General Relativistic Schwarzschild Research Articles

Thin accretion disk signatures of scalarized black holes in Einstein-scalar-Gauss-Bonnet gravity

Einstein-scalar-Gauss-Bonnet gravity has recently been known to exhibit spontaneous scalarization. In the presence of the Gauss-Bonnet term the no-hair theorem can be evaded and novel black hole solutions with non-trivial scalar fields have been found besides the general relativistic solutions. In this paper, we aim to investigate the possibility of observationally testing Einstein-scalar-Gauss-Bonnet gravity using thin accretion disk properties around such scalarized black holes. Using the Novikov-Thorne model, we numerically calculate the electromagnetic flux, temperature distribution, emission spectrum, innermost stable circular orbits and energy conversion efficiency of accretion disks around such black holes and compare the results with the standard general relativistic Schwarzschild solution. We find that the accretion disks around scalarized black holes are hotter and more luminous than in general relativity.

Post-Keplerian effects on radial velocity in binary systems and the possibility of measuring General Relativity with the star S2 in 2018

One of the directly measured quantities which are used in monitoring the orbital motions of many of the S stars revolving around the Supermassive Black Hole (SMBH) in the Galactic Center (GC) is their radial velocity (RV) $V$ obtained with near-infrared spectroscopy. Here, we devise a general approach to calculate both the instantaneous variations $\Delta V\left(t\right)$ and the net shifts per revolution $\left\langle\Delta V\right\rangle$ induced on such an observable by some post-Keplerian (pK) accelerations. In particular, we look at the general relativistic Schwarzschild (gravitoelectric) and Lense-Thirring (gravitomagnetic frame-dragging) effects, and the mass quadrupole. It turns out that we may be on the verge of measuring the Schwarzschild-type 1pN static component of the SMBH's field with the S2 star for which RV measurements accurate to about $\simeq 30-50~\textrm{km s}^{-1}$ dating back to $t_0 = 2003.271$ are currently available, and whose orbital period amounts to $P_\textrm{b} = 16$ yr. Indeed, while its expected general relativistic RV net shift per orbit amounts to just $\left\langle\Delta V^\textrm{GE}\right\rangle = -11.6~\textrm{km s}^{-1}$, it should reach a peak value as large as $\Delta V_\textrm{max}^\textrm{GE}\left(t_\textrm{max}\right) = 551~\textrm{km s}^{-1}$ at $t_\textrm{max} = 2018.35$. The periastron shift $\Delta\omega^\textrm{GE}$ of S2 over the same time span will not be larger than $0.2$ deg, while the current accuracy in estimating such an orbital element for this star is of the order of $0.6$ deg. The frame-dragging and quadrupole-induced RV shifts are far smaller for S2, amounting to, at most, $0.19~\textrm{km s}^{-1},0.0039~\textrm{km s}^{-1}$, respectively. Further studies should be dedicated to the impact on the RV of possible diffused mass distribution in the GC and of other individual stars inside and outside the orbit of S2.

Stability of the graviton Bose–Einstein condensate in the brane-world

We consider a solution of the effective four-dimensional Einstein equations, obtained from the general relativistic Schwarzschild metric through the principle of Minimal Geometric Deformation (MGD). Since the brane tension can, in general, introduce new singularities on a relativistic E\"otv\"os brane model in the MGD framework, we require the absence of observed singularities, in order to constrain the brane tension. We then study the corresponding Bose-Einstein condensate (BEC) gravitational system and determine the critical stability region of BEC MGD stellar configurations. Finally, the critical stellar densities are shown to be related with critical points of the information entropy.

Classical tests of general relativity: Brane-world Sun from minimal geometric deformation

We consider a solution of the effective four-dimensional brane-world equations, obtained from the general relativistic Schwarzschild metric via the principle of minimal geometric deformation, and investigate the corresponding signatures stemming from the possible existence of a warped extra-dimension. In particular, we derive bounds on an extra-dimensional parameter, closely related with the fundamental gravitational length, from the experimental results of the classical tests of general relativity in the Solar system.

Constraining the Kehagias-Sfetsos Solution of the Ho!ava-Lifshitz Modified Gravity with Extrasolar Planets

We consider a spherically symmetric and asymptotically flat vacuum solution of the Horava-Lifshitz (HL) gravity that is the analog of the general relativistic Schwarzschild black hole. In the weak-field and slow-motion approximation, we work out the correction to the third Kepler law of a test particle induced by such a solution and compare it to the phenomenologically determined orbital period of the transiting extrasolar planet HD209458b Osiris to preliminarily obtain an order-of-magnitude lower bound on the KS dimensionless parameter \omega_0 >= 1.4\times 10^-18. As suggestions for further analyses, the entire data set of HD209458b should be re-processed by explicitly modeling KS gravity as well, and one or more dedicated solve-for parameter(s) should be estimated.

Black hole accretion disks in brane gravity via a confining potential

Accretion disks are among the most luminous and ubiquitous sources in astrophysics and they have drawn a good deal of attention from the observational and theoretical communities. In this paper, we study the process of matter forming thin accretion disks around black hole solutions in the context of the brane-world scenario where our universe is a three-brane embedded in an m-dimensional bulk and localization of matter on the brane is achieved by means of a confining potential. The physical properties of thin accretion disks including the time averaged energy flux, temperature distribution, the emission spectrum as well as the energy conversion efficiency are obtained, and the results are compared with the DMPR, CFM and BMD brane black holes and the standard general relativistic Schwarzschild solution.

THE EQUIVALENCE PRINCIPLE IN KALUZA–KLEIN GRAVITY

In four-dimensional general relativity the space–time outside of an isolated spherical star is described by a unique line element, which is the Schwarzschild metric. As a consequence, the "gravitational" mass and the "inertial" mass of a star are equal to each other. However, theories that envision our world as being embedded in a larger universe, with more than four dimensions, permit a number of possible non-Schwarzschild 4D exteriors, which typically lead to different masses, violating the weak equivalence principle of ordinary general relativity. Therefore, the question arises as to whether the violation of this principle, i.e. the equality of gravitational and inertial mass, is a necessary consequence of the existence of extra dimensions. In this paper, in the context of Kaluza–Klein gravity in 5D, we show that the answer to this question is negative. We find a one-parameter family of asymptotically flat non-Schwarzschild static exteriors for which the inertial and gravitational masses are equal to each other, and equal to the Deser–Soldate mass. This family is consistent with the Newtonian weak field limit as well as with the general-relativistic Schwarzschild limit. Thus, we conclude that the existence of an extra dimension, and the corresponding non-Schwarzschild exterior, does not necessarily require different masses. However, to an observer in 4D, it does affect the motion of test particles in 4D, which is a consequence of the departure from the usual (4D) law of geodesic motion.

Stellar models with Schwarzschild and non-Schwarzschild vacuum exteriors

A striking characteristic of non-Schwarzschild vacuum exteriors is that they contain not only the total gravitational mass of the source, but also an {\it arbitrary} constant. In this work, we show that the constants appearing in the "temporal Schwarzschild", "spatial Schwarzschild" and "Reissner-Nordstr{\"o}m-like" exteriors are not arbitrary but are completely determined by star's parameters, like the equation of state and the gravitational potential. Consequently, in the braneworld scenario the gravitational field outside of a star is no longer determined by the total mass alone, but also depends on the details of the internal structure of the source. We show that the general relativistic upper bound on the gravitational potential $M/R < 4/9$, for perfect fluid stars, is significantly increased in these exteriors. Namely, $M/R < 1/2$, $M/R < 2/3$ and $M/R < 1$ for the temporal Schwarzschild, spatial Schwarzschild and Reissner-Nordstr{\"o}m-like exteriors, respectively. Regarding the surface gravitational redshift, we find that the general relativistic Schwarzschild exterior as well as the braneworld spatial Schwarzschild exterior lead to the same upper bound, viz., $Z < 2$. However, when the external spacetime is the temporal Schwarzschild metric or the Reissner-Nordstr{\"o}m-like exterior there is no such constraint: $Z < \infty$. This infinite difference in the limiting value of $Z$ is because for these exteriors the effective pressure at the surface is negative. The results of our work are potentially observable and can be used to test the theory.

Transformation between orbital parameters in different coordinate systems of the general relativistic schwarzschild problem

The relationships between the osculating orbital elements for a family of solutions of the general relativistic Schwarzschild problems are developed. These relationships provide a method for evaluating orbital elements in different Schwarzschild coordinate systems without the necessity of fitting to real data every time the system of coordinates is changed. The objectivity of different coordinate systems is discussed. Considerations of orbital motions favor the standard Schwarzschild metric, but the propagation of light signals is more objective in the metric of Painlevé. Because the orbital motions usually dominate the representation of data, the standard Schwarzschild coordinates are the best objective choice for most applications.