The irreducible mass of Christodoulou–Ruffini–Hawking mass formula

2022 ◽  
Author(s):  
Yuan K. Ha
Keyword(s):  
Black Hole ◽  
Black Hole Physics ◽  
Rest Mass ◽  
Kerr Black Hole ◽  
Rotational Energy ◽  
Compact Objects ◽  
Moment Of Inertia ◽  
External Energy ◽  
Moving Body ◽  
The Moment

We reveal three new discoveries in black hole physics previously unexplored in the Hawking era. These results are based on the remarkable 1971 discovery of the irreducible mass of the black hole by Christodoulou and Ruffini, and subsequently confirmed by Hawking. (1) The Horizon Mass Theorem states that the mass at the event horizon of any black hole — neutral, charged, or rotating — is always twice its irreducible mass observed at infinity. (2) The External Energy Theorem asserts that the rotational energy of a Kerr black hole exists completely outside the horizon. This is due to the fact that the irreducible mass does not contain rotational energy. (3) The Moment of Inertia Theorem shows that every black hole has a moment of inertia. When the rotation stops, the irreducible mass of a Kerr black hole becomes the moment of inertia of a Schwarzschild black hole. This is recognized as the rotational equivalent of the rest mass of a moving body in relativity. Thus after 50 years, the irreducible mass has gained a new and profound significance. No longer is it a limiting value in rotation, it determines black hole dynamics and structure. What is believed to be a black hole is a mechanical body with an extended structure. Astrophysical black holes are likely to be massive compact objects from which light cannot escape.

scholarly journals Weighing the black hole via quasi-local energy

2017 ◽  
Vol 32 (24) ◽  
pp. 1730021 ◽  
Author(s):  
Yuan K. Ha
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Waves ◽  
Kerr Black Hole ◽  
Rotational Energy ◽  
Local Energy ◽  
External Energy ◽  
Event Horizons ◽  
Binary Black Hole ◽  
Asymptotic Values

We set to weigh the black holes at their event horizons in various spacetimes and obtain masses which are substantially higher than their asymptotic values. In each case, the horizon mass of a Schwarzschild, Reissner–Nordström, or Kerr black hole is found to be twice the irreducible mass observed at infinity. The irreducible mass does not contain electrostatic or rotational energy, leading to the inescapable conclusion that particles with electric charges and spins cannot exist inside a black hole. This is proposed as the External Energy Paradigm. A higher mass at the event horizon and its neighborhood is obligatory for the release of gravitational waves in binary black hole merging. We describe how these horizon mass values are obtained in the quasi-local energy approach and applied to the black holes of the first gravitational waves GW150914.

scholarly journals External energy paradigm for black holes

2018 ◽  
Vol 33 (31) ◽  
pp. 1844025 ◽  
Author(s):  
Yuan K. Ha
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Energy ◽  
Electrostatic Energy ◽  
New Paradigm ◽  
External Energy ◽  
Quantum Particles ◽  
Remarkable Result ◽  
The Moment ◽  
Constituent Mass

A new paradigm for black holes is introduced. It is known as the External Energy Paradigm. The paradigm asserts that all energies of a black hole are external quantities; they are absent inside the horizon. These energies include constituent mass, gravitational energy, electrostatic energy, rotational energy, heat energy, etc. As a result, quantum particles with charges and spins cannot exist inside the black hole. To validate the conclusion, we derive the moment of inertia of a Schwarzschild black hole and find that it is exactly equal to mass [Formula: see text] (Schwarzschild radius)2, indicating that all mass of the black hole is located at the horizon. This remarkable result can resolve several long-standing paradoxes in black hole theory; such as why entropy is proportional to area and not to volume, the singularity problem, the information loss problem and the perplexing firewall controversy.

THE EVOLUTION PROPERTIES OF EVEN–EVEN 100-110Pd NUCLEI

2012 ◽  
Vol 21 (12) ◽  
pp. 1250101 ◽  
Author(s):  
I. M. AHMED ◽  
HEWA Y. ABDULLAH ◽  
S. T. AHMAD ◽  
I. HOSSAIN ◽  
M. K. KASMIN ◽  
...  
Keyword(s):  
Rotational Energy ◽  
Moment Of Inertia ◽  
Experimental Results ◽  
Interacting Boson Model ◽  
Gamma Energy ◽  
Boson Model ◽  
The Moment

The properties of the yrast states for 100-110 Pd even–even (e–e) nuclei have been established. The relation between the moment of inertia 2ϑ/ℏ2 and the square of the rotational energy (ℏω)2 has been drawn to identify the back-bending that may occur at a certain state for each isotope. The relation between gamma-energy over spin Eγ/I as a function of spin I has been drawn to determine the evolution in each isotope ranging from vibration to rotational properties. The suitable limit in the interacting boson model IBM-1 has been used to calculate the yrast states for each isotope, which are then compared with the experimental results.

Recent developments in the tidal deformability of spinning compact objects

2016 ◽  
Vol 25 (09) ◽  
pp. 1641001
Author(s):  
Paolo Pani ◽  
Leonardo Gualtieri ◽  
Andrea Maselli ◽  
Valeria Ferrari
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Kerr Black Hole ◽  
Compact Object ◽  
Second Order ◽  
Compact Objects ◽  
Tidal Effects ◽  
First Order ◽  
Love Numbers ◽  
Recent Developments

We review recent work on the theory of tidal deformability and the tidal Love numbers of a slowly spinning compact object within general relativity. Angular momentum introduces couplings between distortions of different parity and new classes of spin-induced, tidal Love numbers emerge. Due to spin-tidal effects, a rotating object immersed in a quadrupolar, electric tidal field can acquire some induced mass, spin, quadrupole, octupole and hexadecapole moments to second-order in the spin. The tidal Love numbers depend strongly on the object’s internal structure. All tidal Love numbers of a Kerr black hole (BH) were proved to be exactly zero to first-order in the spin and also to second-order in the spin, at least in the axisymmetric case. For a binary system close to the merger, various components of the tidal field become relevant. Preliminary results suggest that spin-tidal couplings can introduce important corrections to the gravitational waveforms of spinning neutron star (NS) binaries approaching the merger.

scholarly journals Extraction of Black Hole Rotational Energy by a Magnetic Field

2003 ◽  
Vol 214 ◽  
pp. 87-90
Author(s):  
Shinji Koide
Keyword(s):  
Magnetic Field ◽  
Black Hole ◽  
Large Scale ◽  
Kerr Black Hole ◽  
Negative Energy ◽  
Rotational Energy ◽  
Alfven Wave ◽  
Numerical Result ◽  
General Relativistic ◽  
Magnetohydrodynamic Simulations

We have developed a numerical method for general relativistic magnetohydrodynamic simulations in Kerr space-time. The method is applied to the basic astrophysical problem of the Kerr black hole activity in the large-scale strong magnetic field. The numerical result shows that the magnetic field extracts the rotational energy of the black hole with negative energy-at-infinity and the torsional Alfven wave is induced from the ergosphere.

Ion–polar molecule encounters

1982 ◽  
Vol 384 (1787) ◽  
pp. 289-300 ◽  
Keyword(s):  
Rate Coefficient ◽  
Orbital Plane ◽  
Potential Energy Function ◽  
Rotational Energy ◽  
Moment Of Inertia ◽  
Rate Coefficients ◽  
Angular Momentum Vector ◽  
Dipole Orientation ◽  
Collision Problem ◽  
The Moment

It is permissible to assume that the rate coefficient for collisions between ions and polar molecules does not depend on the moment of inertia of the latter because the rotation time is brief compared with the collision time. On taking the moment of inertia to be vanishingly small the classical collision problem can be solved exactly when the angular momentum vector is normal to the orbital plane. Use is made of the adiabatic invariance of ∮ p d q /2π in which p is an appropriate momentum and q is the conjugate coordinate. This adiabatic invariant fixes the change in the rotational energy in moving from an infinite separation to any chosen position. The average dipole orientation is thereby determined, which fixes the force acting. The potential energy function (including due allowance for the rotational energy stored) is now written down and an integral expression for the primitive rate coefficient is thence obtained. The ratio of the primitive rate coefficient to the Langevin rate coefficient depends only on the initial rotational energy and on the dimensionless parameter β = 2 αkT/D 2 , where α is the polarizability, D is the dipole moment and T is the temperature. Extensive computations have been performed. Tables are presented giving the primitive rate coefficient and also approximations to the thermally averaged rate coefficients for linear and for spherical top molecules.

CHARACTERIZATION OF BACKBENDING IN EVEN–EVEN ISOTOPES OF 164–174Hf AND 154–164Dy NUCLEI BY A MODIFIED PHENOMENOLOGICAL MODEL

2013 ◽  
Vol 22 (07) ◽  
pp. 1350055
Author(s):  
L. A. NAJIM ◽  
MALEK. H. KHEDER
Keyword(s):  
Angular Momentum ◽  
Coriolis Force ◽  
Phenomenological Model ◽  
Energy Levels ◽  
Rotational Energy ◽  
Moment Of Inertia ◽  
Modified Model ◽  
The Moment ◽  
Variable Moment

A modified phenomenological model is used to calculate nuclear energy levels and describe successfully the backbending of the moment of inertia for the ground state bands in even–even isotopes of Hf and Dy nuclei. The model is a combination of the Myers and Swiatecki model with variable moment inertia (VMI) model. Since the Myers and Swiatecki model has a deviation from experimental energies in which it takes into account pairing effect with constant moment of inertia, in the rotation of nuclei, the Coriolis force acts to de-pair the nucleons pair and align their angular momentum with nuclei total angular momentum, thus Coriolis force increasing and decrease the rotational energy. So, the moment of inertia varies with the angular momentum. Therefore, we modified this model by adding a term to make the moment of inertia vary with angular momentum in the same manner of the VMI model which has a term added to the rotational energy equation. The modified model fits remarkably with the experimental observation and other models in many cases with the use of few parameters especially in rotational nuclei regions similar to Hf and Dy nuclei.

scholarly journals NON-COMMUTATIVE KERR BLACK HOLE

2011 ◽  
Vol 08 (03) ◽  
pp. 657-668 ◽  
Author(s):  
ELISABETTA DI GREZIA ◽  
GIAMPIERO ESPOSITO
Keyword(s):  
Black Hole ◽  
Kerr Black Hole ◽  
Rotational Energy ◽  
Rotating Frame ◽  
Energy Extraction ◽  
First Order ◽  
Penrose Process

This paper applies the first-order Seiberg–Witten map to evaluate the first-order non-commutative Kerr tetrad. The classical tetrad is taken to follow the locally non-rotating frame prescription. We also evaluate the tiny effect of non-commutativity on the efficiency of the Penrose process of rotational energy extraction from a black hole.

scholarly journals Multiple rings in the shadow of extremely compact objects

2021 ◽  
Author(s):  
Jingkai Wang
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Event Horizon ◽  
Electromagnetic Waves ◽  
Black Hole Physics ◽  
Compact Objects ◽  
Simple Manner ◽  
Quantitative Evidence ◽  
Exciting Opportunity ◽  
Emission Models

The Event Horizon Telescope’s image of the M87 black hole provides an exciting opportunity to study black hole physics. Since a black hole’s event horizon absorbs all electromagnetic waves, it is difficult to actively probe the horizon’s existence. However, with the help of a family of extremely compact, horizon-less objects, named “gravastars”, whose external spacetimes are nearly identical to those of black holes, one can test the absence of event horizons: absences of additional features that arise due to the existence of the gravastar, or its surface, can be used as quantitative evidence for black holes. We apply Gralla et al. approach of studying black hole images to study the images of two types of gravastars: transparent ones and reflective ones. In both cases, the transmission of rays through gravastars, or their reflections on their surfaces, leads to more rings in their images. For simple emission models, where the redshifted emissivity of the disk is peaked at a particular radius [Formula: see text], the position of a series of rings can be related in a simple manner to light ray propagation: a ring shows up around impact parameter [Formula: see text] whenever rays incident from infinity at [Formula: see text] intersects the disk at [Formula: see text]. We show that additional rings will appear in the images of transparent and reflective gravastars. In particular, one of the additional rings for the reflective gravastar is due to the prompt reflection of light on the gravastar surface, and appears to be well separated from the others. This can be an intuitive feature, which may be reliably used to constrain the reflectivity of the black hole’s horizon.

scholarly journals The multipolar structure of fuzzballs

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Massimo Bianchi ◽  
Dario Consoli ◽  
Alfredo Grillo ◽  
Josè Francisco Morales ◽  
Paolo Pani ◽  
...  
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Global Minimum ◽  
Kerr Black Hole ◽  
Large Family ◽  
Compact Objects ◽  
Multipole Moments ◽  
Abelian Gauge ◽  
Dimensional Parameter ◽  
General Method

Abstract We extend and refine a general method to extract the multipole moments of arbitrary stationary spacetimes and apply it to the study of a large family of regular horizonless solutions to $$ \mathcal{N} $$ N = 2 four-dimensional supergravity coupled to four Abelian gauge fields. These microstate geometries can carry angular momentum and have a much richer multipolar structure than the Kerr black hole. In particular they break the axial and equatorial symmetry, giving rise to a large number of nontrivial multipole moments. After studying some analytical examples, we explore the four-dimensional parameter space of this family with a statistical analysis. We find that microstate mass and spin multipole moments are typically (but not always) larger that those of a Kerr black hole with the same mass and angular momentum. Furthermore, we find numerical evidence that some invariants associated with the (dimensionless) moments of these microstates grow monotonically with the microstate size and display a global minimum at the black-hole limit, obtained when all centers collide. Our analysis is relevant in the context of measurements of the multipole moments of dark compact objects with electromagnetic and gravitational-wave probes, and for observational tests to distinguish fuzzballs from classical black holes.

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