The interior of a black hole
The interior of a black hole
[L52] Theo M. Nieuwenhuizen,
[L51] Theo M. Nieuwenhuizen,
It is generally believed that the interior of a black hole cannot be understood by
present theories. I believe that a black hole is just a normal object, but with a somewhat
large redshift.
In [L51] I consider a black hole which principally has the same structure as a star, but a
very large but finite redshift at the horizon (i.e., its surface). The approach is made
for matter obeying the stiff equation of state: energy density = pressure + constant,
which contains as special case the vacuum equation of state: energy density =
- pressure = constant.
The metric is solved analytically and allows one parameter, the pressure at the surface.
This has to be fixed from a fundamental theory for the matter that fills the
black hole.
Supermassive black holes as giant Bose-Einstein condensates
A supermassive black hole is located in the center of probably each galaxy. Our Galaxy has
one with 3.2 million solar masses, most other ones involve several billion solar masses,
the heaviest weighs 18 billion solar masses. The density in that case is comparable
to air - the heavier they become, the less dense. Indeed, since the Schwarzschild radius
is proportional to the mass, the density M/R^3 is proportional to 1/M^2.
One would expect that such black holes mainly consist of hydrogen, the most abundant element
in the Universe, and partly of Helium, and a few heavy element. If that is indeed the case,
the interior of a supermassive black holes is not completely different from air
- alas, don't forget to carry oxigen with you if you go in there.
It us natural to insist that such large but non-dense objects should be describable by
a known theory.
This appears possible in a specific setup: assume that the hydrogen atoms are
in their Bose-Einstein condensed ground state.
This problem can be modeled by a quartic quantum field theory in the classical gravitational metric.
A coupling of the quantum field to the curvature scalar keeps the matter confined by its own gravitation.
The strength of this coupling should follow from a renormalization treatment.
As a first step one may choose a desired value and then do renormalization from that
starting point. For supermassive black holes that last step is not needed, and one can
just treat this coupling as an adjustable parameter.
It then appears that the metric can be solved within the Relativistic Theory of Gravitation,
in case the quantum field is in its Bose-Einstein condensed ground state,
while General Relativity would fail to solve the so posed problem [L52].
Can black holes have hair?
Surprisingly, this black hole solution [L52] has one "hair", a parameter that describes the interior.
The mass observed at infinity can be any fraction of the mass of the hydrogen that constitutes
the black hole, in other words: the binding energy can be any fraction of the zero point
energy of the constituting matter. In the extreme limit there would be a huge black hole that,
seen from the outside, has no mass, all energy being radiated away, thus causing 100 % binding
energy. An interesting picture for our Universe, embedded in a huge Minkowski background ???
Black holes with hair are forbidden by the "no hair" theorem of General Relativity, but they
may exist in the Universe. Observations of a quasar were already connected to a "magnetic hair",
a large magnetic field that pushes the matter in the surrounding accretion disk
out to some 70 Schwarzschild radii, much farther than non-hairy black holes could do
(Schild et al, Astronomical Journal 132 (2006) 420).
If this hairy picture is confirmed, it provides another reason to abandon General Relativity
and replace it by another theory, the Relativistic Theory of Gravitation ("Not-so-General Relativity")
being the first candidate.
Supermassive Black Holes as Giant Bose-Einstein Condensates
Europhys. Lett. 83 (2008) 10008
Exact solution for the interior of a black hole
Fluct. Noise Lett. 8 (2008) L141-153;
arXiv:0805.4169
[C43] Th. M. Nieuwenhuizen,
The Relativistic Theory of Gravitation and its Application to
Cosmology and Macroscopic Quantum Black Holes ,
AIP Conf. Proc. 962: Quantum Theory: Reconsideration of Foundations-4,
Guillaume Adenier, Andrei Yu. Khrennikov, Pekka Lahti, Vladimir I. Man'ko and Theo M. Nieuwenhuizen
, eds, (Am. Inst. Phys., Melville, NY, 2007), pp 149-161.
[L49] Theo M. Nieuwenhuizen,
Einstein versus Maxwell: Is gravitation a curvature of space,
a field in flat space, or both?
Europhys. Lett. 78 (2007) 10010, 1-5.
[C39] Theo M. Nieuwenhuizen,
On the Field Theoretic Description of Gravitation,
Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity,
edited by H. Kleinert, R.T. Jantzen and R. Ruffini,
World Scientific, Singapore, 2008, to appear.