Aggregate modulus

Template:One source Holeums are hypothetical stable, quantized gravitational bound states of primordial 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 matter. Holeums are not black holes, even though they are made up of black holes.

Properties of Holeums

The binding energy $E_n$ of a Holeum that consists of two identical micro black holes of mass $m$ is given by

$E_n=-\frac{m{c}^2{\alpha }_g^2}{4n^2}$

in which $n$ is the principal quantum number, $n=1,2,...\mathrm{\infty }$ and ${\alpha }_g$ is the gravitational counterpart of the fine structure constant. The latter is given by

${\alpha }_g=\frac{m^{2}G}{\hslash c}=\frac{m^2}{m_P^2}$

where:

$\hslash$ is the Planck constant divided by $2\pi$;

$c$ is the speed of light in vacuum;

$G$ is the gravitational constant.

The $n^{\text{th}}$ 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 $n^{\text{th}}$ 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.

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 $k$ identical micro black holes of mass $m$ are given by

$E_k=-\frac{p^{2}m{c}^2}{2n_k^2}{(1-\frac{p^2}{6n^2})}^2$

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 $n$, 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

$r_k=\frac{{\pi }^{2}kR{n}_k^2}{16p^2(1-\frac{p^2}{6n^2})}$

The mass of the Macro Holeum is given by

$M_k=mk(1-\frac{p^2}{6n^2})$

The Schwarzschild radius of the Macro Holeum is given by

$R_k=kR(1-\frac{p^2}{6n^2})$

The entropy of the system is given by

$S_k=k^{2}S(1-\frac{p^2}{6n^2})$

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 $n=\mathrm{\infty }$ 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 ($n=\mathrm{\infty }$) 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 of Holeums

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 $n=\mathrm{\infty }$, which gives us $m<\mathrm{\infty }$ 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

$r_k⩽R_k$

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

$m⩾\frac{m_P}{2}{\left(\frac{\pi n_k}{k}\right)}^{\frac{1}{2}}$

For the ground state, which is characterized by $n_k=1$, this reduces to

$m⩾\frac{m_P}{2}{\left(\frac{\pi }{k}\right)}^{\frac{1}{2}}$

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 $k$, $m$, $n$, and $n_k$.

Holeums and cosmology

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

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

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

In search of a new condominium or house to remain/invest? Flick through beneath for the new launches round Singapore. This website might be updated with upcoming property launch. If you are trying to residing in consolation with good view, lush green panorama or perhaps a luxurious penthouse.

One of the many explanation why investing on a new condo launch within the country is best than investing on landed homes is due to the truth that the demand on condos are of a better request than the latter. With the rise within the nationwide inhabitants, it is no marvel that a residential unit's value will increase to up three% annually since more and more of Singaporeans are on the lookout for condos across the nation. With each residential unit equipped with branded built-in home equipment, ducted air-conditioning system and have trendy finish; it is a plus for you when investing on these new residential developments.

All contracts with patrons in new Singapore property gross sales, such as the Option Kind and Gross sales & Purchase Agreement, are standard types mandated by the government, ie. the developer can not use his personal model that could be skewed in his favor. From 8 River Suites, it's so handy to get out and discover the sights and sounds of Singapore. Boon Keng MRT is just inside 5 minutes walk away and with the seamless connectivity through the major expressways (CTE, PIE & KPE), completely ease the travelling to all components of Singapore. Kallang Leisure Park, Bugis, Orchard shopping belt , Suntec City and Marina Bay are within brief drive or train-ride away. How do I do know the information of newest new launch in the property market ? featured Iskandar Malaysia property launches

Singapore first retirement condominium ny World Class Development (North) Pte Ltd. With Procuring, dining and leisure services out there on the nearby Bukit Timah Shopping Centre, Magnificence World Centre / Plaza, Rail Mall and many consuming outlets along Jalan Jurong Kechil, Mr Patrick Tan Choon Hong attributed the rise in property prices largely to the observe of banks matching their valuations for brand spanking new property launches with the asking costs of developers ("Evaluation bank valuation process for new launches"; three April 2014). Surrounded by Australia Embassy, Russia Embassy, Singapore Embassy, 5 Star Motels with On line casino and Tourist Relax areas But if you happen to're nonetheless nervous, decide an agent you may trust for getting property in Singapore, to register you.

This rule, which applies to all new Singapore property gross sales, is to make sure that monies for a challenge, whether loans or sale proceeds, solely be used for the mission and never diverted to other makes use of, or worse, absconded with. By Property Soul, a profitable property investor and enthusiast who shares her experiences and information on her blog Posted courtesy of www.Propwise.sg , a Singapore property blog devoted to serving to you understand the true property market and make better decisions. Click here to Milionpeople.com get your free Property Beginner's and Buyer's Information Builders may conduct property launches in Singapore by way of an in-home marketing team, or more doubtless (to minimise staffing), by appointing exterior real estate businesses to do the advertising. The Panorama

The developer should open a Venture Account with a financial institution or financial institution for each housing undertaking he undertakes, earlier than he is issued with a Sale License (license to promote items in his growth). All funds from consumers before completion of the project, and construction loans, go into the undertaking account. New launch condo LA FIESTA, an exciting new condominium situated alongside Sengkang Square / Compassvale Road is a brief stroll to the bustling Sengkang City Centre where the bus interchange, Sengkang MRT and LRT stations are located. Excellent location,Premium condominium with Bayfront resort life-style theme and views ofwaterscape. Near EC pricing - Value for money! Apr 02, 2013 Sengkang New Rental Launch, La Fiesta- Sengkang MRTstation at your gate.

Assured rental return' is completely different from earning rental earnings from actual tenants over the years. Because the quantity given has truly been factored into the price, one may also argue that buyers are literally paying for their guaranteed rental quantity upfront. Strictly talking, the social gathering who advantages most from giving freely the carrot is probably the developer itself. It is as a result of these goodies are usually offered when the market starts to cool down so that developers are able to move properties off the shelves without lowering the worth. The Citron Residences is a novel blended residential and commercial growth located at 1 Marne Road in prime District 08. A mere stone\'s throw aw Read Extra First 3 Years Rental Guarantee at 6% per 12 months