scholarly journals An Approach to Colliding Plane Waves in General Relativity

2021 ◽  
Vol 9 (12) ◽  
pp. 981-988
Author(s):  
Dr. Shailendra Kumar Srivastava
Keyword(s):  
General Relativity ◽  
Plane Waves ◽  
Space Time ◽  
Theory Of Relativity ◽  
Field Equations ◽  
Vast Number ◽  
Gravitational Fields ◽  
Time Singularities ◽  
Linearized Theory ◽  
High Degree

Abstract: For many years after Einstein proposed his general theory of relativity, only a few exact solutions were known. Today the situation is completely different, and we now have a vast number of such solutions. However, very few are well understood in the sense that they can be clearly interpreted as the fields of real physical sources. The obvious exceptions are the Schwarzschild and Kerr solutions. These have been very thoroughly analysed, and clearly describe the gravitational fields surrounding static and rotating black holes respectively. In practice, one of the great difficulties of relating the particular features of general relativity to real physical problems, arises from the high degree of non-linearity of the field equations. Although the linearized theory has been used in some applications, its use is severely limited. Many of the most interesting properties of space-time, such as the occurrence of singularities, are consequences of the non-linearity of the equations. Keywords: General Relativity , Space-Time, Singularities, Non-linearity of the Equations.

scholarly journals Post-Newtonian limit: second-order Jefimenko equations

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
David Pérez Carlos ◽  
Augusto Espinoza ◽  
Andrew Chubykalo
Keyword(s):  
Linear Equations ◽  
Space Time ◽  
Second Order ◽  
Field Equations ◽  
Gravitational Fields ◽  
Mass Distributions ◽  
Minkowski Space Time ◽  
Theory Of Gravitation ◽  
Gravity Probe ◽  
Gravitational Equations

Abstract The purpose of this paper is to get second-order gravitational equations, a correction made to Jefimenko’s linear gravitational equations. These linear equations were first proposed by Oliver Heaviside in [1], making an analogy between the laws of electromagnetism and gravitation. To achieve our goal, we will use perturbation methods on Einstein field equations. It should be emphasized that the resulting system of equations can also be derived from Logunov’s non-linear gravitational equations, but with different physical interpretation, for while in the former gravitation is considered as a deformation of space-time as we can see in [2–5], in the latter gravitation is considered as a physical tensor field in the Minkowski space-time (as in [6–8]). In Jefimenko’s theory of gravitation, exposed in [9, 10], there are two kinds of gravitational fields, the ordinary gravitational field, due to the presence of masses, at rest, or in motion and other field called Heaviside field due to and acts only on moving masses. The Heaviside field is known in general relativity as Lense-Thirring effect or gravitomagnetism (The Heaviside field is the gravitational analogous of the magnetic field in the electromagnetic theory, its existence was proved employing the Gravity Probe B launched by NASA (See, for example, [11, 12]). It is a type of gravitational induction), interpreted as a distortion of space-time due to the motion of mass distributions, (see, for example [13, 14]). Here, we will present our second-order Jefimenko equations for gravitation and its solutions.

scholarly journals CLASSICAL AND QUANTUM STRINGS IN PLANE WAVES, SHOCK WAVES AND SPACE–TIME SINGULARITIES: SYNTHESIS AND NEW RESULTS

2003 ◽  
Vol 18 (26) ◽  
pp. 4797-4809 ◽  
Author(s):  
NORMA G. SANCHEZ
Keyword(s):  
Shock Waves ◽  
Plane Waves ◽  
Momentum Tensor ◽  
Space Time ◽  
Tree Level ◽  
Time Singularities ◽  
String Spectrum ◽  
Key Issues ◽  
Real Mass ◽  
Singular Wave

Key issues and essential features of classical and quantum strings in gravitational plane waves, shock waves and space–time singularities are synthetically understood. This includes the string mass and mode number excitations, energy–momentum tensor, scattering amplitudes, vacuum polarization and wave-string polarization effect. The role of the real pole singularities characteristic of the tree level string spectrum (real mass resonances) and that of the space–time singularities is clearly exhibited. This throws light on the issue of singularities in string theory which can be thus classified and fully physically characterized in two different sets: strong singularities (poles of order ≥ 2, and black holes) where the string motion is collective and nonoscillating in time, outgoing states and scattering sector do not appear, the string does not cross the singularities; and weak singularities (poles of order < 2, (Dirac δ belongs to this class) and conic/orbifold singularities) where the whole string motion is oscillatory in time, outgoing and scattering states exist, and the string crosses the singularities. Common features of strings in singular wave backgrounds and in inflationary backgrounds are explicitly exhibited. The string dynamics and the scattering/excitation through the singularities (whatever their kind: strong or weak) is fully physically consistent and meaningful.

Related to Relativity

2019 ◽  
pp. 265-284
Author(s):  
Steven J. Osterlind
Keyword(s):  
Twentieth Century ◽  
General Relativity ◽  
Special Relativity ◽  
Golden Age ◽  
Albert Einstein ◽  
Space Time ◽  
Theory Of Relativity ◽  
Scientific Exploration ◽  
Richard Burton ◽  
Time Continuum

This chapter provides the context for the early twentieth-century events contributing to quantification. It was the golden age of scientific exploration, with explorers like David Livingstone, Sir Richard Burton, and Sir Ernest Shackleton, and intellectual pursuits, such as Hilbert’s set of unsolved problems in mathematics. However, most of the chapter is devoted to discussing the last major influencer of quantification: Albert Einstein. His life and accomplishments, including his theory of relativity, make up the final milestone on our road to quantification. The chapter describes his time in Bern, especially in 1905, when he published several famous papers, most particularly his law of special relativity, and later, in 1915, when he expanded it to his theory of general relativity. The chapter also provides a layperson’s description of the space–time continuum. Women of major scientific accomplishments are mentioned, including Madame Currie and the mathematician Maryam Mirzakhani.

scholarly journals Space–time singularities and cosmic censorship conjecture: A Review with some thoughts

2020 ◽  
Vol 35 (14) ◽  
pp. 2030007 ◽  
Author(s):  
Yen Chin Ong
Keyword(s):  
General Relativity ◽  
Short Review ◽  
Big Bang ◽  
Cosmic Censorship ◽  
Space Time ◽  
Singularity Theorems ◽  
Time Singularities ◽  
The One ◽  
The Big Bang ◽  
Cosmic Censorship Conjecture

The singularity theorems of Hawking and Penrose tell us that singularities are common place in general relativity. Singularities not only occur at the beginning of the Universe at the Big Bang, but also in complete gravitational collapses that result in the formation of black holes. If singularities — except the one at the Big Bang — ever become “naked,” i.e. not shrouded by black hole horizons, then it is expected that problems would arise and render general relativity indeterministic. For this reason, Penrose proposed the cosmic censorship conjecture, which states that singularities should never be naked. Various counterexamples to the conjecture have since been discovered, but it is still not clear under which kind of physical processes one can expect violation of the conjecture. In this short review, I briefly examine some progresses in space–time singularities and cosmic censorship conjecture. In particular, I shall discuss why we should still care about the conjecture, and whether we should be worried about some of the counterexamples. This is not meant to be a comprehensive review, but rather to give an introduction to the subject, which has recently seen an increase of interest.

Mathematical Models of Spacetime in Contemporary Physics and Essential Issues of the Ontology of Spacetime

1998 ◽  
pp. 1-5
Author(s):  
Maciej Gos
Keyword(s):  
Field Theory ◽  
Mathematical Models ◽  
Space Time ◽  
Theory Of Relativity ◽  
Time Arrow ◽  
Time Singularities ◽  
Time Quantum ◽  
Theory Of Gravitation ◽  
The Difference ◽  
Definition Of

The general theory of relativity and field theory of matter generate an interesting ontology of space-time and, generally, of nature. It is a monistic, anti-atomistic and geometrized ontology — in which the substance is the metric field — to which all physical events are reducible. Such ontology refers to the Cartesian definition of corporeality and to Plato's ontology of nature presented in the Timaeus. This ontology provides a solution to the dispute between Clark and Leibniz on the issue of the ontological independence of space-time from distribution of events. However, mathematical models of space-time in physics do not solve the problem of the difference between time and space dimensions (invariance of equations with regard to the inversion of time arrow). Recent research on space-time singularities and asymmetrical in time quantum theory of gravitation will perhaps allow for the solution of this problem based on the structure of space-time and not merely on thermodynamics.

scholarly journals An Alternative to the Alcubierre Theory: Warp Fields by the Gravitation via Accelerated Particles Assertion

2016 ◽  
Vol 8 (5) ◽  
pp. 44
Author(s):  
Edward A. Walker
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Equilibrium Point ◽  
Space Time ◽  
Particle Accelerators ◽  
Field Equations ◽  
Time Curve ◽  
Published Paper ◽  
Accelerated Particles ◽  
Gravitational Equilibrium

<p class="1Body">A summarization of the Alcubierre metric is given in comparison to a new metric that has been formulated based on the theoretical assertion of a recently published paper entitled “gravitational space-time curve generation via accelerated particles”. The new metric mathematically describes a warp field where particle accelerators can theoretically generate gravitational space-time curves that compress or contract a volume of space-time toward a hypothetical vehicle traveling at a sub-light velocity contingent upon the amount of voltage generated. Einstein’s field equations are derived based on the new metric to show its compatibility to general relativity. The “time slowing” effects of relativistic gravitational time dilation inherent to the gravitational field generated by the particle accelerators is mathematically shown to be counteracted by a gravitational equilibrium point between an arrangement of two equal magnitude particle accelerators. The gravitational equilibrium point produces a volume of flat or linear space-time to which the hypothetical vehicle can traverse the region of contracted space-time without experiencing time slippage. The theoretical warp field possessing these attributes is referred to as the two gravity source warp field which is mathematically described by the new metric.</p>

Time, Topology, and the Twin Paradox

2011 ◽  
Author(s):  
Jean‐Pierre Luminet
Keyword(s):  
High Speed ◽  
Reference Frames ◽  
Thought Experiment ◽  
Flat Space ◽  
Space Time ◽  
Twin Paradox ◽  
Theory Of Relativity ◽  
Apparent Paradox ◽  
Curved Space ◽  
Gravitational Fields

This chapter notes that the twin paradox is the best-known thought experiment associated with Einstein's theory of relativity. An astronaut who makes a journey into space in a high-speed rocket will return home to find he has aged less than his twin who stayed on Earth. This result appears puzzling, as the homebody twin can be considered to have done the travelling with respect to the traveller. Hence, it is called a “paradox”. In fact, there is no contradiction, and the apparent paradox has a simple resolution in special relativity with infinite flat space. In general relativity (dealing with gravitational fields and curved space-time), or in a compact space such as the hypersphere or a multiply connected finite space, the paradox is more complicated, but its resolution provides new insights about the structure of space–time and the limitations of the equivalence between inertial reference frames.

A generalized field theory - I. Field equations

1977 ◽  
Vol 356 (1687) ◽  
pp. 471-481 ◽  
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Geometrical Structure ◽  
Natural Generalization ◽  
Theory Of Relativity ◽  
Field Equations ◽  
Physical Elements

A field theory representing a natural generalization of the theory of relativity is being constructed by using a tetrad-space. A unique set of field equations exactly equal in number (16) to the unknowns used, and having the same strength as those of general relativity, is obtained. All physical elements of interest are related directly to the members of the geometrical structure.

Global General Relativity

1979 ◽  
Vol 368 (1732) ◽  
pp. 19-21
Keyword(s):  
General Relativity ◽  
High Speed ◽  
Equations Of State ◽  
Perturbation Expansion ◽  
Theoretical Work ◽  
Field Equations ◽  
Gravitational Fields ◽  
Highly Nonlinear ◽  
Mathematical Techniques ◽  
Algebraic Forms

Much of the theoretical work that has been carried out in General Relativity, particularly in the earlier years of the subject, has been concerned with finding explicit solutions of Einstein’s field equations, either in the vacuum case or, with suitable equations of state, when matter is present. These have been very useful in giving us some sort of feeling for the nature of more general ‘ physically reasonable ’ solutions, but they can, at best, only be rough approximations to such solutions. Exact solutions must, owing to the limitations of human energy and ingenuity, and to the complexity of Einstein’s equations, involve a number of simplifying assumptions, such as special symmetries or particular algebraic forms for the metric or curvature. Sometimes it is legitimate to regard such a special solution as the first term in some perturbation expansion towards something more realistic. But in the highly nonlinear situations of strong gravitational fields, such as in gravitational collapse to a black hole, or perhaps also in cosmology, it is often not clear when the results of such perturbation calculations (themselves often very complicated) can be trusted. High-speed computers can come to our aid (Smarr 1979, this symposium), of course, and can often give important insights in particular situations. But complementary to these are the global qualitative mathematical techniques that have been introduced into relativity over the past several years (Hawking & Ellis 1973; Penrose 1972).

scholarly journals VACUUMLESS COSMIC STRINGS IN BRANS–DICKE THEORY

2001 ◽  
Vol 10 (04) ◽  
pp. 515-522 ◽  
Author(s):  
A. A. SEN
Keyword(s):  
General Relativity ◽  
Cosmic Strings ◽  
Gravitational Effect ◽  
Weak Field ◽  
Field Equations ◽  
Gravitational Fields

The gravitational fields of vacuumless global and gauge strings have been studied in Brans–Dicke theory under the weak field assumption of the field equations. It has been shown that both global and gauge string can have repulsive as well as attractive gravitational effect in Brans–Dicke theory which is not so in General Relativity.

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