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Register a new userObtaining mass parameters of compact objects from red-blue shifts emitted by geodesic particles around them
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Added by
Susana Valdez Alvarado
Publication date
2016
fields
Physics
and research's language is
English
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The mass parameters of compact objects such as Boson Stars, Schwarzschild, Reissner Nordstrom and Kerr black holes are computed in terms of the measurable redshift-blueshift (zred, zblue) of photons emitted by particles moving along circular geodesics around these objects and the radius of their orbits. We found bounds for the values of (zred, zblue) that may be observed. For the case of Kerr black hole, recent observational estimates of SrgA* mass and rotation parameter are employed to determine the corresponding values of these red-blue shifts.
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We are motivated by the recently reported dynamical evidence of stars with short orbital periods moving around the center of the Milky Way and the corresponding hypothesis about the existence of a supermassive black hole hosted at its center. In this paper we show how the mass and rotation parameters of a Kerr black hole (assuming that the putative supermassive black hole is of this type), as well as the distance that separates the black hole from the Earth, can be estimated in a relativistic way in terms of i) the red and blue shifts of photons that are emitted by geodesic massive particles (stars and galactic gas) and travel along null geodesics towards a distant observer, and ii) the radius of these star/gas orbits. As a concrete example and as a first step towards a full relativistic analysis of the above mentioned star orbits around the center of our galaxy, we consider stable equatorial circular orbits of stars and express their corresponding red/blue shifts in terms of the metric parameters (mass and angular momentum per unit mass) and the orbital radii of both the emitter star (and/or galactic gas) and the distant observer. In principle, these expressions allow one to statistically estimate the mass and rotation parameters of the Kerr black hole, and the radius of our orbit, through a Bayesian fitting, i.e., with the aid of observational data: the red/blue shifts measured at certain points of stars orbits and their radii, with their respective errors, a task that we hope to perform in the near future. We also point to several astrophysical phenomena, like accretion discs of rotating black holes, binary systems and active galactic nuclei, among others, to which this formalism can be applied.
The mass parameter of dilaton space-times is obtained as a function of the redshift-blueshift (zred, zblue) of photons emitted by particles orbiting in circular motion around these objects and their corresponding radii. Particularly, we work with the generalized Chatterjee and Gibbons- Maeda space-times. Both of them become the Schwarzschild black hole in certain limit of one of their parameters. Bounds for the values of these frequency shifts, that may be observed for these metrics, are also determined.
Here we examine the circular motion of test particles and photons in the spacetime geometry of charged black hole surrounded by quintessence and clouds of strings for the equation of state parameter $omega_q=-2/3$. We observe that there exist stable circular orbits in this geometry for very small values of the quintessence and string cloud parameters, i.e., $0<gamma<<1$ and $0<alpha<<1$. We observe that if the values of $gamma$ and $alpha$ increase, the test particle can more easily escape the gravitational field of the black hole. While the effect of the charge $Q$ of the black hole on the effective potential is just opposite to that of the $gamma$ and $alpha$. Further, we investigate the quasi-periodic oscillations of test particles near the stable circular orbits. With the increasing values of $Q$, the stable circular orbits get away from the central object; therefore, one can observe lower epicyclic frequencies away from the central gravitating source with the increase in the values of $Q$. The redshift parameter $z$ of the photons emitted by the charged test particles moving in the stable circular orbits around the central source increases with an increase in the parameter $alpha$ and decreases with an increase in the values of the charge $Q$. In the Banados-Silk-West (BSW) process study, we note that the centre of mass-energy at the horizon of this Riessner-Nordstrom black hole with quintessence and string clouds increases indefinitely if the charge of one of the colliding particles attains its critical value. For a better understanding of the study, we show the dependence of the radii of the circular orbits, energy and angular momentum of the particles, effective potential, effective force, quasi-periodic oscillations and red-blue shifts of photons of the test particles in the circular orbits on the parameters $alpha$, $gamma$ and $Q$ graphically.
We obtain the mass parameter for a class of static and spherically symmetric regular black holes (BHs) (namely Bardeen, Hayward and Ay{o}n-Beato-Garc{i}a BHs) which are solutions of Einsteins field equations coupled to nonlinear electrodynamics (NED) in terms of redshifts and blueshifts of photons emitted by geodesic particles (for instance, stars) orbiting around these BHs. The motion of photons is not governed by null geodesics for these type of spacetime geometries which reflects the direct effects of the electrodynamic nonlinearities in the photon motion; hence, an effective geometry needs to be constructed to study null trajectories [Phys. Rev. D61, 045001 (2000)]. To achieve the above, we first study the constants of motion from the analysis of the motion of both geodesic particles moving in stable circular orbits and photons ejected from them and reaching a distant observer (or detector) in the equatorial plane for the above mentioned regular BHs. The relationship between red/blueshifts of photons and the regular BH observables is presented. We also numerically find the bounds on the photon shifts for these regular BH cases.
In a recent paper (Phys. Dark Univ. {bf 31}, 100744 (2021)) it has been obtained new static black hole solutions with primary hairs by the Gravitational Decoupling. In this work we either study the geodesic motion of massive and massless particles around those solutions and restrict the values of the primary hairs by observational data. In particular, we obtain the effective potential, the innermost stable circular orbits, the marginally bounded orbit, and the periastron advance for time--like geodesics. In order to restrict the values taken by the primary hairs we explore their relationship with the rotation parameter of the Kerr black hole giving the same innermost stable circular orbit radius and give the numerical values for the supermassive black holes at Ark 564 and NGC 1365. The photon sphere and the impact parameter associated to null geodesics are also discussed.
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