scholarly journals Regular Solutions in Vacuum Brans-Dicke Theory Compared to Vacuum Einstein Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Alina Khaybullina ◽  
Ramil Izmailov ◽  
Kamal K. Nandi ◽  
Carlo Cattani
Keyword(s):  
Black Hole ◽  
Weak Field ◽  
Einstein Frame ◽  
Jordan Frame ◽  
Schwarzschild Black Hole ◽  
Positive Mass ◽  
Regular Solutions ◽  
Einstein Theory ◽  
Symmetric Vacuum ◽  
Jordan And Einstein Frames

We will confront some static spherically symmetric vacuum Brans-Dicke solutions in the Jordan and Einstein Frames with the Robertson parameters. While the regular solution in the vacuum Einstein theory is just the Schwarzschild black hole, the same in the Jordan frame Brans-Dicke theory is shown to represent not a black hole but a traversable wormhole. But, in this case, the valid range ofωbecomes too narrow to yield the observed weak field Robertson parameters at the positive mass mouth. The corresponding solution in the Einstein frame also provides a regular wormhole, and it yields the correct parametric values but only up to “one and half order.” We argue that a second-order contribution can in principle distinguish between the signatures of the regular wormhole and the singular Buchdahl solution in the Einstein frame. Thus, at the level of regular solutions, Brans-Dicke theory in each frame predicts effects very different from those of Einstein's theory. To our knowledge, these theoretical distinctions seem not to have received adequate attention so far.

scholarly journals Jordan and Einstein Frames Hamiltonian Analysis for FLRW Brans-Dicke Theory

Universe ◽  
2021 ◽  
Vol 8 (1) ◽  
pp. 14
Author(s):  
Matteo Galaverni ◽  
Gabriele Gionti S. J.
Keyword(s):  
Equations Of Motion ◽  
Einstein Frame ◽  
Jordan Frame ◽  
Inverse Transformation ◽  
Conformal Transformations ◽  
Hamiltonian Equations ◽  
Flrw Universe ◽  
Jordan And Einstein Frames ◽  
Hamiltonian Analysis

We analyze the Hamiltonian equivalence between Jordan and Einstein frames considering a mini-superspace model of the flat Friedmann–Lemaître–Robertson–Walker (FLRW) Universe in the Brans–Dicke theory. Hamiltonian equations of motion are derived in the Jordan, Einstein, and anti-gravity (or anti-Newtonian) frames. We show that, when applying the Weyl (conformal) transformations to the equations of motion in the Einstein frame, we did not obtain the equations of motion in the Jordan frame. Vice-versa, we re-obtain the equations of motion in the Jordan frame by applying the anti-gravity inverse transformation to the equations of motion in the anti-gravity frame.

scholarly journals Vacuum Brans–Dicke theory in the Jordan and Einstein frames: Can they be distinguished by lensing?

2020 ◽  
Vol 35 (37) ◽  
pp. 2050308 ◽  
Author(s):  
Ramil N. Izmailov ◽  
Ramis Kh. Karimov ◽  
Alexander A. Potapov ◽  
Kamal K. Nandi
Keyword(s):  
Order Effect ◽  
Weak Field ◽  
Second Order ◽  
The Other ◽  
Jordan Frame ◽  
Light Deflection ◽  
Total Magnification ◽  
Quantitative Changes ◽  
Image Position ◽  
Jordan And Einstein Frames

Vacuum Brans-Dicke (BD) theory continues to receive widespread attention since it is consistent with solar and cosmological experiments. The theory can be self-consistently described in two frames, the Jordan frame (JF) and the conformally rescaled Einstein frame (EF), the transformations providing an easy passage from one frame to the other at the level of actions and solutions. While coordinate transformations do not change curvature properties, conformal transformations do change them leading to corresponding changes in the numerical values of observables. A previous article by Bhadra et al.[Formula: see text] did exemplify this change between JF and EF using the diagnostic of second-order light deflection. This important work leaves room for further improvements on two points, which we do here. First, the measurement of second-order effect faced technically unsurmountable difficulties even around the Sun, hence actually abandoned. Second, the comparison of quantitative values between JF and EF should be based on a common value of [Formula: see text] connecting the two frames. Keeping these in mind, we investigate a technically easier diagnostic, viz., the weak field lensing (WFL) and compare the quantitative changes at common [Formula: see text] to show that the two frames can indeed be distinguished by lensing experiments. Specifically, the predictions of light deflection, image position, total magnification and magnification factor are computed in the EF and compared with those recently obtained (by Gao et al.[Formula: see text]) directly in the JF BD class I solution. The use of the value of BD coupling constant [Formula: see text], suggested by the Cassini spacecraft solar experiment, reveals that an exceptionally high degree of accuracy is needed to experimentally rule out one or the other frame by means of WFL measurements.

scholarly journals Can accretion properties distinguish between a naked singularity, wormhole and black hole?

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
R. Kh. Karimov ◽  
R. N. Izmailov ◽  
A. A. Potapov ◽  
K. K. Nandi
Keyword(s):  
Black Hole ◽  
Naked Singularity ◽  
Singular Limit ◽  
Jordan Frame ◽  
Coordinate Transformations ◽  
Wick Rotation ◽  
Schwarzschild Black Hole ◽  
Particle Orbits ◽  
Stable Radius ◽  
The Universe

AbstractWe first advance a mathematical novelty that the three geometrically and topologically distinct objects mentioned in the title can be exactly obtained from the Jordan frame vacuum Brans I solution by a combination of coordinate transformations, trigonometric identities and complex Wick rotation. Next, we study their respective accretion properties using the Page–Thorne model which studies accretion properties exclusively for $$r\ge r_{\text {ms}}$$ r ≥ r ms (the minimally stable radius of particle orbits), while the radii of singularity/throat/horizon $$r<r_{\text {ms}}$$ r < r ms . Also, its Page–Thorne efficiency $$\epsilon $$ ϵ is found to increase with decreasing $$r_{\text {ms}}$$ r ms and also yields $$\epsilon =0.0572$$ ϵ = 0.0572 for Schwarzschild black hole (SBH). But in the singular limit $$r\rightarrow r_{s}$$ r → r s (radius of singularity), we have $$\epsilon \rightarrow 1$$ ϵ → 1 giving rise to $$100 \%$$ 100 % efficiency in agreement with the efficiency of the naked singularity constructed in [10]. We show that the differential accretion luminosity $$\frac{d{\mathcal {L}}_{\infty }}{d\ln {r}}$$ d L ∞ d ln r of Buchdahl naked singularity (BNS) is always substantially larger than that of SBH, while Eddington luminosity at infinity $$L_{\text {Edd}}^{\infty }$$ L Edd ∞ for BNS could be arbitrarily large at $$r\rightarrow r_{s}$$ r → r s due to the scalar field $$\phi $$ ϕ that is defined in $$(r_{s}, \infty )$$ ( r s , ∞ ) . It is concluded that BNS accretion profiles can still be higher than those of regular objects in the universe.

scholarly journals PHENOMENOLOGICAL CONSTRAINTS ON THE KEHAGIAS–SFETSOS SOLUTION IN THE HOŘAVA–LIFSHITZ GRAVITY FROM SOLAR SYSTEM ORBITAL MOTIONS

2010 ◽  
Vol 25 (29) ◽  
pp. 5399-5408 ◽  
Author(s):  
L. IORIO ◽  
M. L. RUGGIERO
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Solar System ◽  
Slow Motion ◽  
Analytical Form ◽  
Weak Field ◽  
Schwarzschild Black Hole ◽  
Anomalous Acceleration ◽  
Motion Approximation ◽  
General Relativistic

We focus on Hořava–Lifshitz (HL) theory of gravity, and, in particular, on the Kehagias and Sfetsos's solution that is the analog of Schwarzschild black hole of General Relativity. In the weak-field and slow-motion approximation, we analytically work out the secular precession of the longitude of the pericentre ϖ of a test particle induced by this solution. Its analytical form is different from that of the general relativistic Einstein's pericentre precession. Then, we compare it to the latest determinations of the corrections [Formula: see text] to the standard Newtonian/Einsteinian planetary perihelion precessions recently estimated by E. V. Pitjeva with the EPM2008 ephemerides. It turns out that the planets of the solar system, taken singularly one at a time, allow one to put lower bounds on the adimensional HL parameter ψ0 of the order of 10-12(Mercury)-10-24 (Pluto). They are not able to account for the Pioneer anomalous acceleration for r > 20 AU.

The Schwarzschild black hole

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Equilibrium Configuration ◽  
Original Form ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Metric ◽  
Schwarzschild Geometry

This chapter discusses the Schwarzschild black hole. It demonstrates how, by a judicious change of coordinates, it is possible to eliminate the singularity of the Schwarzschild metric and reveal a spacetime that is much larger, like that of a black hole. At the end of its thermonuclear evolution, a star collapses and, if it is sufficiently massive, does not become stabilized in a new equilibrium configuration. The Schwarzschild geometry must therefore represent the gravitational field of such an object up to r = 0. This being said, the Schwarzschild metric in its original form is singular, not only at r = 0 where the curvature diverges, but also at r = 2m, a surface which is crossed by geodesics.

scholarly journals Black hole S-matrix for a scalar field

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Panos Betzios ◽  
Nava Gaddam ◽  
Olga Papadoulaki
Keyword(s):  
Black Hole ◽  
Normal Modes ◽  
Massless Scalar ◽  
Scattering Process ◽  
Schwarzschild Black Hole ◽  
Asymptotically Flat ◽  
Scalar Particles ◽  
Black Hole Background ◽  
S Matrix ◽  
Do So

Abstract We describe a unitary scattering process, as observed from spatial infinity, of massless scalar particles on an asymptotically flat Schwarzschild black hole background. In order to do so, we split the problem in two different regimes governing the dynamics of the scattering process. The first describes the evolution of the modes in the region away from the horizon and can be analysed in terms of the effective Regge-Wheeler potential. In the near horizon region, where the Regge-Wheeler potential becomes insignificant, the WKB geometric optics approximation of Hawking’s is replaced by the near-horizon gravitational scattering matrix that captures non-perturbative soft graviton exchanges near the horizon. We perform an appropriate matching for the scattering solutions of these two dynamical problems and compute the resulting Bogoliubov relations, that combines both dynamics. This allows us to formulate an S-matrix for the scattering process that is manifestly unitary. We discuss the analogue of the (quasi)-normal modes in this setup and the emergence of gravitational echoes that follow an original burst of radiation as the excited black hole relaxes to equilibrium.

scholarly journals Null Geodesics and Strong Field Gravitational Lensing in a String Cloud Background

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
M. Sharif ◽  
Sehrish Iftikhar
Keyword(s):  
Black Hole ◽  
Gravitational Lensing ◽  
Galactic Center ◽  
Deflection Angle ◽  
Orbital Motion ◽  
Strong Field ◽  
Schwarzschild Black Hole ◽  
Field Limit ◽  
Null Geodesics ◽  
Supermassive Black Hole

This paper is devoted to studying two interesting issues of a black hole with string cloud background. Firstly, we investigate null geodesics and find unstable orbital motion of particles. Secondly, we calculate deflection angle in strong field limit. We then find positions, magnifications, and observables of relativistic images for supermassive black hole at the galactic center. We conclude that string parameter highly affects the lensing process and results turn out to be quite different from the Schwarzschild black hole.

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