Assuming the BH has a stable photon sphere.

I think you may have a point. Specially, for the photons that are orbiting the black hole and are moving at a time in opposite direction to that of the black hole. There must be a light speed lag between actual movement of the singularity, and evolution of the curvature at the edges of the event horizon. So the photons on the rear end of the event horizon are travelling at light speed c (note c is constant), but the EH has moved a little forward, and so they should be outside EH for a moment which should allow them to escape the EH.

Suppose there is a 1 nano second lag between actual movement of the singularity, and evolution of the curvature at the event horizon. The photons are moving as per the EH of singularity 1 nano second ago. Now all of a sudden, (1 nano second later), the EH has moved by (say) 1 micrometer. The photons as per older EH should fall outside EH and thereby escape the EH.

Same can apply to photons on front end of EH and they should fall into the black hole.

I do not know if and how the mathematics accounts for this.

I can understand a north/south satellite around earth because the velocity of the satellite can remain same relative to earth in both directions because, its speed does not have to be constant. But light going north/south around a black hole, its speed has to be same relative to the singularity, at the same time be constant in both the directions, which is hard to grasp.

Assuming the BH had a stable photon sphere.

I think you may have a point. Specially, for the photons that are orbiting the black hole and are moving at a time in opposite direction to that of the black hole. There must be a light speed lag between actual movement of the singularity, and evolution of the curvature at the edges of the event horizon. So the photons on the rear end of the event horizon are travelling at light speed c (note c is constant), but the EH has moved a little forward, and so they should be outside EH for a moment which should allow them to escape the EH.

Suppose there is a 1 nano second lag between actual movement of the singularity, and evolution of the curvature at the event horizon. The photons are moving as per the EH of singularity 1 nano second ago. Now all of a sudden, (1 nano second later), the EH has moved by (say) 1 micrometer. The photons as per older EH should fall outside EH and thereby escape the EH.

Same can apply to photons on front end of EH and they should fall into the black hole.

I do not know if and how the mathematics accounts for this.

I can understand a north/south satellite around earth because the velocity of the satellite can remain same relative to earth in both directions because, its speed does not have to be constant. But light going north/south around a black hole, its speed has to be same relative to the singularity, at the same time be constant in both the directions, which is hard to grasp.

I think you may have a point. Specially, for the photons that are orbiting the black hole and are moving at a time in opposite direction to that of the black hole. There must be a light speed lag between actual movement of the singularity, and evolution of the curvature at the edges of the event horizon. So the photons on the rear end of the event horizon are travelling at light speed c (note c is constant), but the EH has moved a little forward, and so they should be outside EH for a moment which should allow them to escape the EH.

Suppose there is a 1 nano second lag between actual movement of the singularity, and evolution of the curvature at the event horizon. The photons are moving as per the EH of singularity 1 nano second ago. Now all of a sudden, (1 nano second later), the EH has moved by (say) 1 micrometer. The photons as per older EH should fall outside EH and thereby escape the EH.

Same can apply to photons on front end of EH and they should fall into the black hole.

I do not know if and how the mathematics accounts for this.

I can understand a north/south satellite around earth because the velocity of the satellite can remain same relative to earth in both directions because, its speed does not have to be constant. But light going north/south around a black hole, its speed has to be same relative to the singularity, at the same time be constant in both the directions, which is hard to grasp.

Assuming the BH has a stable photon sphere.

I think you may have a point. Specially, for the photons that are orbiting the black hole and are moving at a time in opposite direction to that of the black hole. There must be a light speed lag between actual movement of the singularity, and evolution of the curvature at the edges of the event horizon. So the photons on the rear end of the event horizon are travelling at light speed c (note c is constant), but the EH has moved a little forward, and so they should be outside EH for a moment which should allow them to escape the EH.

Suppose there is a 1 nano second lag between actual movement of the singularity, and evolution of the curvature at the event horizon. The photons are moving as per the EH of singularity 1 nano second ago. Now all of a sudden, (1 nano second later), the EH has moved by (say) 1 micrometer. The photons as per older EH should fall outside EH and thereby escape the EH.

Same can apply to photons on front end of EH and they should fall into the black hole.

I do not know if and how the mathematics accounts for this.

I can understand a north/south satellite around earth because the velocity of the satellite can remain same relative to earth in both directions because, its speed does not have to be constant. But light going north/south around a black hole, its speed has to be same relative to the singularity, at the same time be constant in both the directions, which is hard to grasp.