## Ask a Scientist: How big are black holes?

*Otago Daily Times, 27 May 2016*

Chris Lakomy, of Waikanae, asked:-
*If all black holes are by definition infinitely dense and infinitely small,
how can there be different sized black holes? Isn't infinity non-negotiable?*

**David Wiltshire**, *a theoretical physicist at the University of
Canterbury responded:*
Black holes are not by definition infinitely dense and infinitely small,
so your question is a moot point.

Black holes are defined by the property of having a horizon, namely a surface
that separates the outside Universe from regions from within which light
cannot escape. The black hole horizon has a finite surface area, determined by
the mass, rotation and electric charge of the black hole. Thus black holes can
come in all sizes.

Matter in the Universe is on average electrically neutral - there being as
many protons as electrons, as with atoms - so we do not expect black holes to
have any significant electric charge. Thus it is mainly the mass and the
rotation that determine the size of a black hole, according to the solution of
Einstein's equations discovered by New Zealander Roy Kerr in 1963.

For two decades we have been measuring the mass and spin of the
supermassive black holes that lurk in the centres of galaxies. Because
light cannot escape from a black hole, until recently we could only determine
their properties from the change of wavelength of X-rays given off by matter
falling in. Such X-rays are only visible to our telescopes for the
supermassive variety of black hole.

The recent discovery of gravitational waves from the collision of two
black holes of 29 and 36 solar masses to produce a single black hole of
62 solar masses, and a spin 2/3 of the maximum predicted by the Kerr
solution, is the first time that we have direct evidence of the millions
upon millions of smaller black holes that are out there.

The mathematical solution of Roy Kerr that describes these objects
has a ringlike region deep inside the black hole where our mathematical
description of space and time breaks down. Formally speaking the maths
is saying that the density appears to be getting infinite but what that
really means is that our geometrical concept of volume breaks down - and
density is mass divided by volume. Many physicists hope that a theory of
quantum gravity will resolve the as yet unsolved mysteries of black hole
interiors.

Professor David Wiltshire

Department of Physics and Astronomy

University of Canterbury

Homepage:
http://www2.phys.canterbury.ac.nz/~dlw24/