically bound to 0 < b < M. Using publicly available astrometric data for S2 we derive an upper bound on b ≲ 12 M at 95% confidence level and we demonstrate that only including the measurement of the relativistic orbital precession for S2 is sufficient to reduce this bound to b ≲ 1.4 M at the same confidence level. Additionally, using mock data mimicking future observations of S2 with the GRAVITY interferometer, we show that improved astrometric precision can help further narrow down the allowed dilaton parameter range to b ≲ 0.033 M after monitoring the S2 orbit for one and a half period.
Figure: Logarithmic-scale marginalized likelihoods for the EMDA parameter b in the three cases analyzed both in AU (bottom axis) and in units of gravitational radii (top axis). Dashed vertical lines correspond to the respective 95 % confidence upper limits
Bibliography:
Della Monica R., de Martino I., "Unveiling the nature of SgrA* with the geodesic motion of S-stars", 2022, Journal of Cosmology and Astroparticle Physics, 2022, 007
A. Simpson and M. Visser, "Black-bounce to traversable wormhole", 2019, J. Cosmol. Astropart. Phys. 2019, 042.
M. Cadoni, M. De Laurentis, I. De Martino, R. Della Monica, M. Oi, A. P. Sanna, "Are nonsingular black holes with super-Planckian hair ruled out by S2 star data?", 2023, Physical Review D, 107, 044038
R. Fernández Fernández, R. Della Monica, I. de Martino, "Constraining an Einstein-Maxwell-dilaton-axion black hole at the Galactic Center with the orbit of the S2 star", 2023, Journal of Cosmology and Astroparticle Physics, 2023, 039
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