Modified gravity black hole lensing observables in weak and strong field of gravity

Abstract

We extend a recent work on weak field first order light deflection in the MOdified Gravity (MOG) by comprehensively analyzing the actual observables in gravitational lensing both in the weak and strong field regime. The static spherically symmetric black hole (BH) obtained by Moffat is what we call here the Schwarzschild-MOG (abbreviated as SMOG) containing repulsive Yukawa-like force characterized by the MOG parameter α > 0 diminishing gravitational attraction. We point out a remarkable feature of SMOG, viz., it resembles a regular brane-world BH in the range −1 < α < 0 giving rise to a negative "tidal charge" Q (= 1 4 α 1+α ) interpreted as an imprint from the 5D bulk with an imaginary source charge q in the brane. The Yukawa-like force of MOG is attractive in the brane-world range enhancing gravitational attraction. For −∞ < α < −1, the SMOG represents a naked singularity. Specifically, we shall investigate the effect of α or Yukawa-type forces on the weak (up to third PPN order) and strong field lensing observables. For illustration, we consider the supermassive BH SgrA* with α = 0.055 for the weak field to quantify the deviation of observables from GR but in general we leave α unrestricted both in sign and magnitude so that future accurate lensing measurements, which are quite challenging, may constrain α. * Electronic address: izmailov.ramil@gmail.com † Electronic address: karimov ramis 92@mail.ru ‡ Electronic address: zhdanov@ufanet.ru § Electronic address: kamalnandi1952@yahoo.co.in Recent works [1,13,14,23] have motivated us to comprehensively look into the SMOG from another angle, viz., the weak and strong field lensing phenomena that are fundamentally different from each other. The purpose was

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

“…The story is now quite different -there is a drastic change. The above solution (29)(30)(31)(32)(33) has been listed by Brans [74], which we call Brans II solution, but we see that the Brans I and II are not independent -one can be derived from the other by the transformations in (27). However, though not independent, Brans I and II solutions are by no means equivalent as the former is singular, while the latter is a regular WH [52].…”

“…However, the integrated scalar field energy is of equal and opposite signs on two sides, so they also add to zero. This means the individual sides exhibit gravitational action on light [29]. The massless EBWH does not accrete matter since r EBWH ms → ∞ (see Sect.…”

“…There could be other categories of hypothetical objects such as naked singularity (NS) and wormholes (WH) that are not ruled out either by theory or by experiment to date. On the contrary, there has been a recent surge of interest a e-mail: izmailov.ramil@gmail.com (corresponding author) in the study of their observational signatures, which include, but not limited to, the phenomena of accretion [2][3][4][5][6][7][8][9][10][11][12][13][14][15], gravitational lensing [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], shadow cast on the background of the thin accretion flow [32][33][34][35][36][37][38][39][40][41] and gravitational waves [42][43][44][45][46][47]…”

Gravitational lensing by a quantum deformed Schwarzschild black hole

“…Inspired by these previous works and hoping to gain a whole picture of the weak and strong deflection gravitational lensing [118][119][120][121][122][123][124], we will investigate these two scenarios of gravitational lensing by the quantum deformed Schwarzschild black hole for detecting and searching its quantum signatures. We will carefully compare its observables with those of two other quantum black holes, the renormalization group improved Schwarzschild black hole [41] and the asymptotically safe black hole [107], both of which were proposed in the asymptotic safety scenario in the quantum gravity and which have very similar spacetime metrics.…”

Weak and strong deflection gravitational lensing by a renormalization group improved Schwarzschild black hole

“…Motivated by these considerations, we will investigate the weak and strong deflection gravitational lensing by the renormalization group improved Schwarzschild black hole in the present work. In order to fully understand its lensing signatures, it is necessary to combine these two complementary kinds of lensing, providing a whole picture [77][78][79][80][81][82].…”