Like the radiation the Sun gives out to sustain it's circular shape, will Hawking radiation sustain the black hole's shape?
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4$\begingroup$ Have you read other answers in the hawking-radiation tag? particularly astronomy.stackexchange.com/questions/31635/… $\endgroup$– James KCommented May 9, 2021 at 7:03
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$\begingroup$ Welcome to astronomy SE. Please also make sure you follow the guidance How to Ask. $\endgroup$– B--rianCommented May 9, 2021 at 8:29
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$\begingroup$ "the radiation the sun gives out to sustain it's circular shape" I'm not quite sure what you mean by that. Gravity pulls the Sun into a ball shape. There's a balance between the inward force due to gravity and the outward force due to heat (hot stuff tries to expand). Additionally, the Sun is slightly flattened due to its spin. $\endgroup$– PM 2RingCommented May 9, 2021 at 8:52
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$\begingroup$ @PM2Ring I'm not sure if this is what he means, but the Sun is unexpectedly spherical. (article is a little dated, more recent articles give updated details). theguardian.com/science/2012/aug/16/sun-perfect-sphere-nature $\endgroup$– userLTKCommented May 9, 2021 at 12:04
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$\begingroup$ @userLTK I don't think that's unexpected, the Sun's rotation is slow, with a period of ~25 days at its equator. The centripetal acceleration at the solar equator is ~0.0018658 m/s². The gravitational acceleration is ~274.35 m/s², over 147,040 times greater. $\endgroup$– PM 2RingCommented May 9, 2021 at 14:03
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In a word, no.
A black hole's border or event horizon is just curved space time where the curvature exceeds an escape velocity of the speed of light. Because the inner mass is thought to be very uniform, with essentially zero mass concentrations, it should be one of the most spherical objects in the universe, even more than the sun. A black hole's event horizon's spherical shape has nothing to do with Hawking radiation, which is a quantum effect just outside the event horizon.
That said, a rotating black hole has two distinct event horizons. The inner one is spherical, the outer one is not and that may be a more accurate picture of black holes, so they may not be as spherical as highly spherical stars depending on which event horizon your taking into account.
