By considering a deformation of the Schwarzschild metric in the presence of a minimal measurable length which still respects the equivalence principle, we study corrections to the standard general relativistic predictions for some astrophysical phenomena such as stability of circular orbits of black hole accretion disks, redshift of black hole accretion disks, gravitational tidal forces and the geodetic drift rate. We use the \emph{Gravity Probe B} data to see robustness of our results. Our analysis shows also that the relevant deformation parameter $\varepsilon$ which has a geometric origin, plays the same role as the charge to mass ratio, $\frac{e}{m}$ in the Reissner-Nordström metric.
Prolonging The Inevitable: Maximising survival time of an engine-equipped spacecraft between spatial hypersurfaces, as applied to the Schwarzschild spacetime
We investigate the impact of quantum gravity on accretion onto a modified Schwarzschild black hole within the context of the generalized uncertainty principle (GUP). The minimal measurable length connected to GUP modifies the Schwarzschild black hole, giving it the capacity to accommodate the correction due to quantum gravity. We look at potential critical point locations and calculate the critical speed of the matter accreting. We determine the temperature and total integrated flux correction at the event horizon for the polytropic matter using the least measurable length conjecture offered b…
An analysis of null geodesics in Schwarzschild de Sitter space is presented with special attention to their global `bending angles', local measurable angles, and the involvement of the cosmological constant. We make use of a general technique which allows for finding observable intersection angles of null trajectories analytically. A general relativistic aberration relationship is established as one of its applications. The question of whether or not the cosmological constant, $Λ$, contributes to orbits of light and to related observable quantities is addressed in detail. We also discuss the o…
Equipped with new powerful and efficient methods for computing quantum expectation values in static-spherically symmetric spacetimes in arbitrary dimensions, we perform an in-depth investigation of how the quantum vacuum polarization varies with the parameters in the theory. In particular, we compute and compare the vacuum polarization for a quantum scalar field in the Schwarzschild anti-de Sitter black hole spacetime for a range of values of the field mass and field coupling constant as well as the black hole mass and number of spacetime dimensions. In addition, a new approximation for the va…
Quasi-local energies for constantly accelerating observers in Bañados, Teitelboim, and Zanelli (BTZ), Schwarzschild and Schwarzschild-de Sitter spacetimes are derived. The energies are expressed in terms of acceleration, cosmological constant, and area, quantities measurable by the observers. Based on results from quantum fields in curved spacetime for the redshifted Hawking temperature, entropy and thermodynamic-like laws are briefly explored in the three spacetimes.
A simple model is suggested by assuming an effective interaction at the crossing point of the two curves, the Schwarzschild radius and the Compton wave length, that is at the Planck length and Planck mass. It is argued that there would be a physical effect that may be measurable at, say, nucleon mass and size, while the Schwarzschild radius would remain unaffected for macroscopic lengths and masses.
We investigate the geodesic motion of massless test particles in the background of a noncommutative geometry inspired Schwarzschild black hole. The behaviour of effective potential is analysed in the equatorial plane and the possible motions of massless particles (i.e. photons) for different values of impact parameter are discussed accordingly. We have also calculated the frequency shift of photons in this spacetime. Further, the mass parameter of a non-commutative inspired Schwarzschild black hole is computed in terms of the measurable redshift of photons emitted by massive particles moving a…
In this paper we review and build on the common methods used to analyze null geodesics in Schwarzschild de Sitter space. We present a general technique which allows finding measurable intersection angles of null trajectories analytically, and as one of its applications we establish a general relativistic aberration relationship. The tools presented are used to analyze some standard setups of gravitational deflection of light and gain a clear understanding of the role that the cosmological constant, $Λ$, plays in gravitational lensing phenomena. Through reviewing some recent papers on the topic…
Based on the minimum measurable momentum concepts associated with the quantum gravity effects acting on the large-scale dynamics of the universe, we study the quantum effect of the EUP on the Hawking evaporation of the black hole. The results show the quantum corrections may shorten the lifetime of the massive black hole. To verify the new EUP on the black hole stability, the scalar field and electromagnetic field are derived and the time evolution of the black hole is analyzed in terms of the time domain integration method, the quantum effect alters the oscillation and decay time of black hol…
Accretion, greybody factor, quasinormal modes, power spectrum, sparsity of Hawking radiation, and weak gravitational lensing of a minimum measurable length inspired Schwarzchild black hole
Beyond Schwarzschild-de Sitter spacetimes: II. An exact non-Schwarzschild metric in pure $R^{2}$ gravity and new anomalous properties of $R^{2}$ spacetimes
In this paper, we solved the Einstein's field equation and obtained a line element for static, ellipsoidal objects characterized by the linear eccentricity ($η$) instead of quadrupole parameter ($q$). This line element recovers the Schwarzschild line element when $η$ is zero. In addition to that it also reduces to the Schwarzschild line element, if we neglect terms of the order of $r^{-2}$ or higher which are present within the expressions for metric elements for large distances. Furthermore, as the ellipsoidal character of the derived line element is maintained by the linear eccentricity ($η$…
As incarnations of gravity in its prime, black holes are arguably the best target for us to demystify gravity. Keeping in mind the prominent role black holes play in gravitational wave astronomy, it becomes a must for a theory to possess black hole solutions with only measurable departures from their general relativity counterparts. In this paper, we present black holes in a tensor-vector-scalar representation of relativistic modified Newtonian dynamics. We find that the theory allows Schwarzschild and nearly-Schwarzschild black holes as solutions, while the nontrivial scalar and vector fields…
Accretion Disks in Schwarzschild-MOG and Kerr-MOG Backgrounds: MOG Parameter in terms of Observational Quantities
Mesoamerican Centre for Theoretical Physics, Universidad Autónoma de Chiapas（中美洲理论物理中心，恰帕斯自治大学）；Instituto de Física, Universidad Autónoma de Santo Domingo（物理学研究所，圣多明各自治大学）；Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo（数理科学学院，米却肯圣尼古拉斯德伊达尔戈大学）
The existence of a minimum measurable length could deform not only the standard quantum mechanics but also classical physics. The effects of the minimal length on classical orbits of particles in a gravitation field have been investigated before, using the deformed Poisson bracket or Schwarzschild metric. In this paper, we use the Hamilton-Jacobi method to study motions of particles in the context of deformed Newtonian mechanics and general relativity. Specifically, the precession of planetary orbits, deflection of light, and time delay in radar propagation are considered in this paper. We als…
In this paper we study the accretion of dark energy onto a black hole in the cases that dark energy is equipped with a positive cosmological constant and when the space-time is described by a Schwarzschild-de Sitter metric. It is shown that, if confronted with current observational data, the results derived when no cosmological constant is present are once again obtained in both cases.
The Karlhede invariant is formed from the contraction of the covariant derivative of the Riemann tensor. It is a coordinate invariant that vanishes at the Schwarzschild event horizon $r=2m$. The vanishing of the invariant allows an observer to construct a local measuring device and use it to detect an event horizon while falling into a black hole. Recent proposals postulate the existence of a "firewall" at the event horizon that may incinerate an infalling observer. These proposals face an apparent paradox if a freely falling observer detects nothing special in the vicinity of the horizon. The…
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.
Assuming a static and spherically symmetric spacetime, we propose a novel concept of the total deflection angle of a light ray. The concept is defined by the difference between the sum of internal angles of two triangles; one of the triangles lies on curved spacetime distorted by a gravitating body and the other on its background. The triangle required to define the total deflection angle can be realized by setting three laser-beam baselines as in planned space missions such as LATOR, ASTROD-GW, and LISA. Accordingly, the new total deflection angle is, in principle, measurable by gauging the i…
Some measurable characteristic timescales $\left\{t_\mathrm{trn}\right\}$ of transiting exoplanets are investigated in order to check preliminarily if their cumulative shifts over the years induced by the post-Newtonian (pN) gravitoelectric (Schwarzschild) and gravitomagnetic (Lense-Thirring) components of the stellar gravitational field are, at least in principle, measurable. Both the primary (planet in front of the star) and the secondary (planet behind the star) transits are considered along with their associated characteristic time intervals: the total transit duration $t_D$, the ingress/e…
We illustrate and discuss the view seen by an observer inside the horizon of a Schwarzschild black hole. The view as the observer approaches the central singularity is of particular interest because, according to ideas arising from "observer complementarity," points in opposite directions along the observer's past lightcone are at "the edge of locality," where standard flat-space quantum-field-theory commutation rules may be at the brink of failure. Near the singularity, the observer's view is aberrated by the diverging tidal force into a horizontal plane. The view in the horizontal plane is h…
Gravitational wave `echoes' during black-hole merging events have been advocated as possible signals of modifications to gravity in the strong-field (but semiclassical) regime. In these proposals the observable effect comes entirely from the appearance of nonzero reflection probability at the horizon, which vanishes for a standard black hole. We show how to apply EFT reasoning to these arguments, using and extending earlier work for localized systems that relates choices of boundary condition to the action for the physics responsible for these boundary conditions. EFT reasoning applied to this…
One of the macroscopically measurable effects of gravity is the tidal deformability of astrophysical objects, which can be quantified by their tidal Love numbers. For planets and stars, these numbers measure the resistance of their material against the tidal forces, and the resulting contribution to their gravitational multipole moments. According to general relativity, nonrotating deformed black holes, instead, show no addition to their gravitational multipole moments, and all of their Love numbers are zero. In this paper we explore different configurations of nonrotating compact and ultracom…
The Janis-Newman-Winicour and Papapetrou metrics represent counterparts to the Schwarzschild black hole with scalar and antiscalar background fields, correspondingly (where "anti" is to be understood as in "anti-de Sitter"). There is also a scalar counterpart (the Krori-Bhattacharjee metric) to the Kerr black hole. Here we study analytical connections between these solutions and obtain the exact rotational generalization of the antiscalar Papapetrou spacetime as a viable alternative to the Kerr black hole. The antiscalar metrics appear to be the simplest ones as they do not reveal event horizo…
In this work, in the context of modified gravity, a curved spacetime analogous to the "canonical acoustic black hole" is constructed. The source is a self-interacting scalar field which is non-minimally coupled to gravity through the Gauss-Bonnet invariant. The scalar-Gauss-Bonnet coupling function is characterized by three positive parameters: $σ$ with units of $(length)$, $μ$ with units of $(length)^{4}$, and a dimensionless parameter $s$, thus defining a three-parameter model for which the line element of canonical acoustic black hole is a solution. The spacetime is equipped with spherical …
We study the effect of torques on circular inspirals of intermediate-mass black hole binaries (IMBHBs) embedded in gas discs, wherein both BH masses are in the range $10^2$-$10^5~\rm{M}_\odot$, up to redshift $z = 10$. We focus on how torques impact the detected gravitational wave (GW) waveform in the frequency band of the Laser Interferometer Space Antenna (LISA) when the binary separation is within a few hundred Schwarzschild radii. For a sub-Eddington accretion disc with a viscosity coefficient $α=0.01$, surface density $Σ\approx10^5$ g cm$^{-2}$, and Mach number $\mathcal{M}_{\rm a}\approx…
This paper gives a complete characterization of resonant orbits in a Kerr spacetime. A resonant orbit is defined as a geodesic for which the longitudinal and radial orbital frequencies are commensurate. Our analysis is based on expressing the resonance condition in its most symmetric form using Carlson's integrals. We provide a number of concise formulae for the dependence of resonances on the system parameters. Resonant effects may be observable during the in-spiral of a compact object into a super-massive black hole. When the slowly evolving orbital frequencies pass through a series of low-o…
First-Law Entropy and a Degenerate Extremal Remnant in a Minimal-Length Simpson--Visser-Type Regular Black Hole: Geometrothermodynamics, Phase Structure, and Observational Discriminants
University Moulay Ismail（穆莱·伊斯梅尔大学）；Cadi Ayyad University（卡迪·阿亚德大学）
