- Art Gallery -

Holeums are hypothetical stable, quantized gravitational bound states of primordial or micro black holes. Holeums were proposed by L. K. Chavda and Abhijit Chavda in 2002.[1] They have all the properties associated with cold dark matter. Holeums are not black holes, even though they are made up of black holes.

Properties

The binding energy \( E_{n} \) of a holeum that consists of two identical micro black holes of mass m is given by[2]

\( E_{{n}}=-{\frac {mc^{{2}}\alpha _{{g}}^{{2}}}{4n^{{2}}}} \)

in which n {\displaystyle n} n is the principal quantum number, \( n=1,2,...,\infty \) and \( \alpha _{{g}} \) is the gravitational counterpart of the fine structure constant. The latter is given by

\( \alpha _{{g}}={\frac {m^{{2}}G}{\hbar c}}={\frac {m^{{2}}}{m_{{P}}^{{2}}}} \)

where:

\( \hbar \) is the Planck constant divided by \( 2\pi \);
c c is the speed of light in vacuum;
G is the gravitational constant.

The nth excited state of a holeum then has a mass that is given by

\( m_{{H}}=2m+{\frac {E_{{n}}}{c^{{2}}}} \)

The holeum's atomic transitions cause it to emit gravitational radiation.

The radius of the nth excited state of a holeum is given by

\( r_{{n}}=\left({\frac {n^{{2}}R}{\alpha _{{g}}^{{2}}}}\right)\left({\frac {\pi ^{{2}}}{{8}}}\right) \)

where:

\( R=\left({\frac {2mG}{c^{{2}}}}\right) \) is the Schwarzschild radius of the two identical micro black holes that constitute the holeum.

The holeum is a stable particle. It is the gravitational analogue of the hydrogen atom. It occupies space. Although it is made up of black holes, it itself is not a black hole. As the holeum is a purely gravitational system, it emits only gravitational radiation and no electromagnetic radiation. The holeum can therefore be considered to be a dark matter particle.[3]
Macro holeums and their properties

A macro holeum is a quantized gravitational bound state of a large number of micro black holes. The energy eigenvalues of a macro holeum consisting of k {\displaystyle k} k identical micro black holes of mass m {\displaystyle m} m are given by[4]

\( E_{{k}}=-{\frac {p^{{2}}mc^{{2}}}{2n_{{k}}^{{2}}}}\left(1-{\frac {p^{{2}}}{6n^{{2}}}}\right)^{{2}} \)

where \( p=k\alpha _{{g}} \) and \( k\gg 2 \). The system is simplified by assuming that all the micro black holes in the core are in the same quantum state described by n {\displaystyle n} n, and that the outermost, \( k^{{th}} \) micro black hole is in an arbitrary quantum state described by the principal quantum number \( n_{{k}} \).

The physical radius of the bound state is given by

\( r_{{k}}={\frac {\pi ^{{2}}kRn_{{k}}^{{2}}}{16p^{{2}}\left(1-{\frac {p^{{2}}}{6n^{{2}}}}\right)}} \)

The mass of the macro holeum is given by

\( M_{{k}}=mk\left(1-{\frac {p^{{2}}}{6n^{{2}}}}\right) \)

The Schwarzschild radius of the macro holeum is given by

\( R_{{k}}=kR\left(1-{\frac {p^{{2}}}{6n^{{2}}}}\right) \)

The entropy of the system is given by

\( S_{{k}}=k^{{2}}S\left(1-{\frac {p^{{2}}}{6n^{{2}}}}\right) \)

where S is the entropy of the individual micro black holes that constitute the macro holeum.
The ground state of macro holeums

The ground state of macro holeums is characterized by \( n=\infty \) and \( n_{{k}}=1 \). The holeum has maximum binding energy, minimum physical radius, maximum Schwarzschild radius, maximum mass, and maximum entropy in this state.

Such a system can be thought of as consisting of a gas of k-1 free ( \( n=\infty \) ) micro black holes that is bounded and therefore isolated from the outside world by a solitary outermost micro black hole whose principal quantum number is \( n_{{k}}=1 \).
Stability

It can be seen from the above equations that the condition for the stability of holeums is given by

\( {\frac {p^{{2}}}{6n^{{2}}}}<1 \)

Substituting the relations \( p=k\alpha _{{g}} \) and \( \alpha _{{g}}={\frac {m^{{2}}}{m_{{P}}^{{2}}}} \) into this inequality, the condition for the stability of holeums can be expressed as

\( m<m_{{P}}\left(6\right)^{{{\frac {1}{4}}}}\left({\frac {n}{k}}\right)^{{{\frac {1}{2}}}} \)

The ground state of holeums is characterized by \( n=\infty \), which gives us \( m<\infty \) as the condition for stability. Thus, the ground state of holeums is guaranteed to be always stable.
Black holeums

A holeum is a black hole if its physical radius is less than or equal to its Schwarzschild radius, i.e. if

\( r_{{k}}\leqslant R_{{k}}

Such holeums are termed black holeums. Substituting the expressions for \( r_{{k}} \) and \( R_{{k}} \), and simplifying, we obtain the condition for a holeum to be a black holeum to be

\( m\geqslant {\frac {m_{{P}}}{2}}\left({\frac {\pi n_{{k}}}{k}}\right)^{{{\frac {1}{2}}}} \)

For the ground state, which is characterized by \( n_{{k}}=1 \), this reduces to

\( m\geqslant {\frac {m_{{P}}}{2}}\left({\frac {\pi }{k}}\right)^{{{\frac {1}{2}}}} \)

Black holeums are an example of black holes with internal structure. Black holeums are quantum black holes whose internal structure can be fully predicted by means of the quantities k, m m, n, and \( n_{{k}} \).
Holeums and cosmology

Holeums are speculated to be the progenitors of a class of short duration gamma ray bursts.[5][6] It is also speculated that holeums give rise to cosmic rays of all energies, including ultra-high-energy cosmic rays.[7]
See also

Micro black hole
Black hole electron
Planck particle
Dark matter

References

L. K. Chavda & Abhijit Chavda, Dark matter and stable bound states of primordial black holes
L. K. Chavda & Abhijit Chavda, Dark matter and stable bound states of primordial black holes
M. Yu. Khlopov, Primordial Black Holes
L. K. Chavda & Abhijit Chavda, Quantized Gravitational Radiation from Black Holes and other macro holeums in the Low Frequency Domain
S. Al Dallal, Holeums as potential candidates for some short-lived gamma ray bursts
S. Al Dallal, Primordial black holes and holeums as progenitors of galactic diffuse gamma-ray background

L. K. Chavda & Abhijit Chavda, Ultra High Energy Cosmic Rays from decays of holeums in Galactic Halos

External links

Acta Physica: Chronicles the development of the theory of holeums
A Stable Holeum
Gravitational Radiation from Holeums
Constructing a Macro Holeum from the Inside Out
The Black Holeum

vte

Dark matter
Forms of
dark matter

Baryonic dark matter Cold dark matter Hot dark matter Light dark matter Mixed dark matter Warm dark matter Self-interacting dark matter Scalar field dark matter Primordial black holes


Hypothetical particles

Axino Axion Dark photon Holeum LSP Minicharged particle Neutralino Sterile neutrino SIMP WIMP

Theories
and objects

Cuspy halo problem Dark fluid Dark galaxy Dark globular cluster Dark matter halo Dark radiation Dark star Dwarf galaxy problem Halo mass function Mass dimension one fermions Massive compact halo object Mirror matter Navarro–Frenk–White profile Scalar field dark matter

Search
experiments
Direct
detection

ADMX ANAIS ArDM CDEX CDMS CLEAN CoGeNT COSINE COUPP CRESST CUORE D3 DAMA/LIBRA DAMA/NaI DAMIC DarkSide DARWIN DEAP DM-Ice DMTPC DRIFT EDELWEISS EURECA KIMS LUX LZ MACRO MIMAC NAIAD NEWAGE NEWS-G PandaX PICASSO PICO ROSEBUD SABRE SIMPLE TREX-DM UKDMC WARP XENON XMASS ZEPLIN

Indirect
detection

AMS-02 ANTARES ATIC CALET CAST DAMPE Fermi HAWC HESS IceCube MAGIC MOA OGLE PAMELA VERITAS

Other projects

MultiDark PVLAS

Potential dark galaxies

HE0450-2958 HVC 127-41-330 Smith's Cloud VIRGOHI21

Related

Antimatter Dark energy Exotic matter Galaxy formation and evolution Illustris project Imaginary mass Negative mass UniverseMachine

Physics Encyclopedia

World

Index

Hellenica World - Scientific Library

Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License