Return to Answer

Is black hole singularity a single point?

 

General relativity [(GR or GTR)] expressed in terms of differential geometry [three-dimensional Euclidean space] ... lets you to do interesting things with the coordinates: multiple coordinates may refer to a single point.

 

EG: The equirectangular projection has a whole line at the top and bottom that correspond to North and South poles; or a single coordinate may refer to multiple points, for example by using inversive geometry the origin refers to all the points infinitely far away.

Is black hole singularity a single point?

General relativity [(GR or GTR)] expressed in terms of differential geometry [three-dimensional Euclidean space] ... lets you to do interesting things with the coordinates: multiple coordinates may refer to a single point.

EG: The equirectangular projection has a whole line at the top and bottom that correspond to North and South poles; or a single coordinate may refer to multiple points, for example by using inversive geometry the origin refers to all the points infinitely far away.

Gravity around a black hole is so powerful that it affects both space and time, for that reason a metric (to use your word, map projection) is used to describe the space, and not differential geometry. In order to take gravity into account, physicists use the theory of general relativity, which is formulated in the mathematics of a non-Euclidean geometry.

Gravity around a black hole is so powerful that it affects both space and time, for that reason a metric (to use your word, map projection) is used to describe the space, and not Euclidean differential geometry. In order to take gravity into account, physicists use the theory of general relativity, which is formulated in the mathematics of a non-Euclidean geometry.

A spherical object like the Earth, or a black hole that rotates, becomes an oblate spheroid due to it's rotation. Mapping an oblate spheroid to an equirectangular projection will result in distortion.

Gravity around a black hole is so powerful that it affects both space and time, for that reason a metric (to use your word, map projections) is used to describe the space, and not differential geometry. In order to take gravity into account, physicists use the theory of general relativity, which is formulated in the mathematics of a non-Euclidean geometry.

Even zero sized particles can have ill defined boundaries, and many clumped together make exact analysis and estimation of the center, in order to provide a location, a difficult task. Because of their zero dimension many can occupy the same location, passing through each other, or create an extended object.

A small amount of mass is much larger than a point and so is a black hole. They only occupy such a small area because they compress the area to tiny dimensions. The space surrounding such a large mass occupying such a small area is a point, the black hole would not be if it's gravity could be turned off, if it occupied a significantly larger area (reduced density), or it's mass (weight) where enormously reduced.

The apparent (longitudinal) coordinate singularity at the 90 degree latitude in spherical coordinates is an artifact of the coordinate system chosen, which is singular at the poles. A different coordinate system would eliminate the apparent discontinuity, e.g. by replacing the latitude/longitude representation with an n-vector representation.

A spherical object like the Earth, or a black hole that rotates, becomes an oblate spheroid due to it's rotation. Mapping an oblate spheroid to an equirectangular projection will result in distortion.

Gravity around a black hole is so powerful that it affects both space and time, for that reason a metric (to use your word, map projection) is used to describe the space, and not differential geometry. In order to take gravity into account, physicists use the theory of general relativity, which is formulated in the mathematics of a non-Euclidean geometry.

Even zero sized particles can have ill defined boundaries, and many clumped together make exact analysis and estimation of the center; in order to provide a location, a difficult task. Because of their zero dimension many can occupy the same location, passing through each other, or move minutely apart creating an extended object.

A small amount of mass is much larger than a point and so is a black hole. Black holes only occupy such a small amount of space because they (bend) compress the area to tiny dimensions. The space surrounding such a large mass (often over 10 times the mass of our Sun) occupying such a small area is a point (a singularity). A black hole would not be a point sized dimension if it's gravity could be turned off, if it occupied a significantly larger area (reduced density), or it's mass (weight) where enormously reduced.