Visualization of black hole images
V. Dokuchaev
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow

Moscow State University - 2021

Flat space-time: the closer the light source to the object - the bigger it shadow on the distant wallCurved space-time: the bending of light (gravitational lensing)Kerr metric: equations of motion for test particles

B. Carter 19682D trajectories of two photons from moving hot spot, starting at r = 1.1 rh,(rh =1+(1-a 2) 1/2) from the rotation axis of the Kerr black hole (a=1)
toward a distant observer and providing prime image (green curve)
and 1-st light echo (red curve of clockwise moving photon)

Dashed magenta circle – event horizon (rh =1+(1-a 2) 1/2)
in the imaginary Euclidean space

3D trajectories of the same photons from previous slide, starting at r = 1.1,
and providing prime image (green curve) and 1-st light echo (red curve)

3D trajectories of photons from the outward moving hot spot, starting at r = 1.5, andproviding the prime image and the 1-st light echo (counter-clockwise moving photon) M87 - VLBI radio jetMoving hot spot in the jet from black hole SgrA* in discrete time intervals
 Closed purple curve– outline of the black hole shadow

 Dashed magenta circle – event horizon in the Euclidean space Magenta arrow– event horizon in the Euclidean space Light blue closed region – lensed event horizon globe(“direct view of the event horizon”)
 Light blue closed curves – Meridians and parallels on thelensed event horizon globe
 Hot spot is starting from the north pole of the event horizon
 There are infinite number of lensed images of a separate hotspot (direct image and light echoes) It is shown direct images and 1-st light echoes of a hot spot in
discrete time intervals
 1-st light echoes produced by clockwise and counter-clockwise
moving photons and viewed near the outline of the black holeshadowDirect image and 1-st light echoes of the moving hot spot in the jetfrom the supermassive black hole M87* in discrete time intervals
Closed purple curve– outline of the black hole shadow

Dashed magenta circle – event horizon in the Euclidean space

Magenta arrow– event horizon in the Euclidean space

Light blue and blue

– “direct view of the event horizon”:

Light blue closed region – lensed south hemisphere of the event
horizon globe
Blue closed region
horizon globe– lensed north hemisphere of the event

Hot spot is staring from the north pole of the event horizon
There are infinite number of lensed images of a separate hot spot
(direct image and light echoes)

It is shown direct images and 1-st light echoes of a hot spot in
discrete time intervals
1-st light echoes produced by clockwise and counter-clockwise
moving photons and viewed near the outline of the black holeshadow

Event Horizon Telescope (2019)

Millimetron Space Observatory (2030?)

Closed magenta curve – the position of the classical black hole shadow
Closed black curve - the lensed north hemisphere of the event horizon

Conclusion
Unique information for the verificationof strong gravity will be provided by
the detailed observations of black hole images,
including the motion of bright spots in jets.
Details in:2010.01885, 2007.14121, 1911.07695, 1906.07171,
1903.09594, 1812.06787, 1804.08030, 1802.00817

Animations in: youtube.com/watch?v=P6DneV0vk7U
youtu.be/7j8f_vlTul8
youtu.be/zQzC-lVgdjg
youtu.be/fps-3frL0AM