Effect of the refractive index on the hawking temperature: an application of the Hamilton-Jacobi method

Hawking radiation of a non-asymptotically flat 4-dimensional spherically symmetric and static dilatonic black hole (BH) via the Hamilton-Jacobi (HJ) method is studied. In addition to the naive coordinates, we use four more different coordinate systems that are well-behaved at the horizon. Except for the isotropic coordinates, direct computation by the HJ method leads to the standard Hawking temperature for all coordinate systems. The isotropic coordinates allow extracting the index of refraction from the Fermat metric. It is explicitly shown that the index of refraction determines the value of the tunneling rate and its natural consequence, the Hawking temperature. The isotropic coordinates in the conventional HJ method produce a wrong result for the temperature of the linear dilaton. Here, we explain how this discrepancy can be resolved by regularizing the integral possessing a pole at the horizon.     

Black hole and hawking radiation by type-II Weyl fermions

The type-II Weyl and type-II Dirac fermions may emerge behind the event horizon of black holes. Correspondingly, the black hole can be simulated by creation of the region with overtilted Weyl or Dirac cones. The filling of the electronic states inside the “black hole” is accompanied by Hawking radiation. The Hawking temperature in the Weyl semimetals can reach the room temperature, if the black hole region is sufficiently small, and thus the effective gravity at the horizon is large.     

Relativity and the Quantum

Beams of entities, such as electrons, mayproduce diffraction patterns. These patterns may beinterpreted in terms of particles and waves. One obviousquestion concerning these phenomena is, “What is the functional relation between the momentumof the entity and its wavelength?” While thisrelation is well known, it is of interest to look foranother way to arrive at this function using special relativity theory and the fundamentalobservation that the mathematical form of a law ofnature cannot contain any parameters relating to morethan one reference frame. It is shown, without makingany quantum assumptions, that the relation P = b/λ,where b is a constant, is valid. This result comesdirectly from the application of classical nonquantumphysics.     

Strong-Coupled Relativity Without Relativity

GR can be interpreted as a theory of evolving 3-geometries. A recent such formulation, the 3-space approach of Barbour, Foster and Ó'Murchadha, also permits the construction of a limited number of other theories of evolving 3-geometries, including conformal gravity and strong gravity. In this paper, we use the 3-space approach to construct a 1-parameter family of theories which generalize strong gravity. The usual strong gravity is the strong-coupled limit of GR, which is appropriate near singularities and is one of very few regimes of GR which is amenable to quantization. Our new strong gravity theories are similar limits of scalar-tensor theories such as Brans–Dicke theory, and are likewise appropriate near singularities. They represent an extension of the regime amenable to quantization, which furthermore spans two qualitatively different types of inner product.We find that these strong gravity theories permit coupling only to ultralocal matter fields and that they prevent gauge theory. Thus in the classical picture, gauge theory breaks down (rather than undergoing unification) as one approaches the GR initial singularity.     

Relativity and the lead-acid battery

The energies of the solid reactants in the lead-acid battery are calculated ab?initio using two different basis sets at nonrelativistic, scalar-relativistic, and fully relativistic levels, and using several exchange-correlation potentials. The average calculated standard voltage is 2.13?V, compared with the experimental value of 2.11?V. All calculations agree in that 1.7-1.8?V of this standard voltage arise from relativistic effects, mainly from PbO2 but also from PbSO4.     

Relativity of the metric

Although the form of the metric is invariant for arbitrary coordinate transformations, the magnitudes of the elements of the metric are not invariant. For Cartesian coordinates these elements are equal to one and are on the diagonal. Such a unitary metric can also apply to arbitrary coordinates, but only for a coordinate system inhabitant (CSI), to whom these coordinates would appear to be Cartesian. The meaning for a non-Euclidean metric consequently appears to be a simple coordinate system transformation for the appropriate CSI. The conversion of arbitrary coordinates to the flat Cartesian ones can be accomplished by a sequence of isomorphic mappings linking the arbitrary coordinates to the flat Cartesian ones. This is shown for two, three, and four-dimensional spaces. It is also applied to toroidal metrics and fluidfilled spaces for toroidal vortices that are discontinuous, half-wavelength, electromagnetic dipole field distributions. A number of other applications are discussed.     

Relativity and the status of becoming

The merging of space and time proposed by Minkowski in 1908 is still sometimes misinterpreted as a sort of four-dimensional hyperspace of which time is the fourth dimension, analogous to the other, spatial dimensions. An inevitable consequence of this view is that the future events somehow exist prior to, and independently of, human awareness and that what we call “becoming” is “merely a coming into our awareness” (A. Grünbaum). However, an attentive inspection of the space-time diagram and of Minkowski's formula for the constancy of the world interval shows that the events contained in the absolute future of any frame of reference areintrinsically unobservable not only within this system, but also by any other conceivable observer: consequently, there is no reason to postulate their existence.     

Relativity and indeterminism

It is well known that Albert Einstein adhered to a deterministic world view throughout his career. Nevertheless, his developments of the special and general theories of relativity prove to be incompatible with that world view. Two different forms of determinism—classical Laplacian determinism and the determinism of isolated systems—are considered. Through careful considerations of what concretely is involved in predicting future states of the entire universe, or of isolated systems, it is shown that the demands of the theories of relativity make these deterministic positions untenable.     

Relativity and gravity

A logical sequence of ideas in electromagnetism can be based on the behaviour of a current-carrying coil as a magnetic dipole of moment μiA, where μ is the permeability of the medium in which the coil is situated, i the current and A the effective area (area × number of turns) of the coil (Chalmers 1965). The occurrence of μ rather than μ_o is verified from the effect of permeability on self-inductance.     

Ether and Relativity

We consider one of the fundamental debates in performing the relativity theory, namely, the ether and the relativity points of view, in a way to aid the learning of the subjects. In addition, we present our views and prospects while describing the issues that being accessible to many physicists and allowing broader views. Also, we very briefly review the two almost recent observations of the Webb redshift and the ultra high energy cosmic rays, and the modified relativity models that have been presented to justify them, wherein we express that these justifications have not been performed via a single model with a single mechanism.     

On the Principle of Relativity

In a recent article [1] M.A. Oliver argues there is a conflict between Einstein's Special Theory of Relativity (STR) and Cosmology. In ascertaining this conflict (see below), Oliver finds allies in Bergmann [2] and Bondi [3]. To resolve this conflict, he proposes to restore the classical (mechanical) concepts of space and time [1, p.666] and an absolute rest-frame. I shall devote a few words (1) to the Principle of Relativity and (2) to the notion of cosmic time in cosmology; this enables me (3) to argue that the alleged conflict between STR and Cosmology is based on a misunderstanding of the Principle of Relativity. (4) Finally I take a critical look at Oliver's allies.     

压痕对低温和高温超导股线临界性能影响研究

低温超导股线Nb Ti和Nb3Sn用于核聚变装置用的CICC导体结构,由于绞缆的作用及导体生产过程中的挤压作用,将会导致Nb Ti和Nb3Sn超导股线的表面产生不同形式的压痕,过大的压痕将会影响股线的临界性能;高温超导股线Bi-2212和Mg B2是未来可用于核聚变装置中制成CICC导体潜在的高温超导材料,由于高温超导材料的脆性,在电缆制备及导体制造过程中也会导致股线的表面产生压痕影响股线的性能。文中主要开展对于低温超导股线Nb Ti,Nb3Sn及高温超导股线Bi-2212和Mg B2的临界性能随压痕深度的变化规律,从而为导体制造的改进及未来高温超导导体的制造提供理论依据。     

Modal Interpretations and Relativity

A proof is given, at a greater level of generality than previous no-go theorems, of the impossibility of formulating a modal interpretation that exhibits serious Lorentz invariance at the fundamental level. Particular attention is given to modal interpretations of the type proposed by Bub.     

Relativity and quantum mechanics

Conditions under which quantum mechanics can be made compatible with the curved space-time of gravitation theories is investigated. A postulate is imposed in the formv=v _g wherev is the kinematical Hamilton-Jacobi (geometric optic limit) velocity andv _g is the group velocity of the waves. This imposes a severe condition on the possible coordinates in which the Schrödinger form (the coordinate realization) of quantum mechanics can be set up for purposes of calculating observable effects. Some such effects are calculated for a class of theories and are compared with experiments.     

Relativity of topology and dynamics

Recent developments in quantum set theory are used to formulate a program for quantum topological physics. The world is represented in a Hilbert space whose psi vectors represent abstract complexes generated from the null set by one bracket operator and the usual Grassmann (or Clifford) product. Such a theory may be more basic than field theory, in that it may generate its own natural topology, time, kinematics and dynamics, without benefit of an absolute timespace dimension, topology, or Hamiltonian. For example there is a natural expression for the quantum gravitational field in terms of quantum topological operators. In such a theory the usual spectrum of possible dimensions describes only one of an indefinite hierarchy of levels, each with a similar spectrum, describing nonspatial infrastructure. While c simplices have no continuous symmetry, the q simplex has an orthogonal group 0(m, n). Because quantum theory cannot take the universe as physical system, we propose a third relativity:The division between observer and observed is arbitrary. Then it is wrong to ask for the topology and dynamics of a system, in the same sense that it is wrong to ask for the the psi vectors of a system; topology and dynamics, like psi vectors, are not absolute but relative to the observer.     

同时性的相对性与经典同时性

比较了相对论同时性与经典同时性并指出了它们的区别。     

Third Relativity

It seems likely that quantum dynamical law doesnot have a separate objective existence, but is oneaspect of the quantum process of nature, amatter-spacetime-dynamics unity, and is not onlyvariable, but may be the only variable. This is oneresult of a systematic application of the criteria fora group contraction given by Inonu and Wigner (1952).They point out that nonsemisimplicity is circumstantial evidence for a group contraction in which somecoupling coefficient has been taken to a singular limit.In their example, the coupling coefficient is c and thegroup contraction c passes from special to Galilean relativity.