Holeum
Encyclopedia
Holeums are stable, quantized gravitational bound states of primordial
or micro black holes.
. Holeums are not black holes, even though they are made up of black holes.
of a Holeum that consists of two identical micro black holes of mass 
is given by
in which
is the principal quantum number
,
and 
is the gravitational counterpart of the fine structure constant. The latter is given by
where:
The
excited state of a Holeum then has a mass that is given by
The Holeum's atomic transitions cause it to emit gravitational radiation.
The radius of the
excited state of a Holeum is given by
where:
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.
identical micro black holes of mass 
are given by
where
and 
. The system is simplified by assuming that all the micro black holes in the core are in the same quantum state described by 
, and that the outermost, 
micro black hole is in an arbitrary quantum state described by the principal quantum number 
.
The physical radius of the bound state is given by
The mass of the Macro Holeum is given by
The Schwarzschild radius of the Macro Holeum is given by
The entropy
of the system is given by
where
is the entropy of the individual micro black holes that constitute the Macro Holeum.
of Macro Holeums is characterized by
and 
. 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
free (
) 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 
.
Substituting the relations
and 
into this inequality, the condition for the stability of Holeums can be expressed as
The ground state of Holeums is characterized by
, which gives us 
as the condition for stability. Thus, the ground state of Holeums is guaranteed to be always stable.
Such Holeums are known as Black Holeums. Substituting the expressions for
and 
, and simplifying, we obtain the condition for a Holeum to be a Black Holeum to be
For the ground state, which is characterized by
, this reduces to
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
, 
, 
, and 
.
Primordial black hole
A primordial black hole is a hypothetical type of black hole that is formed not by the gravitational collapse of a large star but by the extreme density of matter present during the universe's early expansion....
or micro black holes.
Introduction
Holeums were proposed by L.K. Chavda and Abhijit Chavda in 2002. They have all the properties associated with cold dark matterCold dark matter
Cold dark matter is the improvement of the big bang theory that contains the additional assumption that most of the matter in the Universe consists of material that cannot be observed by its electromagnetic radiation and whose constituent particles move slowly...
. Holeums are not black holes, even though they are made up of black holes.
Properties of Holeums
The binding energyBinding energy
Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system typically has a lower potential energy than its constituent parts; this is what keeps the system together—often this means that energy is released upon the creation of a bound state...
of a Holeum that consists of two identical micro black holes of mass is given by
in which
is the principal quantum numberQuantum number
Quantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...
,
and is the gravitational counterpart of the fine structure constant. The latter is given by
where:
-
is the Planck constantPlanck constantThe Planck constant , also called Planck's constant, is a physical constant reflecting the sizes of energy quanta in quantum mechanics. It is named after Max Planck, one of the founders of quantum theory, who discovered it in 1899...
divided by
; -
is the speed of lightSpeed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
in vacuum; -
is the gravitational constantGravitational constantThe gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...
.
The
excited state of a Holeum then has a mass that is given by
The Holeum's atomic transitions cause it to emit gravitational radiation.
The radius of the
excited state of a Holeum is given by
where:
-
is the Schwarzschild radiusSchwarzschild radiusThe Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...
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
Hydrogen atom
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively-charged proton and a single negatively-charged electron bound to the nucleus by the Coulomb force...
. 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
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
. The Holeum can therefore be considered to be a dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
particle.
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 identical micro black holes of mass are given by
where
and . The system is simplified by assuming that all the micro black holes in the core are in the same quantum state described by , and that the outermost, micro black hole is in an arbitrary quantum state described by the principal quantum number .The physical radius of the bound state is given by
The mass of the Macro Holeum is given by
The Schwarzschild radius of the Macro Holeum is given by
The entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
of the system is given by
where
is the entropy of the individual micro black holes that constitute the Macro Holeum.The ground state of Macro Holeums
The ground stateGround state
The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...
of Macro Holeums is characterized by
and . 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
free () 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 .Stability of Holeums
It can be seen from the above equations that the condition for the stability of Holeums is given bySubstituting the relations
and into this inequality, the condition for the stability of Holeums can be expressed asThe ground state of Holeums is characterized by
, which gives us 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. ifSuch Holeums are known as Black Holeums. Substituting the expressions for
and , and simplifying, we obtain the condition for a Holeum to be a Black Holeum to beFor the ground state, which is characterized by
, this reduces toBlack 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
, , , and .