Apparent size of a black hole to a moving observer

Apparent size of a black hole to a moving observer

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Photon path in flat space

Photon path in flat space

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Red-shifts and blue-shifts

Red-shifts and blue-shifts

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Apparent size of a black hole

Apparent size of a black hole

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Local flat coordinate systems – four-momentum of photons

Local flat coordinate systems – four-momentum of photons

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Photon equations of motion

Photon equations of motion

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Embedding a 2-d curved surface into 3-d – inverse cosh

Embedding a 2-d curved surface into 3-d – inverse cosh

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Embedding a 2-d curved surface in 3-d – the cosine

Embedding a 2-d curved surface in 3-d – the cosine

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Embedding a 2-d curved surface in 3-d – the cosh

Embedding a 2-d curved surface in 3-d – the cosh

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Embedding 2-d curved space in 3-d – the sphere

Embedding 2-d curved space in 3-d – the sphere

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