The irreducible mass of Christodoulou–Ruffini–Hawking mass formula

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.

Cauchy and Goursat problems for the generalized spin zero rest-mass fields on Minkowski spacetime

In this paper, we study the Cauchy and Goursat problems of the spin-$n/2$ zero rest-mass equations on Minkowski spacetime by using the conformal geometric method. In our strategy, we prove the wellposedness of the Cauchy problem in Einstein's cylinder. Then we establish pointwise decays of the fields and prove the energy equalities of the conformal fields between the null conformal boundaries $\scri^\pm$ and the hypersurface $\Sigma_0=\left\{ t=0 \right\}$. Finally, we prove the wellposedness of the Goursat problem in the partial conformal compactification by using the energy equalities and the generalisation of H\"ormander's result.

Generation of Cold Magnetized Relativistic Plasmas at the Rear of Thin Foils Irradiated by Ultra-High-Intensity Laser Pulses

A scheme to generate magnetized relativistic plasmas in a laboratory setting is proposed. It is based on the interaction of ultra-high-intensity sub-picosecond laser pulses with few-micron-thick foils or films. By means of Particle-In-Cell simulations, it is shown that energetic electrons produced by the laser and evacuated at the rear of the target trigger an expansion of the target, building up a strong azimuthal magnetic field. It is shown that in the expanding plasma sheath, a ratio of the magnetic pressure and the electron rest-mass energy density exceeds unity, whereas the plasma pressure is lower than the magnetic pressure and the electron gyroradius is lower than the plasma dimension. This scheme can be utilized to study astrophysical extreme phenomena such as relativistic magnetic reconnection in laboratory.

Proving the Lorentz Invariance of the Entropy and the Covariance of Thermodynamics

The standard argument for the Lorentz invariance of the thermodynamic entropy in equilibrium is based on the assumption that it is possible to perform an adiabatic transformation whose only outcome is to accelerate a macroscopic body, keeping its rest mass unchanged. The validity of this assumption constitutes the very foundation of relativistic thermodynamics and needs to be tested in greater detail. We show that, indeed, such a transformation is always possible, at least in principle. The only two assumptions invoked in the proof are that there is at least one inertial reference frame in which the second law of thermodynamics is valid and that the microscopic theory describing the internal dynamics of the body is a field theory, with Lorentz invariant Lagrangian density. The proof makes no reference to the connection between entropy and probabilities and is valid both within classical and quantum physics. To avoid any risk of circular reasoning, we do not postulate that the laws of thermodynamics are the same in every reference frame, but we obtain this fact as a direct consequence of the Lorentz invariance of the entropy.

MASS CONVERTED FROM THE ENERGY OF MOTION

In the General Theory of Relativity it is being introduced that the energy of motion is converted to the mass of that particle or matter or we can say that are interchangeable. It has a wide range use in the nuclear physics. The whole equation 𝑬 = 𝒎𝒄 𝟐 is a relativistic mass-energy equivalence and the term “mass” is also relativistic in nature. In special relativity, however, the energy of a body at rest is determined to be 𝒎𝒄 𝟐 . Thus, each body of rest mass m possesses 𝒎𝒄 𝟐 of “rest energy,” which potentially is available for conversion to other forms of energy. Here we initiated a equation from this if the Energy of motion has a vector form and it is in 3D space model as we know the energy of motion converted it to mass here we can do it by quantum mechanics. We think of that if the energy of motion is equal to the kinetic energy (time-independent equation from the Schrödinger equations) then we can solve the vector form of the energy and can find how much mass is being converted from the energy of motion(vector form). Here we have taken the kinetic energy from the Schrödinger equations not that from kinematics if we do then the speed of light will be equal to the velocity of that particle, which is violating the law of relativity thus I used the Schrödinger equations for simplicity .We got the equation and we have to do some calculation of the partial differentials and if the value of 𝑴′ is coming to be negative then the particle doesn’t exist and else we can find the mass converted and also the existence of that particle or matter of the universe. By this process, we can get the mass, the existence of matter/particle in this universe for that instance. We can use it if the energy is in the vector form and given some distance traveled in vacuum/air for some definite time we will get the desired result of mass.

MASS CONVERTED FROM THE ENERGY OF MOTION

In the General Theory of Relativity it is being introduced that the energy of motion is converted to the mass of that particle or matter or we can say that are interchangeable. It has a wide range use in the nuclear physics. The whole equation 𝑬 = 𝒎𝒄 𝟐 is a relativistic mass-energy equivalence and the term “mass” is also relativistic in nature. In special relativity, however, the energy of a body at rest is determined to be 𝒎𝒄 𝟐 . Thus, each body of rest mass m possesses 𝒎𝒄 𝟐 of “rest energy,” which potentially is available for conversion to other forms of energy. Here we initiated a equation from this if the Energy of motion has a vector form and it is in 3D space model as we know the energy of motion converted it to mass here we can do it by quantum mechanics. We think of that if the energy of motion is equal to the kinetic energy (time-independent equation from the Schrödinger equations) then we can solve the vector form of the energy and can find how much mass is being converted from the energy of motion(vector form). Here we have taken the kinetic energy from the Schrödinger equations not that from kinematics if we do then the speed of light will be equal to the velocity of that particle, which is violating the law of relativity thus I used the Schrödinger equations for simplicity .We got the equation and we have to do some calculation of the partial differentials and if the value of 𝑴′ is coming to be negative then the particle doesn’t exist and else we can find the mass converted and also the existence of that particle or matter of the universe. By this process, we can get the mass, the existence of matter/particle in this universe for that instance. We can use it if the energy is in the vector form and given some distance traveled in vacuum/air for some definite time we will get the desired result of mass.

All-optical frequency-encoded Toffoli gate

The construction of an all-optical frequency-encoded Toffoli gate employing a reflecting semiconductor optical amplifier (RSOA) is proposed in this article. By establishing fields such as quantum computing, optical quantum computing, quantum-dot cellular automata, and superconducting flux logic family, quantum gates have been proved to perform reliably in the present day. A nonzero-mass electron, on the other hand, moves far slower than a quantum particle with zero rest mass, such as a photon. Photons can also be utilized to store data while being sent. These photon qualities have motivated researchers to create quantum gates in the all-optical domain based on them. The RSOA-based implementation of the Toffoli gate gives a significant improvement in the case of high speed, low power, and fast switching time. MATLAB Simulink (R2018a) software is used to simulate the devised design. The theoretical prediction is satisfied by the simulation results.

Staticity and regularity for zero rest-mass fields near spatial infinity on flat spacetime

Linear zero-rest-mass fields generically develop logarithmic singularities at the critical sets where spatial infinity meets null infinity. Friedrich's representation of spatial infinity is ideally suited to study this phenomenon. These logarithmic singularities are an obstruction to the smoothness of the zero-rest-mass field at null infinity and, in particular, to peeling. In the case of the spin-2 field it has been shown that these logarithmic singularities can be precluded if the initial data for the field satisfies a certain regularity condition involving the vanishing, at spatial infinity, of a certain spinor (the linearised Cotton spinor) and its totally symmetrised derivatives. In this article we investigate the relation between this regularity condition and the staticity of the spin-2 field. It is shown that while any static spin-2 field satisfies the regularity condition, not every solution satisfying the regularity condition is static. This result is in contrast with what happens in the case of General Relativity where staticity in a neighbourhood of spatial infinity and the smoothness of the field at future and past null infinities are much more closely related.

Implementation of frequency encoded all optical reversible logic

Reversible gate has been one of the emerging research areas that ensure continual process of innovation trends that explore and utilizes the resources. Due to the increasing power consumption of electronic circuits, it has been observed that quantum computing is one of its latest applications. This technology can be utilized by reducing the energy consumption by preserving the bits of information that are still useful. A photon has zero rest mass, while an electron has a nonzero rest mass. These characteristics inspired the researchers to develop an all-optical Fredkin gate. The proposed gate design overcomes the shortcomings of conventional Fredkin gates and provides better performance.

Violation of the Relativistic Energy Conservation Law and Einstein’s Principle of Relativity Caused by the Generation of Mechanical Transverse Waves in a Moving Medium

We study the effect of the generation of the mechanical transverse wave (MTW) travelling in the opposite direction (OD) to a moving medium (MM) on the relativistic energy conservation law (RECL). From the viewpoint of the relativity of simultaneity (RS), the time on the coordinate coinciding with the advance end of the wave (AEW) travelling toward the rear of the MM passes faster than that on the coordinate coinciding with the wave source (WS). Then the AEW in the MM travels forward compared to that in the rest frame of reference (RFR) which is stationary relative to the medium when the time on the coordinate coinciding with the WS is same for each inertial frame of reference (IFR). Hence, the coordinate interval (CI) between the AEW and WS in the MM is observed to be larger than that between them in the RFR. We show that this difference holds true for the CI of any portion having transverse velocities mutually converted by the Lorentz transformation (LT). This difference in the CI leads to that in the rest mass (RM). We demonstrate that the RM included in wave motion (WM) in the MM is larger than one included in WM in the RFR when comparing the portions having transverse velocities mutually converted by the LT. This relation holds true for all portions in WM. Therefore, the total coordinate interval of the portion (CIP) and total RM (TRM) included in WM in the MM (WMMM) are large compared to them included in WM in the RFR. Furthermore, we compare the relativistic kinetic energy (RKE) of the MTW travelling in the OD to the MM (ODMM) with that of the MTW propagating in the direction vertical to the moving direction of the medium. We prove that the CIP and RM included in the former MTW are larger than them included in the latter MTW when comparing each portion with the same transverse velocity (TV). Moreover, the total CIP and TRM included in the former MTW are also large compared to them included in the latter MTW. The reason for these is that the latter CIP and RM are equal to them in the RFR when comparing the portions having transverse velocities mutually converted by the LT. On the other hand, the energy supplied to generate each MTW is the same. From these, we demonstrate that the RKE of the MTW travelling in the ODMM can be larger than the total relativistic energy (TRE) of the MTW propagating in the direction vertical to the moving direction of the medium. Consequently, we propose a violation of the RECL and Einstein’s principle of relativity (EPR) because the TRE is not necessarily conserved in the IFR in which the medium is moving.